Magneto Optical Kerr Effect

Investigation of Domains and Dynamics of DomainWalls by the Magneto-optical Kerr-effect

Rudolf SchaferLeibniz Institute for Solid State and Materials Research, Dresden, Germany

1 Introduction 1

2 Magneto-optics 2

3 Kerr Microscopy 4

4 Dynamic Kerr Microscopy 15

5 Outlook 26

Acknowledgments 26

References 26

1 INTRODUCTION

The magnetic microstucture, that is, the arrangement ofdomains and domain walls, forms the mesoscopic linkbetween basic physical properties of a magnetic material andits macroscopic properties. Hysteresis phenomena, energyloss in inductive devises, noise in sensors, or the magne-toresistive properties of modern spintronic devices can bedecisively determined by the peculiarities of the underlyingmagnetic microstructure, especially by irreversibilities in themagnetization process. The development and optimization ofmagnetic materials therefore requires the knowledge of mag-netic domains and their reaction to magnetic fields, which,in most cases, can only be gained by direct imaging.

Although there has been considerable progress in magneticimaging in recent years, the classical Kerr technique still has

Handbook of Magnetism and Advanced Magnetic Materials. Editedby Helmut Kronmuller and Stuart Parkin. Volume 3: Novel Tech-niques for Characterizing and Preparing Samples. 2007 JohnWiley & Sons, Ltd. ISBN: 978-0-470-02217-7.

unbeatable advantages. The method is based on the magneto-optical Kerr effect, that is, the magnetization-dependent rota-tion of plane-polarized light on reflection from a nontranspar-ent magnetic sample. By means of an analyzer, in an opticalreflection polarization microscope, this rotation is convertedinto a (in general weak) domain contrast that can be enhancedby digital image processing. Among all observation methods,Kerr microscopy is the most versatile and flexible imagingtechnique. With image processing, domain contrast is seenon virtually all ferro- and ferrimagnetic samples. Often, nospecific surface treatment is required and even coatings maybe allowed. Magnetic fields of arbitrary strength and direc-tion can be applied to the sample, making it possible toobserve magnetization processes and to simultaneously andlocally record magnetization loops. Magnetization dynamicscan be studied at arbitrary frequencies, covering the wholerange from slow processes (as fast as the eye can follow)to excitations beyond the gigahertz regime by employingtime-resolved imaging methods. Samples may be heated andcooled in optical heating stages and cryostats respectively sothat magnetic phase transitions or other thermal effects onthe magnetic microstructure can be investigated. Mechanicsample deformation during domain observation is easily pos-sible, which makes the study of stress effects on domainspossible. In- and out-of-plane magnetization components canbe imaged separately, and, for low-anisotropy materials, themagnetization vector field at least on the sample surface canbe quantitatively evaluated. The information depth of Kerrmicroscopy is in the 10-nm regime for metallic materials,allowing the depth-selective observation of magnetizationdistributions in layered sample systems. The magnificationcan easily be varied by changing the microscope objective,so that overview observations in the centimeter regime down

2 Magneto-optical techniques

to detailed studies of samples of micrometer size are possible.The lateral resolution of optical microscopy with visible lightis limited to about 300 nm by the Rayleigh criterion. This canbe a drawback for the study of sub-micrometer patternedstructures or for certain micromagnetic objects like vorticesor stripe domains in very thin films. In bulk samples, onlythe magnetization of the surface region can be seen, but thislimitation also applies to most other imaging techniques.

Since the first application of Kerr microscopy (Williams,Foster and Wood 1951; Fowler and Fryer, 1952), therehas been tremendous progress in methodical developmentsaround the traditional Kerr technique. In this article, the men-tioned possibilities of modern Kerr microscopy are reviewed,together with physical and technological fundamentals. Acomprehensive review on magnetic domains and imagingmethods with emphasis on Kerr microscopy is given in themonograph ‘Magnetic Domains’ (Hubert and Schafer, 1998),where an extended bibliography can also be found.

2 MAGNETO-OPTICS

Magnetic imaging at optical frequencies employs mainly themagneto-optical Kerr and Faraday effect. Both are rotationaleffects, that is, plane-polarized light is rotated somewhaton transmission through an optically transparent specimen(Faraday effect) or on reflection from a nontransparent sam-ple (Kerr effect), respectively. Both effects can also be inter-preted as circular birefringence (i.e., a birefringence of circu-larly polarized light) and are described by the same physicallaws. Another effect, mostly used for transmission observa-tions in magnetic garnets, is the Voigt or Cotton–Moutoneffect, also known as linear magnetic birefringence (i.e., abirefringence of linearly polarized light). This effect can alsobe applied in reflection, together with the magneto-opticalgradient effect. All three reflection effects are helpful fordomain analysis. Owing to its dominating importance, wefocus on the Kerr effect in this article and mention the othereffects only briefly.

2.1 Kerr effect

The rotational action of the Kerr effect (Kerr, 1877) is phe-nomenologically described by the dielectric law D = εE , inwhich an antisymmetric ε tensor (containing the componentsof the magnetization vector) connects the electrical vectorE of an illuminating plane light wave with an induced dis-placement vector D in the regime of optical frequencies. Thisrelation can be written in the form

D = ε(E + iQm × E ) (1)

where ε is the regular dielectric constant and Q is acomplex material parameter that is roughly proportional tothe saturation magnetization of the sample and that describesthe strength of the Kerr effect. The D vector can beinterpreted as secondary light amplitude being generated bythe magneto-optical interaction of E with the magnetizationvector m anywhere in the sample.

The cross product in equation (1) reveals the gyroelectricnature of the Kerr effect. Its symmetry can be derived byusing the concept of a Lorentz force (m × E ) on the electronsset in vibrational motion by the light wave (Figure 1a). Ifthe Lorentz movement vLor (parallel to the second term inequation (1)) is projected onto the plane perpendicular tothe propagation direction of the reflected light wave, themagneto-optic light amplitude K is obtained. This so-calledKerr amplitude is polarized perpendicularly to the regularlyreflected amplitude N that is polarized in the same plane asthe incident light and that is given by the Fresnel equations.By interference of K and N , the polarization vector of thereflected light is rotated by the (small) angle �K = KN−1

(Figure 1b). Here K and N are the effective light amplitudesafter the light has passed through the analyzer. For domainswith opposite magnetization, the Lorentz force acts in reversedirection, that is, the Kerr amplitude changes sign. A domaincontrast is produced if most of the reflected light fromone domain type is blocked by the analyzer, as indicatedin Figure 1(b), transferring the rotation of the polarizationplane to a difference in intensities. The size of the usablesignal that also determines the signal-to-noise ratio if videomicroscopy is applied is important for good domain visibility.The relative signal S, that is, the difference between theintensities of bright and dark domains, is derived as (Hubertand Schafer, 1998)

S ∼= 4βKN (2)

Three properties are noted: (i) The Kerr signal is alinear function of the Kerr amplitude K and thereforeof the respective magnetization components according toequation (1). (ii) The Kerr signal can be enhanced by increas-ing the analyzer angle β beyond �K, allowing to increasethe signal-to-noise ratio and to adjust to the sensitivityof the detector. (iii) The ‘visibility’ of domains is deter-mined by the Kerr amplitude and not by the Kerr rota-tion. Although K depends on material constants, it can beenhanced in case of materials where the incoming light isnot completely absorbed by magneto-optical interaction, but‘uselessly’ reflected to some extent. Antireflection coatingsincrease the absorbed intensity (based on interference effectsthat reduce the regularly reflected light component whileenhancing the Kerr component – see Hubert and Schafer(1998) for a review), proportionally raising K and thus the

Investigation of domains and dynamics of domain walls by the magneto-optical Kerr-effect 3

E

E

K

K

K

N

N

N

m

EK N

m

v

v

vLor

v Lor

(a)

(c) (d)

Compensator

Fastaxis

Linearilypolarized

light

Ellipticallypolarized

light

Reflec

ted

light

K−K

N

(b)P

olar

izer

Analyzer

m

Incident light

b

fk

Figure 1. (a) Illustration of the elementary magneto-optical inter-action for the longitudinal Kerr effect. The sample with in-planemagnetization is illuminated using light that is polarized parallelto the plane of incidence. The electric field vector E of the inci-dent light, together with the magnetization vector m, generates aLorentz movement of the electrons (‘right-hand rule’). If the result-ing Lorentz speed vLor is then projected onto the plane perpendicularto the direction of propagation of the reflected light, the magneto-optical amplitude K is obtained (a similar K component wouldalso be generated if the light would be polarized perpendicular tothe plane of incidence). The interference of the normally reflectedcomponent N and the Kerr component K results in magnetization-dependent light rotation by a small angle �K, which, by using ananalyzer, leads to the domain contrast (b). The analyzer shouldactually be set at the angle β>�K to optimize the domain visibil-ity. The action of the compensator is illustrated in (c). It convertselliptical light into a linear wave by shifting the two constituent,orthogonal wave components. The symmetry of the transverseKerr effect is explained in (d). Only light of parallel polarizationyields an effect, so that a Kerr rotation is only possible at 45◦

polarization.

Without interference layer With ZnS interference layer

100 µm

Figure 2. Effect of a dielectric antireflection coating on the Kerrcontrast, demonstrated for an amorphous ribbon that is coated inthe right image.

useful signal (Figure 2). Effective dielectric coatings are ZnSfor metals and MgF2 for oxides. As the Kerr effect is weakin general, this gain should not be relinquished even if digitalimage processing (see Section 3.1.3) is applied.

In general, the polarization plane of the reflected light isnot just rotated with respect to that of the incident light,but also elliptically polarized. Ellipticity is caused by an‘intrinsic’, material-dependent (Oppeneer, 2001) phase shiftbetween the N and K components (also interference layerson top of the sample surface can add a phase shift). Ifa noticeable ellipticity occurs, the reflected wave is lessdetectable by the analyzer. This problem can be eliminatedby the use of a compensator (see Figure 1c), which should beattached in front of the analyzer. A compensator is an opticaldevice that is based on birefringent materials such as quartzor mica and that is capable of impressing a controllableretardance on a wave, that is, it changes the relative phaseof the constituent orthogonal ordinary and extraordinarycomponents of the wave in a variable way. Highest flexibilityis obtained by using simple wave plates with a fixedretardance of λ4−1, for instance (rather than a regularcompensator as, e.g., of the Babinet type, which requiresthat its optical axes are aligned along and perpendicular,respectively, to the plane of the regularly reflected light – seeFigure 1c). A variable phase shift between N and K isobtained by rotating the plate, which leads to a phase shiftof both components. By means of such a compensator, abeam that is reflected elliptically from the sample can beconverted into a linear wave. The azimuth angle of this waveis different from that of the incident wave, however, requiringan additional analyzer rotation for extinction. In this way, itis possible to extinguish at least the light of one domain thusgenerating a significant Kerr contrast.

Different basic geometries are distinguished in Kerrmicroscopy, which can again be derived with the help ofthe Lorentz concept. To produce a Lorentz movement thatleads to detectable Kerr rotation, an appropriate directionof light incidence and polarization has to be selected for agiven magnetization direction. As a simple rule, the Kerrrotation is proportional to the magnetization component par-allel to the reflected beam of light. This rule implies that


domains that are magnetized parallel to the sample surface(as shown in Figure 1a) require oblique light incidence, andthat for maximum rotation the plane of incidence must beparallel to the axis of magnetization with the polarizer seteither parallel or orthogonal to the incidence plane (lon-gitudinal Kerr effect, ϑ �= 0). The Kerr amplitude is thenproportional to the sine of the angle of incidence ϑ , andtherefore disappears for perpendicular incidence. In this case,maximum rotation is exhibited by domains that are mag-netized perpendicularly to the sample surface (polar Kerreffect, ϑ = 0), while in-plane domains do not cause a Kerramplitude. At oblique incidence, both in- and out-of-planemagnetization components generate a superimposed Kerrcontrast. The separation of the two components is possibleby proper difference images that are obtained at differentmicroscope settings, as demonstrated in Figure 3. Also, thetransverse Kerr effect, illustrated in Figure 1(d), leads to in-plane magnetization sensitivity. Here, the in-plane m vectoris normal to the plane of (oblique) incidence. Light withE parallel to this plane generates a Kerr amplitude, but itspolarization direction is the same as that of the normallyreflected beam. The transverse Kerr effect thus causes anamplitude variation, which can be used for measuring pur-poses. A rotation that is detectable by an analyzer is obtainedwhen the incident light is polarized at 45◦ to the planeof incidence. Then, the E component perpendicular to theincidence plane is not affected (E ||m), while the parallelcomponent is modulated in its amplitude on reflection, lead-ing to polarization rotation by superposition, as also indicatedin Figure 1(d).

Polar contrast

(a) (b) (c)

In-plane contrast

Grainboundary

5 µm

Figure 3. Domains in a coarse-grained NdFeB crystal in whichthe magnetization axes of the four different grains are misalignedrelative to the observed surface as schematically shown in (a).The magnetization components perpendicular to the surface (polarcomponents) can be imaged separately at perpendicular incidence(b). At oblique incidence, polar and in-plane components showup simultaneously (not shown). When the illumination direction isrotated by 180◦, the polar Kerr effect does not change sign, whereasthe longitudinal effect does (see Figure 13b below). By forming theimage difference the polar contrast disappears, leaving just in-planecontrast (c).

2.2 Other magneto-optical effects

Three further magneto-optical effects that can be used fordomain observation in a polarization microscope have tobe mentioned. Related to the Kerr effect is the Faradayeffect (Faraday, 1846). It follows the same symmetry rules,but is restricted to transparent samples such as magneticgarnet films and is observed in transmission experiments(Fowler and Fryer, 1956). The Faraday contrast is muchstronger than the Kerr contrast and does not require electronicmeans for enhancement. In recent years, the Faraday effectfound application in magneto-optic indicator films. These aretransparent garnet films with in-plane anisotropy that arecoated with a mirror layer on one side. If the mirror sideis placed in contact with a magnetic specimen, the stray fieldof the sample induces a polar magnetization component inthe active layer, which can be viewed in the polar Faradayeffect at reflection. Charged domain walls, for instance, canbe indirectly imaged in this way (Nikitenko et al., 1998).

The Voigt effect (Voigt, 1898) was mainly applied fortransmission observations of in-plane domains in garnets(Dillon, 1958). It is quadratic in the magnetization compo-nents, so that only domains magnetized along different axesshow a contrast. The effect is strongest at perpendicular inci-dence (where a Faraday or Kerr contrast of in-plane domainsis not possible) and requires a compensator for adjustment.Later, the Voigt effect was also discovered in reflection exper-iments on metals, together with the magneto-optical gradienteffect (Schafer and Hubert, 1990) that shows up under similarexperimental conditions. The gradient effect is a birefrin-gence effect, which depends linearly on magnetization gra-dients. Both effects (in combination with the Kerr effect) arehelpful in the analysis of domains in cubic materials such asepitaxial thin-film systems by considering their contrast lawsand depth sensitivities (see Schafer (1995) for an overview).The gradient effect can also favorably be applied to imagefine transitions and domain modulations. The phenomeno-logical differences between Kerr, Voigt, and gradient effectare compared in Figure 4, in which a typical domain patternof an iron–silicon crystal with two orthogonal easy axes ofmagnetization in the surface was imaged in an optical polar-ization microscope under different conditions as indicated.

3 KERR MICROSCOPY

Two types of Kerr microscopes are in use: wide-field(regular) microscopes, which immediately provide an imageof a certain sample area, and laser-scanning microscopes,in which a laser spot is scanned relative to the samplesurface building up the image sequentially. Both have theirdrawbacks and advantages, as elaborated in the following


Obliqueincidence

Polarizer

(a) Kerr effect (b) Voigt effect (c) Gradient effect

Perpendicularincidence

Perpendicularincidence

20 µm

Figure 4. Domains on a (100) surface of silicon–iron (Fe 3 wt%Si, sheet thickness 0.3 mm), imaged in the magneto-optical Kerr (a),Voigt (b), and gradient effect (c). The Kerr effect is linear in themagnetization vector, so the four-domain phases in (a) show upin different colors. The same pattern imaged in the Voigt effectdisplays only two colors, one for each magnetization axis. Thiscontrast is independent of the magnetization direction since theVoigt effect depends quadratically on the magnetization vector. Thegradient effect is sensitive to changes in magnetization. Therefore,domain boundaries show up in this effect with a contrast, dependingon the relative magnetization directions of the neighboring domains.Both Voigt and gradient effect are strongest at perpendicularincidence of light and require a compensator for contrast adjustment.(Reproduced from Schafer, R. and Hubert, A. (1990). A newmagnetooptic effect related to non-uniform magnetization on thesurface of a ferromagnet. Physica Status Solidi A, 118, 271–288 bypermission of Wiley-VCH.)

sections. Emphasis is on wide-field microscopy as it is themost commonly applied and most versatile technique.

3.1 Wide-field Kerr microscopy

3.1.1 Microscope

Standard wide-field Kerr microscopes are based on com-mercial reflected light microscopes with strain-free optics toallow for polarization microscopy. Wide-field microscopesapply the Kohler illumination technique, which was intro-duced in 1893 by August Kohler from Carl Zeiss corporation,to obtain homogeneously illuminated images at maximumresolution. This technique is explained by ray diagrams inFigure 5, where the illumination and image-formation raypaths are illustrated separately for the purpose of visual-ization. Light emitted from the lamp is focused onto theplane of the aperture diaphragm by the lamp collector lens,passes through the opening of a variable field iris diaphragm,and is then plane polarized and deflected downward into theobjective lens, for example, by a partially reflecting planeglass mirror. After reflection from the specimen, the lightis captured by the objective and then passes through thehalf-mirror again. Modern optical microscopes are built with

infinity-corrected objectives, that is, the light rays emergefrom the objective in parallel bundles from every azimuthand are projected to infinity. These bundles enter the tubelens, which forms an intermediate image that is further pro-cessed toward the eyepiece or camera. In the ‘infinity’ space,accessories like reflector mirror, analyzer, and compensatorare added with simple design and without distortion of theimage. Polarizers and analyzers in today’s microscopes aremade of dichroic polarizing foils. Although the polarizationdegree (2 × 10−6) of such sheet polarizers is sufficient forKerr microscopy, they suffer from a high light absorption ofmore than 50%. Light intensity by a factor of 2–3 and betterextinction can be gained by replacing sheet polarizers withGlan–Thompson prism polarizers.

The field diaphragm is imaged on the specimen and thusdetermines which part of the sample is illuminated. It doesnot affect the optical resolution or intensity of illumination.The latter is rather controlled by the aperture diaphragmthat also determines the angles of incidence and is there-fore crucial for Kerr microscopy. Closing or opening theaperture diaphragm varies the angle of the light rays reach-ing the specimen from all azimuths, with the largest angleof incidence being limited by the numerical aperture of theobjective. A centered aperture iris (Figure 5a) results in anillumination cone that hits the sample vertically. Owing tosymmetry, the Kerr amplitudes resulting from in-plane mag-netization components cancel each other, so that in this casea sole sensitivity to out-of-plane magnetization is given asrequired for the polar Kerr effect. An off-centered aperturediaphragm (Figure 5c) leads to an obliquely incident bun-dle of rays (with an angle-of-incidence dispersion rangingbetween perpendicular and maximum) as necessary for lon-gitudinal and transverse Kerr sensitivity. Oblique incidenceis also provided by a Berek prism (Figure 5d), which is a90◦ prism constructed in the form of a trapezoid, resultingin a light path where the beam is internally reflected threetimes before it exits the prism. A Berek prism introduceslittle depolarization and causes no light loss, contrary to thementioned glass plate reflectors for which just a quarter ofthe illuminating light is used for image formation. However,the viewing aperture is restricted by the prism itself, leadingto a reduced optical resolution in the direction transverse tothe microscope plane. If light intensity poses no problem, asheet reflector offers optimum resolution and high flexibilityin the observation mode (see next paragraph). In recent years,microscope companies have largely eliminated the option ofBerek prisms in their product lines. The availability of highlysensitive video cameras can partly compensate for this unfa-vorable circumstance.

The plane of the aperture diaphragm is conjugate to theback focal plane of the objective lens, also called diffractionplane or pupil of the objective. As the back focal plane is


Extinction cross and aperture stop positions, observed in back focal plane

Polar Longitudinal Longitudinalwith transverse

sensitivity

Transverse TransverseP A P A P A P A P A

Collector

Lamp

Aperturediaphragm(centered)

Aperturediaphragm(acentric)

Fielddiaphragm

Image-forminglight path

Observation

Tube lens

Analyzer

Compensator

Reflector

Backfocal plane

Objectivelens

Sample

Polarizer

Illumination light pathfor perpendicular incidence

Illumination light pathfor oblique incidence

(a)

(c)

(d)

Berek prism

(b)

Figure 5. The essential components and ray paths of a wide-field Kerr microscope. (a) Illumination path for perpendicular light incidence,and (b) image-forming path. Oblique incidence (c) requires a displaced aperture slit and can also be obtained with a Berek prism (d). Theinset shows the diffraction plane of the microscope for the case of a sheet reflector. Here, the aperture diaphragm can be viewed andadjusted to fulfill the requirements for the polar Kerr effect (centered iris diaphragm) or longitudinal and transverse effects (displaced slitdiaphragm). The orientation of the extinction cross depends on the polarizer setting (indicated by P), with the analyzer (A) and eventuallythe compensator being adjusted for maximum extinction.

not identical for all objectives in conventional microscopes(objectives are rather constructed for identical front focalplanes to guarantee identical sample positions), the relevantlens that images the aperture into the pupil has to be moved orsupported by additional lenses to exactly provide this con-dition for all objectives – a feature that is not available incommercial microscopes. If the aperture diaphragm is notimaged exactly to the pupil, it is not effective uniformly forthe whole observation field and the points on the sample arenot illuminated from the same angular range. This may result

in an inhomogeneous image up to a magnetic contrast inver-sion across the image (see Fig. 2.16 in Hubert and Schafer(1998)). The diffraction plane can be seen in the so-calledconoscopical image of the microscope by replacing the eye-piece by an auxiliary telescope or by a built-in, focusableBertrand lens. This image is characterized by a cross-shapedextinction zone when the polarizer and analyzer are crossedfor maximum extinction (Figure 5, inset), rather than beinghomogeneously dark as would be the ideal case. The reasonfor this ‘Maltese’ cross, which becomes more pronounced


as the numerical aperture of the objective increases, is thata convergent light bundle, rather than a parallel laser beam,is used in wide-field microscopy. All beams not lying in acentral incidence plane along or perpendicular to the polar-ization plane cannot be extinguished by the analyzer as theyare reflected in an elliptical and rotated polarization state ingeneral. This is due to differential transmission of the p (Evector parallel to plane of incidence) and s (E vector perpen-dicular to plane of incidence) components at the steep opticalinterfaces of lenses. This depolarization results in four brightquadrants, separated by the Maltese cross, in the conoscopicimage. For best contrast conditions, the illumination shouldbe restricted to the area of maximum extinction in the cono-scopic image by properly positioning the aperture stop, asillustrated in the inset of Figure 5 for the case of a sheetreflector (by using a Berek prism, half of the pupil wouldbe occupied by an image of the prism itself). For the polarKerr effect, a centered iris diaphragm is used, while the lon-gitudinal effect is preferably adjusted by an off-centered slitaperture that is oriented parallel to the plane of incidence. Forthe transverse Kerr effect, the polarizer and consequently alsothe extinction cross are rotated by 45◦ (due to depolarizationat the reflector, the use of a compensator is mandatory in thiscase to obtain a closed extinction cross). Here, a displacedslit perpendicular to the plane of incidence or a V-shapedslit are the best solutions. Both, longitudinal and transverseeffects can be adjusted as well by using a Berek prism, whilethe polar effect requires a sheet reflector. If a sheet reflectoris used, the ‘true’ transverse Kerr effect can be replaced bythe longitudinal effect by placing the slit aperture on the side-ward branch of the extinction cross, thus causing a transverseplane of incidence, that is, transverse sensitivity.

3.1.2 Lateral resolution

The lateral resolution in optical microscopy is determinedby the numerical aperture (NA = n sin α) of the objectivelens, where α is half the opening angle of the objective(i.e., half the angle of the cone of light from the specimenthat is accepted by the objective) and n is the refractiveindex of the medium used between objective and object(n = 1 for air; n ≈ 1.5 for immersion oil). The higher α

and n, the more orders of diffracted light are collected bythe objective, which increases the resolution. The smallestdistance between two objects that can be resolved is givenby dmin = 0.5 λNA−1 according to the Rayleigh criterion (λis the wavelength of light, e.g., 550 nm for green light).The highest numerical aperture available is 1.4, obtainedwith oil-immersion objectives of 100× magnification. Usingsuch an objective and blue light for illumination, domainsas narrow as 150 nm can be resolved (Schmidt and Hubert,1986). Smaller magnetic objects like domain walls down

to a size of some 10 nm may also become visible bydigital contrast enhancement, but their image is diffractionbroadened. Ultraviolet (UV) light would further improveresolution; however, UV light with a wavelength of 400 nmis already absorbed to 50% by conventional lenses (at 360 nmwavelength, the absorption is 100%). UV microscopes withall-quartz optics, permitting resolutions down to about 80 nmat deep-UV wavelengths, have been developed mainly fordefect inspection in semiconductors. The implementation ofpolarization optics in such microscopes, however, appears tobe problematic (Yamasaki, 2006, Private communication).

In Figure 6, some examples of high-resolution observa-tions, using white light and oil immersion, are collected. Thesurface magnetization of asymmetric Bloch walls on bulksoft magnets is well resolved, even in the case of iron–siliconwith a surface wall width of just 150 nm (Figure 6a). Thesame is true for all kinds of domain walls in magnetic films,as shown for the examples of crosstie walls (Figure 6b) inthin films and asymmetric Bloch and Neel walls in thickfilms (Figure 6c). Also, small-angle magnetization modula-tions (ripple or patchy modulations) are easily identified. Thepractical limit for the observation of small particles is demon-strated in Figure 6(d) for cobalt thin-film elements. Faintcontrasts are still visible on the 230-nm-wide dot. A reli-able judgment on the magnetization distribution, however,requires elements larger than a micrometer (Figure 6e). Theimages in Figure 6(f) demonstrate an in situ observation ofcurrent-induced domain wall propagation (Klaui et al., 2005)in a NiFe stripe structure with a width close to the resolutionlimit.

Restrictions in the resolution of Kerr microscopy areoutweighed by a highly flexible magnification. Sample areasranging between 5 mm and 30 µm can be covered by simplychanging objective lenses in standard microscopes. Often,a low-resolution overview of domain patterns on a stilllarger lateral scale is required, even in the research onnovel, nanoscale objects such as film systems for spintronics(Schafer, Hubert and Parkin, 1993). Custom-made Kerrsetups with separated illumination and observation paths aresuited for this purpose (see Fig. 2.14 in (Hubert and Schafer,1998)). An elegant way of realizing such microscopes is tomodify an optical stereomicroscope by using one path forillumination and the other for observation. An example formultiscale imaging in shown in Figure 7, which, at the sametime, is an example for the possibility of sample manipulationby stress.

3.1.3 Image processing

As the Kerr effect is weak, polarization effects from imper-fect surfaces, showing up especially at nearly crossed polar-izers, can strongly obscure the magnetic image. Magnetic


(a)

(b)

(c)

(d)

(e) (f)

40 50 80 Mr+ − Mr

− Mr− − Mr

+

230

330

2000

120

430

1000

110

540

800

(nm)

magn.field

Beforecurrent pulse

Aftercurrent pulse

Current

FeSi sheet

CoFeBSi amorphous ribbon

FeNbZrBCu nanocrystallineribbon

10 µm

10 µm

2 × 2 µm2

10 µm

Figure 6. High-resolution Kerr observations. (a) Domain wallimaging on different bulk samples. The surface wall width for theFeSi Goss sheet (300 nm thick) with (110) surface orientation is150 nm, for the metallic glass (25 µm thick) it is 0.9 µm, and forthe nanocrystalline ribbon (20 µm thick) a surface wall width of1.6 µm is measured, as expected due to the decreasing anisotropyin the order of materials. The black–white contrast of the wall seg-ments is caused by the rotation sense of magnetization (see alsoFigure 4a). (b) Crosstie wall in a 40-nm-thick Permalloy film, and(c) coexisting asymmetric Bloch- and Neel walls in a 460-nm-thickPermalloy film, the latter being characterized by a double contrast.See (Hubert and Schafer, 1998) for details. (d) Regular image (left)and difference images between the remanent states after positiveand negative saturation (middle) and vice versa (right) on quadraticcobalt elements of various sizes. The saturation field is aligned ver-tically; the edge length of the elements is indicated in nanometers.(e) Domain patterns in an array of 2-µm-wide Co elements after acdemagnetization. In (f) the head-on domain walls in 500-nm-wideNiFe stripes were shifted by current pulse injection (See also Cur-rent Induced Domain-wall Motion in Magnetic Nanowires, Vol-ume 2). (Sample for (d,e): courtesy A. Carl , Duisburg. Images (f):courtesy T. Moore, M. Klaui (University Konstanz) and J. McCord(IFW Dresden).)

contrast enhancement is possible by the interference lay-ers mentioned in Section 2. A much more powerful option,however, is the implementation of video microscopy anddigital image processing (Schmidt, Rave and Hubert, 1985;Argyle, Petek and Herman, 1987). Magnetic materials areideally suited for difference imaging because the magnetic

1 mm

(a) (b)

10 µm

Figure 7. Demonstration of magnification range and samplemanipulation abilities of Kerr microscopy. (a) Low-magnificationdomain overview on FeSi transformer steel sheet, showing threegrains of different misorientation (characterized by the density oflancet domains (Hubert and Schafer, 1998)) in the demagnetizedstate. Sixteen images, obtained with a 3.2× objective lens, werecombined in this composite picture. Details of the lancet domainsare presented in the inset, which was obtained with a 100× oilimmersion objective at high resolution. The Kerr sensitivity wasrotated by 90◦, so that the domain walls are imaged rather thanthe domains. In (b) an external tensile, a stress of 2 kg mm−2 wasapplied to the sheet in vertical image direction, leading to domainrefinement and suppression of the supplementary domains.

state can be manipulated by external magnetic fields with-out changing the topography of the specimen. The standardprocedure (Figure 8a) starts with a digitized, averaged imageof the magnetically saturated state, where in an external dcmagnetic field all domains are eliminated. Alternatively, analternating field of moderate amplitude can be applied, whichmixes up the domains during averaging with the advantagethat forces on the sample may be smaller than in the high sat-urating field. This domain-free background (reference) imageis then subtracted from a state containing domain informa-tion, so that in the difference image a clear micrograph ofthe domain pattern is obtained, which can be improved byaveraging and digital contrast enhancement, free of topo-graphic contrasts. Often, it is desirable to study domains indifferent aspects, for example, under longitudinal and trans-verse contrast conditions. This is possible by a combinationexperiment, as also demonstrated in Figure 8(a). After hav-ing created a regular difference image of a certain domainpattern, an image of the same pattern, but under differentcontrast conditions, is stored as a reference image that is


(a)

(b)

Original imageChange

Contrast

Saturated state

Originalimage

Regulardifference

image

Saturationdifference

image

Normalizeddifference

image

Reference image(saturated)

Difference image

Difference imageReference image(domains)

20 µm

100 µm

Figure 8. (a) Difference techniques for contrast enhancement,demonstrated for stress-induced domains on an iron-rich metallicglass. In a combination experiment, difference images of the samedomain pattern are obtained under longitudinal (upper row) andtransverse (lower row) contrast conditions. (b) Nonmagnetic con-trast contributions in a ‘regular’ difference image can be removedby normalization by a ‘saturation difference image’, which is thedifference image between two saturated states along opposite direc-tions. The sample is an amorphous ribbon with a wavy surface.

then subtracted from a saturated state obtained under thesame contrast conditions. Sometimes, inhomogeneities in theillumination or nonplanar surfaces produce strong contrast inthe direct image, which can remain visible as artificial con-trast in a ‘regular’ difference image. An enhanced method(McCord and Hubert, 1999) that normalizes the standarddifference image by a ‘saturation difference image’, thusremoving these artifacts, is demonstrated in Figure 8(b). Fur-ther experimental possibilities applying difference techniquesare shown in Section 4.

3.1.4 Setup

The complete experimental setup for video-enhanced, wide-field Kerr microscopy is schematically shown in Figure 9.As most of the light is thrown away in Kerr microscopy

Digital CCDcamera

Functiongenerator

Poweramplifier

Microscope

Sample

SpeckleSpeckleremoved

Laser

Rotating glass disk

Glass fiber

Hg-, Xe arc lamp,or LED lamp

Magnetizing stages

In-plane field Out-of-plane field

Imageprocessing

Video-rateCCD camera

Magnet

Display,Recording

Figure 9. Experimental setup for wide-field Kerr microscopy.Options are shown for illumination, video processing, and mag-netizing stages. Also shown is the presence and suppression ofinterference patterns by laser illumination with and without rotat-ing glass disk respectively on a 28 by 28 µm2 Permalloy thin-filmelement. (Courtesy A. Neudert, IFW Dresden.)

due to the small opening of the polarizer and analyzer, lightsources with a high luminous density are mandatory. Thebest light source in most cases is a high-pressure mercuryarc lamp. It offers sufficient brightness and a color spectrumthat can be monochromatically used in the yellow-green aswell as the blue range by suitable spectral filters. The useof monochromatic light can be useful for the imaging ofcertain materials, for example, ferrites. Here, the portion oflinear Kerr light is largest at 400 nm so that the domains canbe imaged without additional means, while at 550 nm theelliptical contribution is strongest, requiring a compensator.The disadvantage of the mercury lamp is its instability andshort lifetime. Xenon-arc lamps are more stable and offerwhite light at a luminous density of just one-quarter of themercury lamp. This is still sufficient if a Berek illuminator


and prism polarizers are used to avoid light loss, or if loss iscompensated by a highly sensitive video camera. In any case,the infrared radiation component of these lamps has to beremoved by heat-reflecting filters to protect the specimen and,possibly, sheet polarizers from damage (also video camerasmay be sensitive to the near infrared).

Much higher light intensity at better stability is obtainedby laser illumination (Argyle, Petek and Herman, 1987) (theluminous density of a 5-mW laser is comparable to thatof a 100-W mercury lamp). The laser light is fed into themicroscope by a multimode glass fiber of typically some100 µm diameter, replacing the conventional arc lamp. Theimage of the fiber output is then focused to a small spotin the back focal plane of the objective by the microscopeoptics (alternatively, the fiber end can also be directlypositioned in the back focal plane). This ensures an almostparallel illumination of the sample. As the laser spot issmaller than the arc image of a conventional lamp, thespot image can be directly placed on the extinction crossso that an aperture stop is not necessary. By moving thefiber output around in the back focal plane, the plane ofincidence and the sensitivity axis is adjusted. A varietyof different lasers is available that cover a wide range ofwavelengths. Traditional argon ion lasers can be replacedby modern diode lasers or diode-pumped solid-state laserssuch as Nd:YAG lasers with a wavelength in the infraredthat can be shifted to the visible range by frequencydoubling. Also, blue solid-state lasers are available. Laserscan be run in continuous wave or pulsed modes, thelatter making them suitable for time-resolved imaging (seeSection 4). The coherence of the laser light introducesproblems in wide-field microscopy. Light scattering anddiffraction patterns (speckle) develop because of interferenceat surfaces and dirt particles in the optics. Such mottleunsteadiness (Figure 9, inset) makes it impossible to observemagnetic responses in real time. These artifacts can beeliminated by temporally scrambling the laser light. If theinterference patterns fluctuate substantially faster than theintegration time of the detector (e.g., the video frame rateof the camera), the speckle and scattering artifacts disappearin the image. Several methods for despeckling have beendeveloped (Inoue and Spring, 1997; Argyle and McCord,2000): inserting a spinning glass wedge or a glass disk witha randomly undulated surface in the illumination, sendingthe light over tumbling and rotating mirrors, or mechanicallyvibrating the glass fiber and additionally vibrating the tipof the fiber so that its image covers a suitable area in theback focal plane. In any case, satisfactory results with laser-illuminated microscopes are only obtained in multiframeaccumulated images where residual laser effects are averagedout. A promising alternative to laser illumination are high-intensity light-emitting diodes (LEDs), which are also fed

into the microscope by an optical glass fiber (Kleinefeld,2006 Private Communication). They combine high stabilitywith the absence of speckle and interference fringes. Bycooling the LED in liquid nitrogen, it tolerates highercurrents, thus delivering higher intensity.

A sensitive video camera transforms the optical imageinto an electrical signal that is displayed on a screen,either directly or after image processing. Charge-coupleddevice (CCD) cameras or highly sensitive complementarymetal oxide semiconductor (CMOS) cameras have replacedclassical Nevicon tube cameras in recent years. A numberof ‘regular’ integrating video-rate CCD cameras, whichhave been optimized for bright-field video microscopy, areavailable. Also, digital CCD cameras can be used for Kerrmicroscopy if their frame rate is fast enough (at least videofrequency) to allow real-time imaging. The read-out speedof digital cameras can be enhanced by joining adjacentpixels together into super pixels (binning), though at thecost of resolution. An approximately 1000 × 1000 pixelresolution at a frame rate of 30 frames per second (fps) arereasonable numbers for standard Kerr microscopy. Owing tothe low light level in Kerr imaging, high camera sensitivityis important. Image intensifiers (see Figure 22, below) canfurther increase sensitivity, and cooling of the CCD chipimproves the signal-to-noise ratio. The option of electronicshading correction that allows to improve inhomogeneouslyilluminated images is advantageous. In practice, the imagebrightness has to be adapted properly to meet the signalrequirements and optimum dynamic range of the videocamera. Increasing the analyzer angle β (Figure 1b – theintensity increases with β2) or opening the aperture stopbeyond the width of the extinction cross, thus increasingthe background intensity, are practical means to achieve alarge signal-to-noise ratio. A possible loss in contrast isnot a severe problem, as contrast can easily be enhancedelectronically.

Image processing for contrast enhancement requires digitalimage acquisition. Digital CCD and CMOS cameras directlyprovide a digitized data stream, while for video-rate CCDcameras the analogous output has to be converted by ananalog-to-digital converter. At least 8-bit resolution (meaningthat the intensity amplitude of an image is represented by 256discrete values) is required in the (optimized) original imageto avoid visually obvious gray-level steps in the processedimage (for digital cameras, this number may be higher). Tocreate a difference image, first an averaged reference imageis stored by summation of repeated images (typically 64 or128 frames) of the same sample state. The digital framememory, which holds the accumulated images, must havea storage capacity of at least 16 bits to also accommodatethe brightest pixels of the sum of digital 8-bit images.The reference image is stored and continuously subtracted


from all following images, being displayed on the monitorat the same time. As the visual observation of domainmotion is fundamental for any kind of domain analysis, it isadvantageous if the subtraction process is performed in ‘realtime’ at (at least) video frequencies without averaging. Forrecording and presentation purposes, noise can be reduced byadding each of the digitized images in a recursive procedureto produce a running average of the incoming images.Because noise is random and the signal is not, a runningaverage both reduces the noise contribution and enhancesthe signal component of the output digital image. The resultis an image of constant brightness, the noise of which iscontinuously reduced with increasing averaging time. Owingto the small magnitude of the Kerr contrast, the resultingdifference image may contain relevant information often onlyin the lower bit levels. The visually meaningful 8 bits areselected and displayed. Domain images in 8-bit resolution aresufficient for pleasing visual observation as the human eyecan distinguish, at most, 50 discrete shades of gray withinthe intensity range of a video monitor. By difference-imageprocessing, the Kerr contrast is typically enhanced by a factorof 30; this means that contrasts below 0.1% can be visualized(the contrast sensitivity of the human eye is some percent atbest). Digitized images open the way for further computerprocessing depending on specific demands.

The free space around the nosepiece of the microscopeallows a variety of sample manipulations. The application ofmechanical stress, as an example, was already documentedin Figure 7. In-plane magnetic fields of arbitrary directioncan be applied by rotatable coils or electromagnets. In thedesign of Figure 9, the specimen is mounted on a stamp thatis placed between the pole pieces of an independently piv-oted electromagnet. Magnetic fields µ0H up to some tenthsof a Tesla can be achieved in such setups, reaching the Teslaregime at proper pole-tip geometry and close pole distance.Sample displacement of centimeters in the X and Y direc-tions is possible and the entire stage unit is capable of preciseup and down movement with the conventional coarse andfine focusing mechanism of the microscope. In-plane fieldsof arbitrary direction may alternatively be created by propersuperposition of the fields of two fixed, perpendicular elec-tromagnets. Also, perpendicular magnetic fields (i.e., parallelto the objective) can be generated in a Kerr microscope,either by regular coils or by specially designed electromag-nets, as sketched in Figure 9, which provide fields up to theTesla range. Other applications may require special designs(see Section 4.2.5 on dynamic imaging). Optical cryostatsor heating stages, which fit between the pole pieces of anelectromagnet, allow temperature-dependent observation ofmagnetization processes. As vacuum insulation is requiredfor these devices, the sample has to be observed througha glass window. Long-distance objectives have to be used

then which suffer from a reduced optical resolution of about0.5 µm at best, as given by the numerical aperture of theseobjectives. A problem for the application of stronger fieldsis parasitical Faraday rotations in the lenses or glass win-dows of the optical temperature stages that may be muchstronger than the Kerr effect. The Faraday contribution canbe compensated by rotating the analyzer.

As extremely weak contrasts are enhanced by the differ-ence imaging procedure, a high mechanical, thermal, andelectrical stabilization of the microscope and electronics isindispensable to obtain optimal results (at least during thetime where the same reference image is used). A stable lightsource, heat-reflection filters to avoid sample heating, andplacing the microscope on a damped table to avoid vibra-tions are fundamental. Mechanical stabilization is most crit-ical. Rough surfaces cause light scattering that immediatelydestroys the Kerr contrast in a difference image if the sampleis displaced relative to the state where the reference imagehas been accumulated. Displacements of the order of the res-olution limit of the used objective are sufficient to deterioratea difference image. Considerable sample movement may becaused on larger samples in the gradient of the magnetiz-ing fields. Using stiff sample holders and stiff gluing of thespecimen reduces the problem (care has to be taken to avoidunwanted mechanical stress in the samples). All magneticparts in the sample space should additionally be replaced bynonmagnetic ones as far as possible.

3.1.5 Kerr microscopy and magneto-opticalmagnetometry

Plotting the average image intensity in a sample area, whichis defined by the objective and field diaphragm, as a functionof the applied magnetic field yields a local magneto-opticalhysteresis curve. At the same time, the domain images canbe recorded, thus providing a visualization of the underlyingmagnetization process. Figure 10 shows an example of suchan experiment, performed on an exchange-coupled bilayersystem.

3.1.6 Quantitative Kerr microscopy

Owing to its linearity and direct sensitivity to the magneti-zation, the Kerr effect can be used for a quantitative deter-mination of the magnetization direction (Rave, Schafer andHubert, 1987). The principle of quantitative Kerr microscopyis explained in Figure 11(a). The Kerr intensity has a sinu-soidal dependence on the direction of the magnetization vec-tor. This sensitivity function, which is used for calibration, isobtained by measuring the intensity of saturated states alongdifferent directions. Also, domain intensities can be used forcalibration if their magnetization direction is known a priori,


1

Domainwall

motion

Domainwall

motion

Partialrotation

Rotation

a

bl

kj

kj

ihg

ihg

f

f

e

e

d

d

c

c

a

b

M/M

s

0

−1

−60 −40 −20 0Magnetic field in A cm−1

20 µm

Figure 10. Magneto-optical hysteresis curve, directly measuredin a wide-field Kerr microscope, together with domain imageson a CoFe (20 nm)/IrMn (10 nm) bilayer film. The domains inthe ferromagnetic CoFe film, which is exchange coupled to theantiferromagnetic IrMn film that is responsible for the loop shift(exchange bias effect, See also Exchange Coupling in MagneticMultilayers, Volume 1) are shown. The steep forward branch of themagnetization curve is caused by domain wall motion (a–c), whileinhomogeneous rotational processes (d–k) are responsible for therounded part of the recoil branch. The wall motion along the forwardbranch is so fast that it cannot be recorded by static images. Themagnetization M is normalized to the saturation magnetization Ms

in the plot. (Reproduced from J. McCord, R. Schafer, R. Matthesi,K.-U. Barholz: Observations by permission of American Instituteof Physics.)

for example, due to crystal anisotropy or at sample edges.The intensity of unknown domains is then compared withthe calibration function and so the angle of m in the surfacecan be measured. The problem is that due to the sinusoidaldependence there are two possible angles for a given domainintensity. To resolve this ambiguity, the domain pattern ofinterest has to be imaged twice under different sensitivityconditions that should be shifted by 90◦ (e.g., by choosinglongitudinal and transverse Kerr effects). Figure 11(b) showsdomains on an iron single crystal with [100] surface orienta-tion that were imaged under these conditions. If the domain

Polarizer Analyzer

(a)

Inte

nsity

Longitudinal

DomainIntersity

Transverse

0° 90° 180°

Sensitivity horizontal Sensitivity vertical(b)

(c)

10 µm

5 µm

j

j

270° 360°

m

Figure 11. Principle and application of quantitative Kerrmicroscopy. (a) Calibration functions of the Kerr intensity at lon-gitudinal and transverse sensitivity as a function of magnetizationdirection (schematically). The intensities of an unknown domain,measured under the same conditions, are compared with thecalibration functions, as indicated by arrows. (b) Domain patternon iron–silicon [100] sheet, imaged under two complementaryKerr sensitivities. (c) Quantitative images on a Co-rich amorphousribbon. The domain wall width of the as-quenched state (left) isstrongly enlarged (right) if residual anisotropies are reduced byannealing in a rotating magnetic field (Schafer and Herzer, 2001).A vector plot and color code (here shown in black and white) canbe used for presentation.

magnetization is transverse to the contrast sensitivity, thedomain walls show up as black or white contrast, as givenby their surface rotation sense. In Figure 11(c), the quanti-tative method was applied to domain walls in a cobalt-richmetallic glass ribbon. Originally, these images are displayedwith a color code, where the in-plane magnetization direc-tions are mapped by a color wheel. The quantitative methodcan reliably be applied only to soft magnetic materials forwhich no polar magnetization components are present at thesurface, which would otherwise be difficult to calibrate orseparate from in-plane contrast.


3.1.7 Depth-selective Kerr microscopy

The magnetic information depth of the Kerr effect is about20 nm in metals. A quantification of this depth sensitivityhas to consider the phase of the magneto-optic amplitude(Trager, Wenzel and Hubert, 1992). The total magneto-optical signal can be seen as a superposition of contributionsfrom different depths, which are damped exponentially andwhich differ in phase as a function of depth according to acomplex amplitude penetration function (Figure 12a).

These phase differences can be exploited in Kerr micro-scopy (Schafer, 1995). Using a rotatable compensator, thephase of the Kerr amplitude, generated in a certain depth,can be adjusted relative to that of the regularly reflectedlight amplitude (as shown in Section 2, a detectable Kerr

1

Ker

r am

plitu

de k

(nor

mal

ized

to s

urfa

ce v

alue

)N

orm

aliz

ed K

err am

plitu

de

Re (k)

Im (k)

Depth

Bottom layerTop layer Spacer

0

0 40 80Depth in nm

Bottom layerinvisible

Depth

(c) Both layers

(b)

(a)

Top layer Bottom layer

10 µm

Top layerinvisible

0

N

K

Figure 12. (a) Depth sensitivity of the normalized Kerr amplitudeκ in iron. The relative phase of K and N was selected so that Nis allowed to interfere with the K generated right at the surface(after Trager, Wenzel and Hubert, 1992). Proper phase selection(b) Proper phase selection (b-schematically) allows layer-selectiveKerr imaging on thin-film sandwiches, as demonstrated in (c) for asputtered Co/Cu/Ni81Fe19 (5 nm/5 nm/50 nm) trilayer. (Sample: D.Burgler, FZ Julich, imaging: J. McCord, IFW Dresden.)

rotation is only possible if K and N are in phase). In thisway, light from a selected depth zone may get invisible ifits Kerr amplitude is adjusted out of phase with respect tothe regular light. In sandwich films, (See also ExchangeCoupling in Magnetic Multilayers, Volume 1) consistingof ferromagnetic layers that are interspaced by nonmag-netic layers, the zero of the information depth can be putsomewhere into the middle of one layer so that the inte-gral contributions of this layer just cancel, leaving onlycontrast from the other layer (Figure 12b). This kind of layer-selective Kerr microscopy is demonstrated in Figure 12(c)for a Co/Cu/NiFe sandwich sample. Demagnetization in analternating field leads to a complicated mixture of widedomains in the low-coercivity bottom layer and fine, irreg-ular domains in the high-coercivity top layer. After contrastseparation, traces of these fine domains are also seen in thebottom layer, most likely induced by dipolar interaction withthe magnetically charged domain walls of the top layer.

3.2 Laser-scanning Kerr microscopy

In a laser-scanning Kerr microscope, a polarized laser beamis scanned relative to the specimen and its polarizationstate after reflection is analyzed by a photodetector. Theearly approaches of this technique were stimulated by theinterest in the dynamics of magnetization processes in thin-film recording heads (see Section 4.2.1). First measurements,using a fixed laser spot and a line scan of the sample (Re,Shenton and Kryder, 1985), were soon extended to a two-dimensional scanning technique (Kasiraj, Shelby, Best andHorne, 1986). Elimination of nonmagnetic signals (due tononideal surfaces) was achieved by synchronous detection:the magnetization was modulated by a high-frequency mag-netic field. The corresponding modulation in the polarizationof the Kerr light was then extracted from the optical detectorwith a phase-sensitive lock-in technique. Thus, a map of thehigh-frequency magnetization response (permeability) wasobtained, in which the domain structure was revealed owingto domain wall motion. In succeeding developments, thedomain information could be directly extracted by advanceddetection schemes that even have the capability of vectormagnetomery (Egelkamp and Reimer, 1990; Clegg, Heyes,Hill and Wright, 1991; Silva and Kos, 1997; Nagai, Sekiguchiand Ito, 2003).

The principle of such an advanced laser-scanning Kerrmicroscope is illustrated in Figure 13(a). A collimated andpolarized laser beam is focused onto the specimen surfaceusing an infinity-corrected objective lens. Argon lasers arewidely used because of their brightness and excellent geom-etry. The laser spot is then moved across the specimen by


scanning probe and sample relative to each other. In com-mercial instruments, which have been designed mainly forbiological applications, the laser spot is scanned in a TV-raster fashion (beam scanning). For Kerr microscopy, how-ever, moving the sample itself in a rasterlike way by usinga precision XY stage is more favorable. Although this stagescanning is relatively slow (the time required to produce animage is of the order of tens of seconds), it ensures that both,the angle of incidence and the polarization state of the illu-minating ray bundle, are constant over the entire scan. Byscanning, the image is constructed in a point-by-point man-ner with a lateral resolution that is basically determined bythe size of the probing laser beam. Using a 100× oil immer-sion objective with a numerical aperture of 1.3, a laser spotsize of 0.8 µm is obtained. A smaller focused spot size of0.16 µm is achieved if the beam diameter is first increasedby beam expansion to completely fill the objective aperturebefore it is focused on the sample (Inoue and Spring, 1997).

The reflected light, which is collected by the same objec-tive lens, passes a rotatable quarter-wave plate to compensateellipticity and finally enters a Thomson polarizing beam split-ter. To obtain maximum sensitivity and flexibility, the splitteris set at 45◦ to the incident (undisturbed) polarization (Free-man and Hiebert, 2002a). Alternatively, the beam splittercan be set at 0◦ and the polarization plane can be rotatedby 45◦ by using a half-wave plate before the light entersthe splitter (Wright, Heyes, Clegg and Hill, 1995). The split-ter provides two beams of orthogonal polarization direction(Figure 13a, inset) that hit a pair of quadrant photodiodes.Each pair of opposing quadrants is aligned along the pro-jection of the samples x and y axes, respectively. The twobeams are of equal intensity for the case of undisturbed45◦ polarization, while any sample-induced polarization rota-tion leads to equal but opposite intensities (45◦ is the anglemost sensitive to small polarization changes). By suitablycombining the outputs of the eight photodiode quadrants,the three orthogonal components of magnetization can besimultaneously detected and separated, provided that theyare sampled nearly equally, which is true for objectives witha high numerical aperture. As illustrated in Figure 13(b)(and demonstrated experimentally in Figure 3), the longitu-dinal Kerr contrast changes sign if excited by two beamsof opposite directions of incidence, while the polar con-trast remains unchanged. By adding the signals of all fourdiodes of one quadrant detector, the longitudinal componentsare cancelled, while the polar components are added. Asthe total intensity that reaches each detector is reduced andenhanced, respectively, by equal amounts owing to the beamsplitting, the pure polar contrast can thus be separated bysubtracting the two sum signals (i.e., taking the quadrantcombinations (X1

+ + X1− + Y1

+ + Y1−) − (X2

+ + X2− +

Y2+ + Y2

−)), whereas a nonmagnetic surface-contrast image

Quadrantphotodiodes

Thomsonpolarizing

beam spilitter

Colimator

Laser

Pinhole

Polarizer

Objective

(a) (b)

Specimen onx – y scanner

E

E

E

E

E

y

x

l/4 plate

E

E

E

Quadrantphotodiodes

Stop

Beamsplitter

Topperspective

view

k2out

k1out

k2in

k 1in

k1

k2

m

X2+Y2

+

X2− Y2

−

X1+Y1

+

X1− Y1

−

Figure 13. (a) Principle of laser-scanning Kerr microscopy (basedon setups realized by Wright, Heyes, Clegg and Hill, 1995, andFreeman and Hiebert, 2002a). The polarization plane of light isindicated by the E vector. The inset shows a perspective view fromtop to illustrate the orthogonal polarization directions of the twobeams leaving the polarizing beam splitter. (b) Contrast of in- andout-of-plane magnetization components depending on the directionof the k vector.

is generated by simply adding the signals. The longitudinalKerr contrast of magnetization components along the x-axisis revealed by combining (X1

+ − X1−) − (X2

+ − X2−), and

that along the y-axis by (Y1+ − Y1

−) − (Y2+ − Y2

−). Sinceall data are collected from the quadrants simultaneously,the three magnetization components at one sample spot arecaptured at the same time. This elegant method of vectormagnetometry requires a highly symmetrical beam profile sothat each quadrant receives the same quarter of the beam(Freeman and Hiebert, 2002a). The longitudinal contrast canbe further enhanced by introducing a set of four aperturesinto the optical path in the back aperture of the objective lens.This restricts the range of the angles of incidence to providea bundle of rays around an incidence angle of approximately60◦, depending on the used objective’s numerical aperture(Wright, Heyes, Clegg and Hill, 1995).


Another advantage of the differential detection techniqueis the common mode rejection of laser noise while at thesame time the signal is doubled. Further enhancement ofthe signal-to-noise ratio can be achieved by applying lock-intechniques: the illuminating laser beam is modulated by somephotoelastic (Silva and Kos, 1997), acousto-optic (Wright,Heyes, Clegg and Hill, 1995), or electro-optic (Egelkampand Reimer, 1990) device and the reflected light is measuredby a phase-sensitive detection amplifier, thus selecting onlysignals that are proportional to the Kerr amplitude. By usingac detection, contrast arising from nonmagnetic surface struc-tures is suppressed, the 1/f noise – inherent in the laser lightsource – is avoided, and polarization changes can be mea-sured independently of intensity fluctuations in the reflectedlight. Signal enhancement by the lock-in technique (sup-ported by additional subtraction of a constant backgroundintensity in the preamplified signal) makes it possible foreven the small light amplitude modulation of the transverseKerr effect to be used for imaging purposes (Egelkamp andReimer, 1990; Acremann et al., 2000). The technique, whichis not easily possible in conventional Kerr imaging, hasthe advantage of being sensitive only to one magnetizationcomponent. By illumination from two directions, quantita-tive Kerr images can be obtained (Buscher and Reimer,1993). Since the spots on the sample are illuminated sequen-tially in a laser-scanning microscope, interference speckleis less important and can be even completely eliminated byusing an aperture (pinhole) in the detection system (Wright,Clegg, Boudjemline and Heyes, 1994). The aperture is placedconjugate to the spot being scanned so that only the lightoriginating directly from the scanned spot is transmitted tothe photodetector (such confocal systems also offer three-dimensional imaging capabilities, which is highly attractivein biological studies (Sheppard and Wilson, 1984)). The useof confocal imaging schemes has been shown to enhance thelateral resolution in non-magneto-optical microscopes by afactor of

√2, which has, however, not been verified in Kerr

imaging (Nutter and Wright, 1998).A disadvantage of laser-scanning Kerr microscopy is its

slow speed compared to regular imaging microscopes. Theimage acquisition time of some tens of seconds in stage-scanning microscopes can be lowered by beam scanning(Ping et al., 1995). This requires, however, special opticaldesign to ensure a constant mean angle of incidence acrossthe whole scan. Depolarization errors can be minimized byrealizing the scanning with a vibrating single-mode opticalfiber (Ping, See and Somekh, 1996). Scan rates of one frameper second can be obtained in this way, which, however, isstill not fast enough for live observations of domains at videofrequencies.

To conclude, scanning Kerr microscopy falls short inreplacing conventional microscopy for ‘routine’ domain

research as real-time imaging of domain motion cannot berealized. The capability to simultaneously image all threemagnetization components (vector magnetometry) and toeasily eliminate background contrast by lock-in techniques isadvantageous. Static Kerr images of satisfactory quality, bothof in- and out-of-plane domains, can therefore be obtained.Also, other quantities like permeabilities or magnetizationcurves can conveniently be measured on a microscopic scale,thus probing the spatial variation of magnetic properties. Thebiggest potential of laser-scanning microscopes, however,lies in their predestination for stroboscopic imaging of fastdynamic processes (see Section 4.2.4).

4 DYNAMIC KERR MICROSCOPY

Dynamic magnetization processes cover a wide range oftimescales. Relaxation processes, wall creep, and aftereffectphenomena may last up to minutes and longer, eddy-current-limited processes in thick, electrically conducting specimenslast microseconds, and precessional phenomena in metal-lic films occur in the nano- and sub-nanosecond regime(See also Magnetization Dynamics Including ThermalFluctuations: Basic Phenomenology, Fast Remagnetiza-tion Processes and Transitions Over High-energy Barri-ers, Volume 2). Wide-field Kerr microscopy is suitable fordynamic domain studies in a frequency range from arbi-trarily slow to beyond the gigahertz regime. Slow domaindynamics can be observed visually as fast as the eye canfollow, either directly in the microscope or on contrast-enhanced images on the video screen if contrast enhance-ment by real-time image subtraction is used. As an example,domain growth by wall motion in an amorphous ribbonis presented in Figure 14(a–c) by three difference images,each obtained after stopping the field change during the(slow) magnetization cycle. However, on fast magnetiza-tion processes also, valuable information can be obtainedby regular difference-image processing. In Figure 14(d), thedomain state of (c) was excited by a 25-Hz sinusoidal fieldof small amplitude. Blurred domain boundary contrast inthe averaged difference image indicates vibrational domainwall motion. Increasing the field amplitude (e) reveals immo-bile domains in the middle of the image and strong domainactivity on the sides, as evident by the strongly blurredcontrast in these areas. After switching off the alternatingfield (f), the domain pattern differs in details from the ini-tial one (c), indicating irreversible processes. Reversible andirreversible wall displacements can immediately be distin-guished in the experiment of Figure 14(g–i). In (g) and (h),the domain state of (f) was subtracted from averaged imagesof two states in which the sample was subjected to alternatingfields (25 Hz) of weak and moderate amplitudes, respectively.


(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

Figure 14. Studying the dynamics of a domain pattern in anamorphous ribbon (Fe78Si9B13, thickness 20 µm) by conventionaldifference-image processing. The area shown is characterized by180◦ domains that change their direction by about 90◦ at the topowing to stress-induced magnetic anisotropy. (a–c) Growth of darkdomains in vertically aligned magnetic field. State (c) is excited byan alternating magnetic field of 25 Hz and increasing amplitude in(d) and (e). The moving parts of the domain pattern get blurredin the averaged difference image. In (g,h), the configuration (f) issubtracted from images with the same alternating fields applied asbefore. Changes in the domain pattern show up as strong black andwhite contrast in these dynamically averaged difference images.After switching off the ac field, some walls remain displacedirreversibly as can be seen by residual contrasts in the differenceimage (i).

Those parts of the domain pattern that do not move stay grayin the dynamically averaged difference images, while chang-ing parts show up as contrast. After turning down the field(i), contrast in the static difference image is left in those areaswhere irreversible processes took place. Such difference tech-niques can also be used to study periodic or quasi-periodicprocesses, as demonstrated in Figure 15. Here, oscillatingdomain walls were recorded with long exposure times at dif-ferent frequencies with the static domain state subtracted. Theblack and white contrast gives information on the amplitudeof wall motion that decreases with increasing frequency dueto eddy-current damping. An asymmetry in the wall ampli-tude is also seen clearly. Two further examples of dynamicstudies by regular image subtraction, showing domain multi-plication processes as a consequence of dynamic field exci-tation, are presented in Figures 16 and 17.

Although dynamic effects can be studied by the aforemen-tioned methods, such experiments do not reveal the dynamicprocesses by themselves because they are either smeared out

(a) (b) (c)

200 µm

500 Hz 1000 Hz

Figure 15. Imaging of periodic wall oscillation processes in ananocrystalline ribbon (Fe73Cu1Nb3Si16B7, thickness 20 µm). Thedomain state (a) is subtracted from images with a sinusoidal fieldof 500 Hz (b) and 1000 Hz (c) of same amplitude applied along thedomain direction. (Courtesy S. Flohrer, IFW Dresden.)

1 mm

1 Hz 50 Hz 500 Hz

Figure 16. Eddy current–driven domain refinement in an ideallyoriented grain on FeSi transformer steel. Three static domainstates are shown after the sample was demagnetized with differentfrequencies as indicated. (Courtesy S. Flohrer, IFW Dresden.)

by averaging procedures (as in Figure 14) or they are alreadyover when images are taken (as in Figure 16). Time-resolved,high-speed imaging is rather required for detailed dynamicinvestigations. Kerr microscopy offers these possibilities bothin the wide field and in the laser-scanning modes, as shownin the following sections.

4.1 Principle of high-speed microscopy

The principle of time-resolved high-speed microscopy isillustrated in Figure 18. The sample is excited by acontinuously changing or pulsed periodic magnetic field. Atcertain time delays relative to the excitation, the magneti-zation is microscopically probed in a finite time window.Shifting the time delay of the probing window yields a seriesof time-resolved images of the magnetization process. Timeresolution is either obtained by a gated high-speed videocamera using a constant light source for illumination, or bya pulsed light source and continuous detection.

An ideal dynamic experiment should deliver a time-delayed series of single-shot images, as indicated inFigure 18(a), each of them representing the momentary mag-netic state of the sample during the evolution of the magne-tization process within the same excitation cycle. Repeatingthe imaging sequence in a number of following cycles wouldallow the study of the most general case that may alsoinclude nonreproducible and stochastic magnetization events,


(a)

40 µm

(b)

(d)(c)

Figure 17. The dynamic multiplication of Bloch lines in a crosstiedomain wall of a Ni81Fe19-film element of 50-nm thickness, againstudied by conventional image processing. Image (a) shows aregular difference image in the demagnetized ground state. Image(b) was acquired after applying a single field pulse (amplitude400 A m−1, pulse length 1.2 ns, rise and fall time 120 and 170 ps,respectively) along the short axis of the element, leading to anincreasing number of cross-ties, that is, the nucleation of newBloch lines. The locations of Bloch line generation are evidentin (c), where the difference of the two images before and afterthe field pulse is shown. In (d), a train of field pulses with arepetition rate of 23 MHz is applied. In these experiments, onlythe domain states before (a) and after pulse-field application (c–d)are displaced – the mechanism of Bloch line generation is not seen.(Courtesy A. Neudert, IFW Dresden. Reproduced from A. Naudert,J. McCord, R. Schafer, R. Kaltofen, I. Monch, H. Vinzelberg,L. Schultz: Bloch line generation in cross-tie walls by fast magneticfield pulses. Journal of Applied Physics (2006) by permission ofAmerican Institute of Physics.)

which may change from cycle to cycle. Single-shot imag-ing, however, requires a sufficient amount of photons to beaccumulated in the detector during the probing time in orderto obtain a sufficient signal-to-noise ratio. Very bright lightsources and highly sensitive image detectors are thereforenecessary. Also, the repetition rate of the experiment has tobe fast enough to provide adequately short time delays forin-cycle imaging. Both conditions are increasingly difficult tomeet with rising excitation frequency or if the magnetizationresponse is too fast after pulse-field excitation.

If the repetition rate is the limiting factor (due to restric-tions in the speed of light-pulse sequence, camera trigger,or delay electronics), single-shot imaging can nonetheless beapplied as long as the detector sensitivity poses no limita-tion. By capturing images at identical time delays relativeto the field excitation period (Figure 18b), but in differentcycles, it is still possible to identify stochastic events. In caseof repetitive processes, the full magnetization process mayeven be recovered by shifting the time delay of probing. Ifboth detector sensitivity and repetition rate of the experimentare limited, time-resolved microscopy has to be performed

Magnetizingfield

Continuous

Pulsed

Probing

Magnetizingfield

Probing

etc.

(a)

(b)

t1

t1 + ∆t

Time

Figure 18. Principle of time-resolved imaging, (a) for an idealsingle-shot experiment, and (b) in the stroboscopic mode. Thesample is excited either by alternating magnetic fields or a by trainof field pulses.

in a different way, known as stroboscopic imaging (though,strictly speaking, the other methods are also of stroboscopicnature). In a strobed system, image acquisition is preciselysynchronized to a periodic excitation, so that images are cap-tured in the same time period of successive cycles (like inFigure 18b) and accumulated over many cycles (up to some10◦ for fast pulse-field experiments) until a sufficient signal-to-noise ratio is achieved. The time delay is then periodicallyshifted to temporarily scan along the magnetization process.This accumulation technique, however, requires repetitivemagnetization processes during successive cycles. If the pro-cess is different for every excitation period, a complicatedmixture of contrasts (or even no contrast at all) is seen inthe averaged images – in other words: only the repeatableevents are seen as sharp features in the accumulated images,statistical events, and fluctuations are averaged out. A possi-bility to extract stochastic events (‘noise’) from stroboscopicimages of nonrepetitive processes was described in Freeman,Steeves, Ballentine and Krichevsky (2002b).

The limitations of single-shot and stroboscopic imag-ing are demonstrated in Figure 19 by time-resolved (wide-field) studies on the same location of the amorphousribbon that was already investigated in Figure 14. The pic-tures uncover the domain activity hidden in the blurredcontrast of Figure 14(e). Time-resolved, stroboscopicallyobtained pictures at 25-Hz sinusoidal excitation are shownin Figure 19(a). They were recorded at three delay times asindicated, starting from an almost saturated high-field state.About 800 pictures of successive cycles, each with an illumi-nation time of 0.4 ms, were collected and averaged for eachimage. Repeatable as well as nonrepetitive processes are evi-dent in the probed area, indicated by strong and faint (or evenblurred) domain contrast respectively. A strong reversibility


(a)

(b)

(c)

Cycle 1

Cycle 2

200 µm

6 ms 8 ms 12 ms

20 ms 25 Hz

Figure 19. Dynamic studies at 25-Hz sinusoidal excitation on thesame sample area as in Figure 14. (a) Stroboscopic images, obtainedby a gated image intensifier and a digital CCD camera. Sevenhundred and sixty-eight frames of 0.4-ms illumination time havebeen accumulated for each picture. The time delay relative tothe maximum field is indicated. (b) Single-shot images at 2-msillumination time, obtained by a high-speed CMOS camera withsufficiently large frame rate. The pictures in each row were takensuccessively within the same cycle. (c) Single-shot images at 0.4-msillumination time. The difference images in which an averagedimage of the saturated state is subtracted are shown in each case(together with S. Flohrer and J. McCord , IFW Dresden).

in the middle zone is confirmed by this experiment, whichwas already indicated by domain stiffening in the exper-iments of Figure 14. By single-shot imaging (Figure 19b)also, the irreversible processes are resolved by sharp con-trasts. The two rows of images were recorded in differentcycles of excitation, with the images within one row havingbeen obtained subsequently within the same cycle at similardelay times as in Figure 19(a). A comparison of the two rowsreveals similar and different domains that appear within thetwo cycles, indicating reversible and irreversible processes.The reversible domains add up to the strong contrast in thestroboscopic experiment of Figure 19(a). The illuminationtime for each image in Figure 19(b) was 2 ms, which was

obviously sufficient to get a reasonable signal-to-noise ratio,but which occasionally left unsharp boundaries caused bynonnegligible wall movement within this time window. Thiseffect should be strongly reduced if the illumination time ofthe single shots is reduced to 0.4 ms (Figure 19c) as for thestroboscopic image. However, strongly noisy pictures withalmost vanishing domain contrast are obtained then, indicat-ing the limits of single-shot imaging. As the conditions forserial single-shot imaging are (so far) impossible to meet forfrequencies above the 50-Hz regime due to the mentionedlimitations, most of the time-resolved imaging experimentsat power frequencies and beyond have to follow a strobo-scopic scheme.

4.2 Experimental setups for time-resolvedmicroscopy

High-speed imaging requires the following main compo-nents: microscope (or at least objective lens in case of laser-scanning microscopy), image detection, pulsed light sourceor triggered video camera to obtain time resolution, powersupply connected to a coil or stripe line for magnetic excita-tion of the sample, and some synchronous means includingdelay electronics to adjust and shift, respectively, the exci-tation and probing time. Time resolution and repetition ratesof excitation and probing have to be chosen appropriately tomeet the specific requirements of the sample and processesto be studied. If, for instance, the relaxation processes ina magnetic thin-film element after pulse-field excitation last20 ns, the repetition rate of the field pulses should be less than50 MHz to allow complete relaxation before the next pulseis applied. To provide repetitive conditions for stroboscopicimaging, it also has to be assured that the initial domainstate is identically recovered between the excitation periods.For time-resolved imaging, both laser-scanning microscopywith a pulsed laser as well as wide-field microscopy can beused, the latter either based on a pulsed light source or ona triggered video camera. The three methods are comparedin this chapter, following a brief historical review on thedevelopment of time-resolved Kerr microscopy.

4.2.1 Historical review

First time-resolved Kerr imaging techniques emerged in theearly 1960s, based on regular wide-field microscopy andmotivated by the interest of that time in the fast reversalof soft magnetic films for memory applications and in thedynamic processes and losses in electrical steel. In 1963, anoptical strobing apparatus for imaging the flux reversal inNiFe films was introduced (Conger and Moore, 1963), inwhich light pulses of about 100-ns duration were generated


using sunlight and a mirror that was fastened to a spinningturbine. Simultaneously, Drechsel (1961) used a xenon flash-lamp to create single light pulses of 1 ms duration that wereapplied to single-shot imaging of iron crystals after sharplychanging the magnetic field. Stroboscopic imaging on Gosssheets with several minutes averaging time at sinusoidal exci-tation up to 200 Hz was realized by Passon (1963) by addinga rotating disk with holes in the illumination light path of acontinuously shining halogen lamp. Pictures were recordedby photographic films in these early experiments. Some yearslater, high-speed motion-picture cameras with frame ratesup to 5000 pictures per second allowed single-shot imag-ing on transformer steel up to the 100-Hz regime (Houze,1967; Haller and Kramer, 1970). The motion pictures couldbe examined frame by frame to analyze the character ofdomain wall motion. In the experiment of Houze, the high-speed camera was synchronized with a xenon flash lamp,that is, one flash per frame was recorded. In another setupof Passon (1968), time resolution was realized by a com-mercial television camera, equipped with a sensitive imageintensifier that could be gated by trigger pulses. Stroboscopicobservation of periodic processes up to 20 kHz with a gat-ing time as low as 2 µs was possible with this system. Walldamping and wall multiplication phenomena with increas-ing frequency (due to eddy-current effects) were observedin these pioneering experiments. Also found was an increasein the reproducibility of magnetization processes in trans-former steel with raising frequency – the precondition forstroboscopic imaging. An excellent review on these findingsis given in Shilling and Houze (1974). In the meantime, laserillumination had entered the scene. A Kerr optical ‘appara-tus’ with a Q-switched ruby laser for pulsed illuminationwas set up by Kryder (Kryder and Humphrey, 1969a). Timeresolution of 10 ns was obtained by synchronizing the laserlight pulses with the actuation of a Kerr electro-optic shut-ter in front of the photo camera. The intensity of the laserpulses (of some megawatts) was sufficient to provide single-shot photographs of the dynamic state during flux reversal inpermalloy thin films (Kryder and Humphrey, 1969b). Manyof these early dynamic Kerr experiments became possibleonly after contrast enhancement by optical interference layers(see Figure 2).

A decade later, the emerging bubble memories again stim-ulated interest in dynamic imaging. Most setups of that time(Humphrey, 1975; Kryder and Deutsch, 1976) were basedon dye lasers that were triggered by pulsed nitrogen ionlasers, generating light pulses in the 10-ns-duration range ata low repetition rate of about 10 Hz. Owing to the high laserenergy, caution had to be taken to avoid sample damage byoverheating, for example, by defocusing the laser beam (Mal-ozemoff, 1973). Such effects could be avoided by using con-tinuous illumination and a gated image intensifier to obtain

25 µm 25 µm

(a) (b)

Figure 20. (a) Single-shot picture of ‘exploding’ magnetic bubblesin a garnet film. (b) Stroboscopic image from the yoke of a thin-film recording head, excited with a 1-MHz drive field. A differenceimage between two states is shown that were acquired by series of5-ns laser pulses, where the pulses of the second series are delayedsomewhat relative to the pulses of the first series. (Reproduced bypermission of Springer from Hubert and Schafer, 1998, the picturesare courtesy of F. Humphrey (a) and B. Argyle (b).)

high-speed photographs of bubble devices (Vella-Coleiro andNelson, 1974). In Kryder’s system (Kryder and Deutsch,1976), the laser pulse frequency corresponded to the trig-ger rate of a TV camera so that each frame recorded hadonly one laser pulse for illumination. By recording on avideotape recorder, the repeatability of the magnetizationprocess could be examined by frame-by-frame analysis ofthe tape. Transient bubble domain shapes during expansionand collapse in pulsed magnetic fields have been observed byhigh-speed photography (Gal, Zimmer and Humphrey, 1975).A snapshot of ‘exploding’ bubble domains, as an impressiveexample, is shown in Figure 20(a). Single-shot imaging inmagnetic garnet films profited from strong contrasts due tothe polar Faraday effect that can be favorably applied inbubble films.

Dynamic imaging in the following decade focused on theunderstanding of the sources of wiggle and noise in thin-filmrecording heads. First measurements were performed in aphotometric way (Re, Shenton and Kryder, 1985): an Ar laserspot was focused on the pole tip in a regular optical polariz-ing microscope. The head was excited by high-frequency cur-rents up to 50 MHz, sent through the drive coil. The reflectedlight, modulated by the polar Kerr effect, was then recov-ered with a photomultiplier and a lock-in amplifier detectionscheme. By line scanning across the pole tip, the profileof the switching magnetization could be determined. Thismethod was then extended to a two-dimensional scanningtechnique (Kasiraj, Shelby, Best and Horne, 1986), deliv-ering spatially resolved images of magnetization changeswith a time resolution of 50 ns. Since nonmagnetic signalswere eliminated by the lock-in technique in this approach,the weak Kerr contrast of permalloy films was greatlyenhanced. Different approaches, applied to the imaging ofthin-film head yokes, were based on stroboscopic wide-fieldKerr microscopy and background subtraction for contrast


enhancement (Petek, Trouilloud and Argyle, 1990; Liu,Schultz and Kryder, 1990; Kryder, Koeppe and Liu, 1990). Atime resolution of 5–10 ns was obtained by dye laser pulses,pumped by Nd:YAG and nitrogen lasers, respectively. Anexample of such a stroboscopic image from the yoke of athin-film head is presented in Figure 20(b), showing the aver-aged domain states at different phase positions in a differenceimage to emphasize wall motion.

A revival of (still ongoing) interest in high-speed imag-ing began in the late 1990s, owing to increasing demandsfor higher speeds and densities from data storage technolo-gies, and for newer approaches such as magnetic randomaccess memories (MRAMs) or spin electronics. The switch-ing speeds of magnetization in metallic thin films haveapproached the sub-nanosecond regime where intrinsic mag-netic response times due to spin-precessional effects becomethe limiting factor in devices, asking for an understandingand control of fast magnetization reversal processes. Moti-vated by these accumulated interests, dynamic behavior inmicro- and nanosized particles is being actively studied inrecent years by micromagnetic simulations and direct obser-vation of the magnetization processes with simultaneous spa-tial and temporal resolution. The necessary breakthrough interms of time resolution was related to the development ofps- and fs-laser systems that are most frequently applied inscanning Kerr microscopes. The first laser-scanning micro-scope with a time resolution of 50 ps (Freeman and Smyth,1996) was applied for polar Kerr measurements of magneticflux propagation in recording head pole tips. This apparatuswas then extended to in-plane sensitivity (Stankiewicz et al.,1998) and time-resolved vector magnetometry (Ballentine,Hiebert, Stankiewicz and Freeman, 2000) (see Section 3.2)and used to study the switching behavior of patterned thin-film elements with lateral extensions of some micrometersthat were deposited on coplanar transmission lines to createmagnetic field pulses (see Section 4.2.5). A strongly modu-lated, nucleation-dominated magnetization configuration wasobserved during dynamic switching, which was replaced bydomain wall motion if a transverse biasing field was applied,leading to a dramatic enhancement of switching speed atthe same time (Choi et al., 2001). Excellent reviews of theoutstanding work of the Freeman group are found in (Free-man and Hiebert, 2002a; Choi and Freeman, 2004; Choi,Krichevsky and Freeman, 2005b).

Laser-scanning Kerr microscopy with a temporal reso-lution in the 10-ps regime is now well established andused for a wide variety of time-resolved observations. (Seealso Investigation of Spin Waves and Spin Dynamics byOptical Techniques, Volume 3, Time-resolved Kerr-effectand Spin Dynamics in Itinerant Ferromagnets, Volume 3,and Ultrafast Magnetodynamics with Lateral Resolu-tion: A View by Photoemission Microscopy, Volume 3).

This includes investigations in magnetic recording heads andmedia (Back, Heidmann and McCord, 1999; Wakana, Nagaiand Sakata, 2001; Veerdonk et al., 2001; Nagai, Sekiguchiand Ito, 2003), as well as in patterned soft magnetic filmelements. ‘Precessional switching’ as reversal mechanismof small elements could be demonstrated by time-resolvedimaging (Hiebert, Ballentine and Freeman, 2002; Hiebert,Lagae and Boeck, 2003b). In this method, a fast-rising fieldpulse is applied perpendicular to the initial direction of themagnetization, causing a large angle precession that is usedto revert the magnetization if the field is stopped exactly after180◦ precessional rotation. It could also be demonstratedthat post-switching oscillations (‘ringing’) can be avoided(Krichevsky and Freeman, 2004) by properly combiningeasy- and hard-axis field pulses in a crossed-wire stripelinegeometry (see Section 4.2.5). Other experiments using scan-ning Kerr microscopy focus onto the spin-wave eigenmodesof magnetization (Acremann et al., 2000; Park et al., 2002;Barman et al., 2004; Buess et al., 2004 (See also MagneticModes in Circular Thin Film Elements, Experiment andTheory, Volume 2)) and the gyrotropic motion of a centralvortex in magnetic thin-film elements (Park et al., 2003; Parkand Crowel, 2005). Though most of the research groups areusing laser-scanning microscopy, there was also progress inpicosecond wide-field imaging, both based on triggered videocameras (Chumakov et al., 2005) as well as on pulsed-laser-illuminated microscopes (Neudert et al., 2005).

At the moment, the interest in magnetization dynamicsis shifting from field-induced to current-induced switching(Stiles and Miltat, 2006) (See also Spin Angular Momen-tum Transfer in Magnetoresistive Nanojunctions, Vol-ume 5 and Theory of Spin-transfer Torque, Volume 2),while at the same time the lateral dimensions of the relevantmagnetic structures are getting well smaller than microme-ter. Microscopy at optical frequencies will therefore meet itslateral resolution limit. Other methods with an order of mag-nitude higher resolution, based on X-ray dichroism (Choeet al., 2004; Kuksov et al., 2004; Stoll et al., 2004) or X-rayholography (Eisebitt et al., 2004), offer an alternative. Onthe basis of the latter technique, a spatial resolution of 5 nmin conjunction with a time resolution of the order of 20 fsis predicted for imaging at future X-ray free electron lasers,offering the potential for stroboscopic snapshot imaging ofextremely fast magnetic switching processes of very smallparticles in the future.

4.2.2 Camera-based stroboscopic wide-field Kerrmicroscopy

In camera-based stroboscopic microscopes (Figure 21), themagnetic field excitation of the specimen is exactlysynchronized with the exposure time of the video camera.


SampleTrigger

Trigger

CCDcamera

Gated imageintensifier

Microscope

Wave, pulsegenerator

Delaygenerator

High-speedCCD camera

Xe or Hgarc lamp

Figure 21. Block diagram for camera-based stroboscopic wide-field Kerr microscopy. Time resolution is provided by triggeringa high-speed video camera or a gated image intensifier at constantillumination with precise timing relative to the field excitation.

A function generator, which also provides the signal for themagnetic field, creates trigger pulses that are delayed in adefined way relative to the field excitation by an electricdelay generator or optical delay line. These trigger pulsescontrol the moment when the camera is exposed for a shorttime. The sample may be continuously illuminated in suchexperiments or in synchronization with a pulsed light source.

Today a variety of digital CCD and CMOS camera systemsare available for time-resolved microscopy, which havereplaced the traditional high-speed movie cameras of theearly days of stroboscopy (see Section 4.2.1). A criticalfactor is the read-out time of the camera that determinesthe repetition rate of the experiment. Digital high-speedCCD and CMOS cameras with frame rates ranging betweensome hundred up to some thousand frames per second(at sufficient pixel resolution) are presently available. Forcomparison, the high-speed motion-picture camera used byHouze (1967) already offered rates of 5000 pictures persecond (see Section 4.2.1). Frame rates up to the megahertzregime are also possible with digital cameras. Such speeds,however, are either reached by pixel binding on cost ofresolution or they only allow to capture very few consecutivepictures that are stored in the (limited) memory of thecamera head before being transmitted to the computer. Theother important criterion is the time resolution given by theelectronic or mechanic shutter of the camera, which cantypically be varied from seconds down to the sub-100-nsrange in present cameras. The smallest opening time insingle-shot experiments depends on the sensitivity of theCCD or CMOS chip and the intensity of the light source.Single-shot imaging up to power frequencies is possiblewith the mentioned cameras. Higher frequencies require

Secondary electrons

Photoelectrons

Photocathode

Electrically conducting layerChannels

e–e–

e–

e–

e–

e–ee

e–

e–

Coupling system(lens or fiber taper)

CCDchip

Light

Microchannelplate

Luminescentscreen

(a)

(b)

Figure 22. (a) Schematics of an image intensifier (second genera-tion). Significant signal amplification up to four orders of magnitudeis due to the microchannel plate (b). It consists of millions of verythin, electrically conducting glass capillaries with typically 10-µmdiameter, which act as independent secondary electron multipli-ers. Their luminous gain ranges from 10 000 Lm/Lm up to 107

for intensifiers having two microchannel plates. Beside their gat-ing capability, image intensifiers (combined with a CCD camera)can also be used to enhance low light level images in regular Kerrmicroscopy.

stroboscopic imaging and the accumulation of images atgiven time delays (see Figure 19a). Background subtractionfor contrast enhancement is recommended just as in regularwide-field microscopy.

Much higher time resolution at increased sensitivity canbe gained by using a gateable image intensifier in combi-nation with a regular CCD camera. The intensifier primar-ily functions as an electronic shutter (Figure 22). A pho-tocathode in a vacuum tube is permanently exposed to apositive potential, which prevents the emitted photoelec-trons from leaving its surface. On the arrival of a triggersignal, an impulse of negative voltage is applied to thephotocathode, pushing the photoelectrons into a microchan-nel plate (MCP) where they are accelerated and multi-plied. After leaving the MCP, the multiplied electrons arefurther accelerated before they finally hit the phosphorlayer of the output window generating photons. A regu-lar CCD camera accumulates these photons during integra-tion time. The gating time of the fastest image intensifiersreaches currently the 200-ps regime at a repetition rate ofaround 100 MHz (or less than 100 ps at kilohertz repetitionrates).

Equipped with such modern, highly sensitive CCD orCMOS cameras and fast-image intensifiers, camera-basedwide-field strobes have been set up in recent years fordynamic investigation of magnetic films (Chumakov et al.,


2005) and bulk soft magnetic materials (Moses, Williamsand Hoshtanar, 2005; Flohrer et al., 2006). An advantage ofcamera-based systems is the possibility to vary the effec-tive opening time of the camera or intensifier, respectively,between shortest and continuous exposure (as opposed tolaser-based stroboscopes with usually fixed pulse frequen-cies – see following sections). This gives the opportunity tocompare time-resolved data directly with the images acquiredby static or quasistatic imaging. This comparison can behelpful in the interpretation of dynamic processes, becausethe peculiarities of the high-speed magnetization processescan be readily identified.

Examples for camera-based dynamic experiments havealready been presented in Figure 19. The single-shot images(Figure 19b,c) were recorded with a high-speed digitalCMOS camera, while time resolution in the stroboscopic pic-tures (Figure 19a) was achieved by a gated image intensifier.Two further examples, again obtained with image intensi-fiers, show the characteristic features of fast magnetizationprocesses in bulk material (Figure 23) and thin-film elements(Figure 24). In Figure 23 (Flohrer et al., 2006), the outermostribbons of nanocrystalline tape-wound cores with centimeterdimension and different uniaxial anisotropy were imaged atdifferent frequencies of a sinusoidal magnetic field. Domainrefinement (wall multiplication) was visible with increasingfrequency for all three cores (Figure 23a). In the materialwith the weakest anisotropy, regular domains were replacedby patches at higher frequency. The partly blurred domainboundary contrast at 50 Hz resulted from domain movementduring the exposure time or from slightly nonreproduciblewall displacement processes. An increase in the reproducibil-ity of the magnetization process with rising frequency anddecreasing anisotropy was observed. Figure 23(b) demon-strates the high-frequency magnetization process of the low-anisotropy material that is dominated by nucleation andgrowth of patch domains rather than by wall motion.

The thin-film switching process in Figure 24(a) (Chu-makov et al., 2005) was imaged at a much higher time reso-lution of 250 ps. A square-shaped film element was switchedbetween two (nearly) saturated states in a sharply risingpulse-field applied along the elements diagonal and generatedby a coplanar waveguide (see Section 4.2.5). A ‘concertina’pattern developed, which became visible at transverse Kerrsensitivity and consisted of alternating areas of clock- andcounterclockwise magnetization rotation. The magnetizationwas finally reverted by a mixture of rotation and domainboundary motion that lasted several nanoseconds. Two vor-tices were created and pushed toward the edges during thisprocess. Quasistatic switching in a slowly changing fieldoccured differently (Figure 24b): there was also a concertinaformed when the magnetic field was decreased from satura-tion, which, however, broke down abruptly in the reversed

Ku

Magneticfield

Ground state

0.2 mm

50 Hz 1 kHz 5 kHz 10 kHz

Stronganisotrophy

Moderateanisotrophy

Weakanisotrophy

(a)

(b)

0.2 mm

–10 –5 5 10

1

–1

M/M

s

Field in A m–1

f = 1 kHz

Figure 23. Time-resolved domain observations on Fe73Cu1

Nb3Si16B7 nanocrystalline tape-wound cores (See also Soft Mag-netic Materials – Nanocrystalline Alloys, Volume 4) in circum-ferential magnetic field (core width 20 mm, outer diameter 25 mm,ribbon thickness 20 µm). A gated image intensifier with a gatingtime of one-hundredth of the magnetic field period was applied fortime resolution; several thousand frames of independent events wereaccumulated for each image. (a) Stroboscopic images, taken aroundthe point of zero induction during sinusoidal excitation with saturat-ing peak induction at different frequencies as indicated. Three coreswith different strength of induced anisotropy Ku were studied (toprow: 29 J m−3, middle row: 10 J m−3, bottom row: 5 J m−3). Thedomain ground state, consisting of 180◦ domains and obtained bystatic imaging, is shown for comparison. (b) Inductively measuredhysteresis loop and stroboscopic images obtained at 1 kHz on thecore with weak anisotropy. (Reprinted from Acta Materialia, 2006,Flohrer et al., 2006. Magnetization loss and domain refinement innanocrystalline tape wound cores. Acta Materialia, 54 3253–3259,with permission from Elsevier.)

field by the unpinning and fast motion of Bloch lines, leav-ing the element in a four-domain Landau state with a singlevortex.


∆t = 1 ns 1.6 ns 2.8 ns 4.8 ns

1.1 kA m–1

(a)

(b)

0.1 kA m–1 –0.1 kA m–1 –0.7 kA m–1

Pulsefield

Magneticfield

Concertinadecay

Figure 24. Comparison of magnetization processes in a Permalloythin-film element (edge length 28 µm, thickness 50 nm) in diagonalmagnetic fields. The time-resolved images in (a) were obtained afterapplying a pulsed magnetic field (rise time several nanoseconds,duration 1000 ns, amplitude 2 kA m−1) opposite to a saturating biasfield. A gated image intensifier with a gating time of 250 ps wasapplied for time resolution. To achieve a reasonable signal-to-noiseratio, the Kerr images of some 108 independent events, excited bya train of field pulses that are repeated periodically, were integratedin time. The delay time of recording after onset of the fieldpulses is indicated. (b) Quasistatic process in slowly changing fieldthat is decreased from saturation and inverted. Similar states areshown at two orthogonal Kerr sensitivities as indicated by doublelines. The magnetization vector fields are drawn schematically.(Reprinted with permission from D. Chumakov et al., Phys Rev. BVol. 71, 014410 (2005). Copyright (2005) by the American PhysicalSociety.)

4.2.3 Light-based stroboscopic wide-field Kerrmicroscopy

The components of a stroboscopic wide-field microscopebased on pulsed illumination are shown in Figure 25. The

Wave, pulsegenerator

Delaygenerator Trigger

Pulsed light source

Trigger

Camera

Microscope

Sample

Figure 25. Block diagram for light-based stroboscopic wide-fieldmicroscopy. A pulsed light source is employed for time resolution.

wave or pulse generator is triggered by the light sourcewith some intermediate delay electronics. The images, shotat a defined time delay, are accumulated in a regularCCD camera. For comparative (quasi) static imaging, it isadvantageous to switch to a steady light source, which canbe easily realized in wide-field microscopes. Like in allother wide-field techniques, contrast can be enhanced bybackground subtraction.

Lasers are most widely employed as a pulsed light source.The laser light is fed into the microscope by a glass fiber afteremploying proper means to prevent speckle patterns (seeSection 3.1.4). A portion of the laser light shines on a pho-todiode giving the trigger pulses. Today, the traditional dyelasers (see Section 4.2.1) can be replaced by mode-lockedsolid-state lasers such as Nd-YVO4 that deliver light pulseswith a length in the 10-ps range at visible wavelengths afterfrequency doubling. The repetition rate of these lasers is fixedat some 10 MHz, and their output power has to be limited tothe 100-mW range (e.g., by a rotatable half-wave plate) tomatch the sensitivity range of the detection CCD camera andto avoid sample damage. Externally triggerable, pulsed laserdiodes can be operated in the same time regimes and are alsosuited for stroboscopic imaging (Wakana, Nagai and Sakata,2001; Nagai, Sekiguchi and Ito, 2003). Still shorter pulses of30–100 fs are achieved if the mentioned picosecond lasersare used to pump a mode-locked Ti:sapphire laser. The emit-ted femtosecond pulses have a wavelength around 800 nmat a repetition frequency of about 80 MHz. At present, mosttime-resolved experiments are carried out with the mentionedlaser light sources. The ongoing progress in laser technologyhas already brought along sub-femtosecond lasers (Hentschelet al., 2001), which so far have not been employed for imag-ing. A problem with laser light sources is the repetitionrate that is usually fixed at a certain frequency (e.g., some10 MHz in case of solid-state lasers), limiting the flexibil-ity of the experiment as compared to camera-based systems.Also possible for wide-field microscopy are pulsed xenon-arcflashlamps. They provide light pulses of the typical order of


1 µs at a low repetition rate in the 100 Hz regime, but they areintense enough to allow single-shot imaging, for example,in magnetic films with perpendicular anisotropy and thusstrong polar Kerr effect (Romanens et al., 2005). Flashlampsare an alternative to lasers if lower time resolution is suffi-cient. Signal-to-noise ratios like in quasistatic imaging canbe obtained, however, at strongly reduced exposure times.

An example for a laser-based wide-field strobing experi-ment on a NiFe square element is presented in Figure 26,again in comparison with the quasistatic process. Vortexmotion and wall displacement are characteristic for slowlychanging magnetic fields (Figure 26a). By applying a sharpfield pulse (b), fast rotational processes and spike domainnucleation are observed (c), which are slowly resolvedafter several nanoseconds. The development of small-angledomains with oscillatory behavior in the low-permeabilityclosure domain is also noteworthy.

4.2.4 Stroboscopic laser-scanning Kerr microscopy

The principle components of a stroboscopic experimentbased on laser-scanning microscopy are shown in Figure 27.The pulsed laser beam is split into a pump and probe beam.The probe beam is directly used for imaging, as describedin Section 3.2, whereas the pump beam triggers the fieldexcitation via an electric delay generator (or optical delayline) and pulse generator. Most of the modern scanningmicroscopes are based on today’s standard laser, the mode-locked and frequency-doubled titanium-sapphire femtosec-ond laser. ‘Pulse picking’ may eventually be required toadapt the high repetition rate of the laser to the rates ofthe delay electronics (unless an optical delay line is applied).To avoid sample damage or unwanted thermal effects onthe magnetization, the laser pulses may require attenuation(to an optical power of typically below 100 µW), therebyincreasing the number of shots to be accumulated. The sup-pression of nonmagnetic contrasts and signal enhancementcan be achieved by modulating the field excitation at kilo-hertz frequencies (as indicated in Figure 27 for a train offield pulses that is periodically interrupted) and using lock-in detection (Hicken et al., 2002; Buess et al., 2004). Thetime resolution achievable with laser-scanning microscopyis ultimately limited by the laser pulse width, but may prac-tically be limited by trigger jitter from the delay electronics(Freeman and Hiebert, 2002a). A resolution of the order ofsome 10 ps is typically achieved in present laser-scanningmicroscopes.

Two stroboscopic operation modes can be employed ina laser-scanning microscope: temporal and spatiotemporal-resolving modes. In the temporal mode, (See alsoInvestigation of Spin Waves and Spin Dynamics by Opti-cal Techniques, Volume 3, Time-resolved Kerr-effect and

H = 0

t = 0.0 ns t = 0.28 ns t = 0.93 ns t = 15.8 ns

H = 0.3 kA m–1

Fie

ld

0

1

Fie

ld in

kA

m–1

–3 0 3Time in ns

(a)

(c)

(b)

Figure 26. Excitation of a Landau ground state in a permalloy thin-film element (edge length 40 µm, thickness 50 nm) in magneticfields parallel to the edge. (a) Quasistatic process. The dynamicprocess (c), excited by a sharp field pulse (b), is completelydifferent. The difference images are shown as follows: In theupper row of (c), an image of the saturated state was subtracted,while images of the Landau ground state were subtracted in themiddle and lower row at different Kerr sensitivity directions asindicated, highlighting changes in the magnetization. The timedelays where the images have been captured in a stroboscopic wayare indicated. The accumulation of some 106 single pictures, eachof them obtained with a laser pulse of about 20 ps length, wasnecessary to obtain an image of sufficient contrast. (Reprinted withpermission from A. Neudert et al., Phys. Rev. B. Vol. 71, 134405.Copyright (2005) by the American Physical Society.)

Spin Dynamics in Itinerant Ferromagnets, Volume 3, andUltrafast Magnetodynamics with Lateral Resolution: AView by Photoemission Microscopy, Volume 3), the sam-ple response is measured locally by focusing on a particularplace of the sample and changing the time delay. The Kerrsignal of a train of light pulses is accumulated after each timestep, building up the time-dependent profile for selected mag-netization components (see Park et al., 2003, e.g., of such


Sampleon piezo

scanning stage

Wave, pulse,generator

Delaygenerator

Trigger

Beamsplitter

Beamsplitter

Objective

Polarizingbeamsplitter

Pump beam

Probe beam

Trigger

Polarizer

Pulsed laser

Lock-inamplifier

Photodiode

Quadrantphotodiodes

t

Figure 27. Block diagram of the main components of a typical stro-boscopic imaging setup based on laser-scanning Kerr microscopy.Instead of the electronic delay generator, an optical delay line (notshown) may be used for the synchronization of probe beam andmagnetic pulse, in which the travel path of the probe beam withrespect to the pump beam is computer controlled using mirrorsmounted on a slider. (After Choi and Freeman, 2004.)

local magnetometry). For spatiotemporal imaging, the time-dependent profile is locally measured and then the sampleis scanned at a particular fixed time delay to obtain a two-dimensional mapping of the magnetic response. Repeatingthe procedure at a different time delay leads to a stroboscopicimage series of the dynamic process. Like in stroboscopicwide-field microscopy, only repetitive phenomena can beimaged by this technique, while single-shot imaging is notpossible at all. A review of stroboscopic laser-scanning Kerrmicroscopy is given in Freeman and Hiebert (2002a).

An example of a spatiotemporal stroboscopic laser-scanning experiment is presented in Figure 28. A smallcobalt disk was excited by sharp magnetic field pulses per-pendicular to the film plane. The temporal evolution ofthe polar magnetization component at various time delays,revealing precessional magnetization oscillations that lastseveral 100 ps is shown in the figure.

To conclude, laser-scanning-based stroboscopes have threemain advantages: (i) The time evolution of magnetizationcan in a convenient and highly sensitive way be measuredlocally in an area of the laser beam size. (ii) The laserpulse can be used for pumping and probing by employ-ing photoconductive switches (see Section 4.2.5). (iii) Lon-gitudinal, transverse, and polar magnetization componentscan be recorded simultaneously, as described in Section 3.2.A drawback of the method is clearly related to the scan-ning procedure that is required to obtain full images,which makes it difficult to obtain static domain images forcomparison.

t = 20 ps t = 60 ps t = 100 ps t = 140 ps

t = 180 ps t = 220 ps t = 260 ps t = 300 ps

Figure 28. Stroboscopic laser-scanning Kerr microscopy of thepolar magnetization component in a cobalt disk with a diameterof 6 µm and a thickness of 20 nm at increasing time delays afterpulse-field excitation. Laser pulses with a width of 100 fs wereused for imaging, and the magnetic field pulse was created witha photoconductive switch. (Courtesy of Ch. Back, Regensburg. SeeAcremann et al., 2000, for details.)

4.2.5 Magnetic field generation

For time-resolved studies, the magnetic system has to beexcited by an external magnetic field with a well-definedtime structure (in recent years it could be shown thatexcitation is also possible by spin-polarized electric currents(Stiles and Miltat, 2006), by heating with femtosecond laserpulses (Koopmans, 2003) or by photomagnetic interaction(Hansteen et al., 2006)). In most experiments, this timestructure is either harmonic (e.g., sine wave excitation)or consists of a train of periodic field pulses of variableshape and duration (pulse-field excitation) provided by asignal generator. The excitation field can be created bymagnetic coils or electromagnets if large samples are tobe magnetized at power frequencies. For small samples,coil/yoke systems like in magnetic recording heads can beused well up into the megahertz regime. The field risetimes in these systems, however, are limited to a fewnanoseconds due to inductivity. Much faster rise times arepossible by overcoming the inductivity problem in coplanarwaveguides (Figure 29) that are fabricated from copper orgold thin films by lithography using etching or lift-offtechniques. Such approaches are of course restricted to theexcitation of patterned magnetic film samples, which canbe deposited onto the conductor line. The impedance of thewaveguide has to be carefully matched to the current sourceto avoid unwanted reflections or damping of the currentpulse. Magnetic fields up to the order of 10 kA m−1 arepossible with such transmission lines. Coplanar waveguidesmay also be fabricated in cross-wire geometry, which allows,for example, to study precessional switching by excitingalong and perpendicular to the easy axis of the deposited filmelements (Hiebert et al., 2003a), or to control post-switchingmagnetization oscillations by varying the delay between twoorthogonal pulses (Krichevsky and Freeman, 2004).


Ground plane

(a) (b)

Conductive strip

H

H

Figure 29. Coplanar waveguides, consisting of a conductor trans-mission line that is separated from a pair of ground lines (all onthe same plane), for the generation of fast magnetic field pulses insmall elements. The microcoil in (a) provides perpendicular fields,while the waveguide in (b) generates in-plane fields, as indicated.The sample elements are deposited on top of the conductor line.For wide-field Kerr microscopy, it is advisable to coat the stripby antireflection layers to prevent disturbing light effects on thesample (Chumakov et al., 2005). (Reprinted figure with permissionfrom D. Chumakov et al., Phys Rev. B Vol. 71, 014410 (2005).Copyright 2005 by the American Physical Society.)

Magnetization dynamics is critically determined by the risetime of the excitation pulses (Choi, Ho, Arnup and Freeman,2005a). Commercial electronic pulse generators may providecurrent pulses of down to 50-ps rise time with variable pulsewidth down to about 500 ps and repetition rates of severalhundred megahertz. Faster rise times of a few picosecondsare possible by so-called Auston switches (Auston, 1975),which have been adapted from semiconductor physics tothe fast excitation of magnetic films (Freeman, 1994). Inthe Auston switch, an above–band gap optical pulse froma picosecond laser strikes a biased coplanar transmissionline structure, fabricated on a semi-insulating semiconductorsubstrate, to create a transient photoconductivity and launcha current pulse down the transmission line. The decay ofthe photoexcitation is determined by the recombination rateof the electron–hole pairs and is usually much slower inthe nanosecond range, preventing the creation of ultrashortpulses. Laser-scanning microscopes are ideally suited forthe application of photoconductive switches in stroboscopicexperiments, as the probing laser can simultaneously be usedfor current launching after employing beam splitting anddelay (Choi and Freeman, 2004). The biggest advantageof photoconductive switches is the fact that the samplecan be pumped without the introduction of electronic jitter(Hicken et al., 2002). Examples for the application of theseswitches to the study of precessional excitation spectra orlocalized spin-wave modes in film elements may be foundin Acremann et al. (2000); Park et al. (2002); Park et al.(2003); Gerrits et al. (2002); Barman et al. (2004); Buesset al. (2004).

5 OUTLOOK

The classical Kerr technique for magnetic domain observa-tion has strongly gained in efficiency after the introductionof digital image processing in the mid-1980s. By contrastenhancement, domains get visible on virtually all relevantferro- and ferrimagnetic materials and magnetization direc-tions can be determined quantitatively and even selectivelybased on depth. The dynamic capability and the compatibilitywith arbitrary applied magnetic fields make Kerr microscopyideally suited for the investigation of magnetization pro-cesses on arbitrary timescales. On bulk materials, just thesurface region can be seen (like in most other domain obser-vation techniques); therefore theoretical arguments combinedwith domain studies in magnetic fields are required to get athree-dimensional understanding of the magnetic microstruc-ture. The optical resolution limit of about 200 nm limits theapplication of Kerr microscopy when small objects are tobe studied as they are increasingly getting addressed withrising miniaturization of devices. Yet, Kerr microscopy willremain the method of choice for the visualization of movingdomains in the laboratory.

ACKNOWLEDGMENTS

The careful reading of the manuscript and supply of imagesby Jeffrey McCord, Sybille Flohrer, and Andreas Neudert (allIFW Dresden) is highly appreciated. Thanks also to DmitryChumakov (IFW Dresden) and Christian Back (Regensburg)for providing images.

REFERENCES

Acremann, Y., Back, C.H., Buess, M., et al. (2000). Imaging pre-cessional motion of the magnetization vector. Science, 290,492–495.

Argyle, B.E. and McCord, J. (2000). New laser illumination methodfor Kerr microscopy. Journal of Applied Physics, 87, 6487–6489.

Argyle, B.E., Petek, B. and Herman, D. Jr. (1987). Optical imagingof magnetic domains in motion. Journal of Applied Physics, 61,4303–4306.

Auston, D.H. (1975). Picosecond optoelectronic switching andgating in silicon. Applied Physics Letters, 26, 101–103.

Back, C.H., Heidmann, J. and McCord, J. (1999). Time resolvedKerr microscopy: magnetization dynamics in thin film writeheads. IEEE Transactions on Magnetics, 35, 637–642.

Ballentine, G.E., Hiebert, W.K., Stankiewicz, A. and Freeman, M.R.(2000). Ultrafast microscopy and numerical simulation study ofmagnetization reversal dynamics in permalloy. Journal of AppliedPhysics, 87, 6830–6832.


Barman, A., Kruglyak, V.V., Hicken, R.J., et al. (2004). Imagingthe dephasing of spin wave modes in a square thin film magneticelement. Physical Review B, 69, 174426.

Buess, M., Hollinger, R., Haug, T., et al. (2004). Fourier transformimaging of spin vortex eigenmodes. Physical Review Letters, 93,077207.

Buscher, P. and Reimer, L. (1993). Imaging and colour codingof magnetic domains by Kerr scanning optical microscopy.Scanning, 15, 123–129.

Choe, S.-B., Acremann, Y., Scholl, A., et al. (2004). Vortex-coredriven magnetization dynamics. Science, 304, 420–422.

Choi, B.C., Belov, M., Hiebert, W.K., et al. (2001). Ultrafast mag-netization reversal dynamics investigated by time domain imag-ing. Physical Review Letters, 86, 728–731.

Choi, B.C. and Freeman, M.R. (2004). Nonequilibrium spin dynam-ics in laterally defined magnetic structures. In Ultrathin MagneticStructure IV, Heinrich, B. and Bland J.A.C. (Eds.), Springer:Berlin, pp. 211–232.

Choi, B.C., Ho, J., Arnup, G. and Freeman, M.R. (2005a). Nonequi-librium domain pattern formation in mesoscopic magnetic thinfilm elements assisted by thermally excited spin fluctuations.Physical Review Letters, 95, 237211.

Choi, B.C., Krichevsky, A. and Freeman, M.R. (2005b). Magneti-zation dynamics using time-resolved magneto-optic microscopy.In Modern Techniques for Characterizing Magnetic Materials,Zhu, Y. (Ed.), Kluwer Academic Publishers: Boston,pp. 517–542.

Chumakov, D., McCord, J., Schafer, R., et al. (2005). Nanosecondtime-scale switching of permalloy thin film elements studied bywide-field time-resolved Kerr microscopy. Physical Review B, 71,014410.

Clegg, W.W., Heyes, N.A.E., Hill, E.W. and Wright, C.D. (1991).Development of a scanning laser microscope for magneto-optic studies of thin magnetic films. Journal of Magnetism andMagnetic Materials, 95, 49–57.

Conger, R.L. and Moore, G.H. (1963). Direct observation of high-speed magnetization reversal in films. Journal of Applied Physics,34, 1213–1214.

Dillon, J.F. Jr. (1958). Observation of domains in the ferrimagneticgarnets by transmitted light. Journal of Applied Physics, 29,1286–1291.

Drechsel, W. (1961). Eine Anordnung zur photographischen Reg-istrierung von Weißschen Bereichen bei Belichtungszeiten derGroßenordnung 1 msec. Zeitschrift fur Physik, 164, 324–329.

Egelkamp, S. and Reimer, L. (1990). Imaging of magnetic domainsby the Kerr effect using a scanning optical microscope. Measure-ment Science and Technology, 1, 79–83.

Eisebitt, S., Luning, J., Schlotter, W.F., et al. (2004). Lenslessimaging of magnetic nanostructures by X-ray spectro-holography.Nature, 432, 885–888.

Faraday, M. (1846). On the magnetization of light and the illumi-nation of magnetic lines of force. Philosophical Transactions ofthe Royal Society of London, 136, 1–20.

Flohrer, S., Schafer, R., McCord, J., et al. (2006). Magnetizationloss and domain refinement in nanocrystalline tape wound cores.Acta Materialia, 54, 3253–3259.

Fowler, C.A. Jr. and Fryer, E.M. (1952). Magnetic domains onsilicon iron by the longitudinal Kerr effect. Physical Review,86, 426.

Fowler, C.A. Jr. and Fryer, E.M. (1956). Magnetic domains in thinfilms by the Faraday effect. Physical Review, 104, 552–553.

Freeman, M.R. (1994). Picosecond pulsed-field probes of magneticsystems. Journal of Applied Physics, 75, 6194–6198.

Freeman, M.R. and Hiebert, W.K. (2002a). Stroboscopic micro-scopy of magnetic dynamics. In Spin Dynamics in ConfinedMagnetic Structures I, Hillebrands, B. and Ounadjela K. (Eds.),Springer: Berlin, pp. 93–126.

Freeman, M.R. and Smyth, J.F. (1996). Picosecond time-resolvedmagnetization dynamics of thin-film heads. Journal of AppliedPhysics, 79, 5898–5900.

Freeman, M.R., Steeves, G.M., Ballentine, G.E. and Krichevsky, A.(2002b). Noise imaging using magneto-optical sampling tech-niques. Journal of Applied Physics, 91, 7326–7330.

Gal, L., Zimmer, G.J. and Humphrey, F. (1975). Transient magneticbubble domain configurations during radial wall motion. PhysicaStatus Solidi A, 30, 561–569.

Gerrits, T., van den Berg, H.A.M., Hohlfeld, J., et al. (2002). Ultra-fast precessional magnetization reversal by picosecond magneticfield pulse shaping. Nature, 418, 509–512.

Haller, T.R. and Kramer, J.J. (1970). Observation of dynamicdomain size variation in a silicon-iron alloy. Journal of AppliedPhysics, 41, 1034–1035.

Hansteen, F., Kimel, A., Kirilyuk, A. and Rasing, T. (2006).Nonthermal ultrafast optical control of the magnetization ingarnet films. Physical Review B, 73, 014421.

Hentschel, M., Kienberger, R., Spielmann, Ch., et al. (2001).Attosecond metrology. Nature, 414, 509–513.

Hicken, R.J., Hughes, N.D., Moore, J.R., et al. (2002). Magneto-optical studies of magnetism on pico and femtosecond timescales (invited). Journal of Magnetism and Magnetic Materials,242–245, 559–564.

Hiebert, W.K., Ballentine, G.E. and Freeman, M.R. (2002). Com-parison of experimental and numerical micromagnetic dynamicsin coherent precessional switching and modal oscillations. Phys-ical Review B, 65, 140404.

Hiebert, W.K., Lagae, L., Das, J., et al. (2003). Fully controlledprecessional switching of a macrospin in a cross-wire geometry.Journal of Applied Physics, 93, 6906–6908.

Hiebert, W.K., Lagae, L. and Boeck, J.D. (2003). Spatially inhomo-geneous ultrafast precessional magnetization reversal. PhysicalReview B, 68, 020402.

Houze, G.L. (1967). Domain-wall motion in grain-oriented siliconsteel in cyclic magnetic fields. Journal of Applied Physics, 38,1089–1096.

Hubert, A. and Schafer, R. (1998). Magnetic Domains. The Analysisof Magnetic Microstructures, Springer-Verlag: Berlin.

Humphrey, F.B. (1975). Transient bubble domain configuration ingarnet materials observed using high speed photography. IEEETransactions on Magnetics, 11, 1679–1684.

Inoue, S. and Spring, K.R. (1997). Video Microscopy: The Funda-mentals, Plenum Press: New York and London.


Kasiraj, P., Shelby, R.M., Best, J.S. and Horne, D.E. (1986). Mag-netic domain imaging with a laser scanning Kerr effect micro-scope. IEEE Transactions on Magnetics, 22, 867–839.

Kerr, J. (1877). On rotation of the plane of polarization by reflectionfrom the pole of a magnet. Philosophical Magazine, 3(5),321–343.

Klaui, M., Jubert, P.-O., Allenspach, R., et al. (2005). Direct obser-vation of domain-wall configurations transformed by spin cur-rents. Physical Review Letters, 95, 026601.

Koopmans, B. (2003). Laser-induced magnetization dynamics.In Spin Dynamics in Confined Magnetic Structures II, Hille-brands, B. and Ounadjela, K. (Eds.), Springer: Berlin, pp.253–316.

Krichevsky, A. and Freeman, M.R. (2004). Precessional switchingof a 3 × 1 micrometer elliptical element in a crossed-wiregeometry. Journal of Applied Physics, 95, 6601–6603.

Kryder, M.H. and Deutsch, A. (1976). A high-speed magneto-opticcamera system. SPIE High Speed Optical Techniques, 94, 49–57.

Kryder, M.H. and Humphrey, F.B. (1969a). A nanosecond Kerrmagneto-optic camera. The Review of Scientific Instruments, 40,829–840.

Kryder, M.H. and Humphrey, F.B. (1969b). Dynamic Kerr obser-vations of high-speed flux reversal and relaxation processes inpermalloy thin films. Journal of Applied Physics, 40, 2469–2474.

Kryder, M.H., Koeppe, P.V. and Liu, F.H. (1990). Kerr effectimaging of dynamic processes in magnetic recording heads. IEEETransactions on Magnetics, 26, 2995–3000.

Kuksov, A., Schneider, C.M., Oelsner, A., et al. (2004). Investigat-ing magnetization dynamics in permalloy microstructures usingtime-resolved x-ray photoemission electron microscope. Journalof Applied Physics, 95, 6530–6532.

Liu, F.H., Schultz, M.D. and Kryder, M.H. (1990). High frequencydynamic imaging of domains in thin film heads. IEEE Transac-tions on Magnetics, 26, 1340–1342.

Malozemoff, A.P. (1973). Nanosecond camera for garnet bub-ble domain dynamics. IBM Technical Disclosure Bulletine, 15,2759–2757.

McCord, J. and Hubert, A. (1999). Normalized differential Kerrmicroscopy – an advanced method for magnetic imaging. Phys-ica Status Solidi A, 171, 555–562.

McCord, J., Schafer, R., Mattheis, R. and Barholz, K.-U. (2003).Kerr observations of asymmetric magnetization reversal pro-cesses in CoFe/IrMn bilayers. Journal of Applied Physics, 93,5491–5497.

Moses, A.J., Williams, P.I. and Hoshtanar, A. (2005). A novelinstrument for real time dynamic domain observation in bulkand micromagnetic materials. IEEE Transactions on Magnetics,41, 3736–3738.

Nagai, T., Sekiguchi, H. and Ito, A. (2003). Magnetization vectormeasurement with wide-band high spatial resolution Kerr micro-scope. IEEE Transactions on Magnetics, 39, 3441–3443.

Neudert, A., McCord, J., Chumakov, D., et al. (2005). Small-amplitude magnetization dynamics in permalloy elements inves-tigated by time-resolved wide-field Kerr microscopy. PhysicalReview B, 71, 134405.

Neudert, A., McCord, J., Schafer, R., et al. (2006). Bloch linegeneration in cross-tie walls by fast magnetic field pulses. Journalof Applied Physics, 99, 08F302.

Nikitenko, V.I., Gornakov, V.S., Dedukh, L.M., et al. (1998).Asymmetry of domain nucleation and enhanced coercivity inexchange-biased epitaxial NiO/NiFe bilayers. Physical Review B,57, R8111–R8114.

Nutter, P.W. and Wright, C.D. (1998). Resolution issues in confocalmagnetooptic scanning laser microscopy. Japanese Journal ofApplied Physics, 37, 2245–2254.

Oppeneer, P.M. (2001). Magneto-optical Kerr spectra. In Handbookof Magnetic Materials, Buschow, K.H.J. (Ed.), North-Holland:Amsterdam, pp. 229–422, Vol. 13.

Park, J.P. and Crowel, P.A. (2005). Interactions of spin waves witha magnetic vortex. Physical Review Letters, 95, 167201.

Park, J.P., Eames, P., Engebretson, D.M., et al. (2002). Spatiallyresolved dynamics of localized spin-wave modes in ferromagneticwires. Physical Review Letters, 89, 277201.

Park, J.P., Eames, P., Engebretson, D.M., et al. (2003). Imaging ofspin dynamics in closure domain and vortex structures. PhysicalReview B, 67, 020403.

Passon, B. (1963). Eine Anwendung des Magnetooptischen Kerr-effektes zur Untersuchung schnellablaufender Magnetisierungs-prozesse. Zeitschrift fur Angewandte Physik, 16, 81–90.

Passon, B. (1968). Uber die Beobachtung ferromagnetischer Bere-iche bei Magnetisierung in Wechselfeldern bis zu 20 kHz.Zeitschrift fur Angewandte Physik, 25, 56–61.

Petek, B., Trouilloud, P.L. and Argyle, B.E. (1990). Time-resolveddomain dynamics in thin-film heads. IEEE Transactions onMagnetics, 26, 1328–1330.

Ping, G.L., See, C.W. and Somekh, M.G. (1996). A confocal fibrescanning microscope for magnetic domain imaging. Journal ofMicroscopy, 184, 149–156.

Ping, G.L., See, C.W., Somekh, M.G., et al. (1995). A fast-scanningoptical microscope for imaging magnetic domain structures.Scanning, 18, 8–12.

Rave, W., Schafer, R. and Hubert, A. (1987). Quantitative observa-tion of magnetic domains with the magneto-optical Kerr effect.Journal of Magnetism and Magnetic Materials, 65, 7–14.

Re, M., Shenton, D.N. and Kryder, M.H. (1985). Magnetic switch-ing characteristics at the pole tips of thin film recording heads.IEEE Transactions on Magnetics, 21, 1575–1577.

Romanens, F., Pizzini, S., Yokaichiya, F., et al. (2005). Magneticrelaxation of exchange biased Pt/Co multilayers studied by time-resolved Kerr microscopy. Physical Review B, 72, 134410.

Schafer, R. (1995). Magneto-optical domain studies in coupledmagnetic multilayers. Journal of Magnetism and Magnetic Mate-rials, 148, 226–231.

Schafer, R. and Herzer, G. (2001). Continuous magnetization pat-terns in amorphous ribbons. IEEE Transactions on Magnetics,37(4), 2245–2247.

Schafer, R. and Hubert, A. (1990). A new magnetooptic effectrelated to non-uniform magnetization on the surface of a fer-romagnet. Physica Status Solidi A, 118, 271–288.


Schafer, R., Hubert, A. and Parkin, S.S.P. (1993). Domain anddomain wall observations in sputtered exchange-biased wedges.IEEE Transactions on Magnetics, 29, 2738–2740.

Schmidt, F. and Hubert, A. (1986). Domain observations on CoCrlayers with a digitally enhanced Kerr microscope. Journal ofMagnetism and Magnetic Materials, 61, 304–320.

Schmidt, F., Rave, W. and Hubert, A. (1985). Enhancement ofmagneto-optical domain observation by digital image processing.IEEE Transactions on Magnetics, 21, 1596–1598.

Sheppard, C. and Wilson, T. (1984). Theory and Practise of Scan-ning Optical Microscopy, Academic Press: London.

Shilling, J.W. and Houze, G.L. (1974). Magnetic properties anddomain structure in grain-oriented 3% Si-Fe. IEEE Transactionson Magnetics, 10, 195–222.

Silva, T.J. and Kos, A.B. (1997). Nonreciprocal differential detec-tion method for scanning Kerr-effect microscopy. Journal ofApplied Physics, 81, 5015–5017.

Stankiewicz, A., Hiebert, W.K., Ballentine, G.E., et al. (1998).Dynamics of magnetization reversal in a 20 × 4 µm permalloymicrostructure. IEEE Transactions on Magnetics, 34, 1003–1005.

Stiles, M.D. and Miltat, J. (2006). Spin transfer torque and dynam-ics. In Spin Dynamics in Confined Magnetic Structures III, Hille-brands, B. and Thiaville A. (Eds.), Springer: Berlin.

Stoll, H., Puzic, A., van Waeyenberge, B., et al. (2004). High-resolution imaging of fast magnetization dynamics in magneticnanostructures. Applied Physics Letters, 84, 3328–3330.

Trager, G., Wenzel, L. and Hubert, A. (1992). Computer experi-ments on the information depth and the figure of merit in mag-netooptics. Physica Status Solidi (A), 131, 201–227.

Veerdonk, R.J.M., Ju, G., Svedberg, E.B., et al. (2001). Real-timeobservation of sub-nanosecond magnetic switching in perpendic-ular multilayers. Journal of Magnetism and Magnetic Materials,235, 138–142.

Vella-Coleiro, G.P. and Nelson, T.J. (1974). Stroboscopic observa-tion of magnetic bubble circuits using a gated image-intensifiertube. Applied Physics Letters, 24, 397–398.

Voigt, W. (1898). Doppelbrechung von im Magnetfeld befind-lichem Natriumdampf in der Richtung normal zu den Kraftlin-ien. Nachrichten der Koniglichen Gesellschaft der WissenschaftenGottingen, Math.-Phys. Kl., 4, 335–359.

Wakana, S.-I., Nagai, T. and Sakata, Y. (2001). Wide bandwidthscanning Kerr microscope based on optical sampling techniqueusing externally triggerable pulse laser diode. Journal of Mag-netism and Magnetic Materials, 235, 213–217.

Williams, H.J., Foster, F.G. and Wood, E.A. (1951). Observationof magnetic domains by the Kerr effect. Physical Review, 82,119–120.

Wright, C.D., Clegg, W.W., Boudjemline, A. and Heyes, N.A.E.(1994). Scanning laser microscopy of magneto-optic storagemedia. Japanese Journal of Applied Physics, 33, 2058–2065.

Wright, C.D., Heyes, N.A.E., Clegg, W.W. and Hill, E.W. (1995).Magneto-optic scanning laser microscopy. Microscopy and Anal-ysis, 46, 21–23.

Documents

Magneto Optical Kerr Effect