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Evolution of structural and magnetic properties of sputtered nanocrystalline Co thin films with thermal annealing

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Page 1: Evolution of structural and magnetic properties of sputtered nanocrystalline Co thin films with thermal annealing

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0304-8853/$

doi:10.1016

�CorrespE-mail a

Journal of Magnetism and Magnetic Materials 308 (2007) 318–324

www.elsevier.com/locate/jmmm

Evolution of structural and magnetic properties of sputterednanocrystalline Co thin films with thermal annealing

Dileep Kumar, Ajay Gupta�

UGC-DAE Consortium for Scientific Research, University Campus, Khandwa Road, Indore-452017, India

Received 28 February 2006; received in revised form 22 May 2006

Available online 10 July 2006

Abstract

Ultrafine grain films of cobalt prepared using ion-beam sputtering have been studied using X-ray diffraction (XRD), X-ray reflectivity

(XRR), atomic force microscopy (AFM) and magneto-optical Kerr effect (MOKE) measurements. As-prepared films have very smooth

surface owing to the ultrafine nature of the grains. Evolution of the structure and morphology of the film with thermal annealing has

been studied and the same is correlated with the magnetic properties. Above an annealing temperature of 300 1C, the film gradually

transforms from HCP to FCC phase that remains stable at room temperature. A significant contribution of the surface energy, due to

small grain size, results in stabilisation of the FCC phase at room temperature. It is found that other processes like stress relaxation, grain

texturing and growth also exhibit an enhanced rate above 300 1C, and may be associated with an enhanced mobility of the atoms above

this temperature. Films possess a uniaxial anisotropy, which exhibits a non-monotonous behaviour with thermal annealing. The

observed variation in the anisotropy and coercivity with annealing can be understood in terms of variations in the internal stresses,

surface roughness, and grain structure.

r 2006 Elsevier B.V. All rights reserved.

Keywords: Magnetic thin film; MOKE; Uniaxial magnetic anisotropy; IBS; Thermal annealing

1. Introduction

Cobalt thin films have been studied extensively in recentyears because of their potential use as magnetic material invarious devices. Most of the studies in literature have beendone on epitaxial films deposited on substrates like Al2O3,GaAs, Si, Pd, Cu, W [1–7]. In case of a film deposited onAl2O3 (1 1 2 0) substrate, the as-prepared film is a mixtureof HCP and FCC phase. Thermal annealing results ingrowth of the FCC phase. Increasing annealing tempera-ture above a critical value results in a reorientationtransition from FCC (1 1 1) to FCC (0 0 1), accompaniedby a smoothing of the surface. Recently, Kharmouche et al.have studied structural and magnetic properties of Co filmsevaporated on Si (1 0 0) as a function of the Co thickness[3]. The films were polycrystalline with (0 0 1) texture. Itwas found that surface and stress-induced uniaxial

- see front matter r 2006 Elsevier B.V. All rights reserved.

/j.jmmm.2006.06.008

onding author. Tel.: +91731 2472200; fax: +91 731 2465437.

ddress: [email protected] (A. Gupta).

magnetic anisotropy decreases as the film thicknessincreases.Nanocrystalline particles of cobalt prepared by different

techniques have also been studied extensively in order toelucidate the relation of magnetic properties with theatomic structure, size and shape of the nanoparticles[8–10]. Depending on the preparation methods andtemperature, the particles form either in FCC or in HCPphases. The FCC particles maintain their structure toambient temperature without structural transformationfrom FCC to HCP, although in bulk it is known that FCCis stable only at temperatures above 425 1C [11]. Nodetailed study exists in the literature on the evolution ofstructural and magnetic properties of nanocrystalline Cothin films.In the present work, evolution of structural and

magnetic properties of ultrafine-grain polycrystalline co-balt films with increasing annealing temperatures has beenstudied with an aim to correlate the structural andmorphological properties with magnetic properties.

Page 2: Evolution of structural and magnetic properties of sputtered nanocrystalline Co thin films with thermal annealing

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ity

(a.u

.)

400°C

450°C

500°C

HCP

550°C

(101)(002)

(111)

(100)

(200)FCC

D. Kumar, A. Gupta / Journal of Magnetism and Magnetic Materials 308 (2007) 318–324 319

2. Experimental

Co film with nominal thickness of 45 nm was depositedby sputtering a Co target with 1 keV Ar ions incident at theangle of 451. The film was deposited on a float glasssubstrate kept parallel to the target at a distance of �16 cm.The substrate was kept at room temperature. The basepressure in the chamber was 2� 10�7 Torr. Ex-situ X-rayreflectivity (XRR) measurements on the films were done inorder to determine the deposition rate, which was found tobe 4.5 nm/min. The exact thickness of the deposited filmwas again confirmed using XRR. Isochronal thermalannealing of the films has been done in vacuum �10�7 Torrin order to avoid the surface oxidation. A turbo-molecularpump backed by a scroll pump has been used in order toachieve clean vacuum. Sample kept in an evacuated quartztube was inserted in a pre-heated furnace. This ensures thatthe heating and the cooling time of the sample was about5min. Structure of the films as a function of thermalannealing was determined from X-ray diffraction (XRD)measurements. The magnetic properties of the samples atroom temperature were characterised by ex-situ magneto-optical Kerr effect (MOKE) measurements. Measurementsin the longitudinal geometry were performed with themagnetic field, H, applied along different directions in theplane of the film. Angle-dependent magnetic remanence orcoercivity obtained from the MOKE hysteresis curve givesinformation about magnetic anisotropy in the film. Thesurface morphology of the film in different states (as-prepared, annealed at 200 and 500 1C) was imaged byatomic force microscopy (AFM) using nanoscope III,version ‘E’ from digital electronics.

3. Results and discussion

Fig. 1 gives the XRR pattern of as-prepared Co/floatglass film. The reflectivity pattern was fitted using Parratt’s

0.5 1.0 1.5 2.0 2.5 3.0 3.5

10-6

10-5

10-4

10-3

10-2

10-1

100

Ref

lect

ivity

(a.

u.)

q (nm-1)

Experimental

Fitted

Fig. 1. Reflectivity pattern of the as-prepared Co film on the float-glass

substrate. Continuous curve represents the fitting of data using Parratt’s

formalism.

formulism [12]. In order to get good theoretical fit of thedata, it was found necessary to incorporate a thin surfacelayer with somewhat lower electron density. This surfacelayer was 1.8 nm thick with electron density �15% lessthen that of the film and may be attributed to surfaceoxidation. The mass density of the film as calculated fromthe electron density obtained from the fitting of the XRRdata comes out to be �8.7 g/cm3, which is only �2.0% lessthan that of the bulk Co. The total thickness of the film wasfound to be 41.9 nm. The surface roughness of the film wasfound to be 0.6 nm, which is comparable to that of the baresubstrate (�0.7 nm).Fig. 2 gives the XRD pattern of the as-prepared film as

well as after isochronal annealing for a period of 1 h atdifferent temperatures ranging from 200 to 500 1C.Annealing at 550 1C has been done for 5 h. The XRDpattern of the as-prepared film exhibits a broad hump atposition 2y�44.71. This broad hump may be interpretedeither in terms of an amorphous structure of the film, orarising due to overlapping of a number of crystalline peaks.

35 42 49 56

2θ (deg.)

as-deposited

Inte

ns

300°C

350C

200°C

Fig. 2. X-ray diffraction pattern of the as-prepared film as well as after

isochronal annealing for 1 h at different temperatures ranging from 200 to

500 1C. Annealing at 550 1C has been done for 5 h.

Page 3: Evolution of structural and magnetic properties of sputtered nanocrystalline Co thin films with thermal annealing

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(a)

σrms=2.1 nm

σrms=1.2 nm

(b)

σrms=4.1 nm

x 0.500 µµm/div z 25.000 µm/div

0.5

1.0

1.5

2.0

µm

µm

x 0.500 µm/div

z 25.000 µm/div

0.5

1.0

1.5

2.0

µm

0.5

D. Kumar, A. Gupta / Journal of Magnetism and Magnetic Materials 308 (2007) 318–324320

Since 41.9 nm thick film of pure Co is not expected to beamorphous, the broad peak is most likely due to an overlapof a number of crystalline peaks. The width of the broadpeak is about 6.51, which encompasses the (1 0 0), (0 0 2)and (1 0 1) peaks of HCP phase; accordingly, this broadpeak was fitted using an overlap of the above three peaks ofHCP phase. The particle size is calculated using the widthof the strongest diffraction peak corresponding to HCP(0 0 2) reflection at 2y�44.71 using Scherer formula, andcomes out to be �2.0 nm. This value of particle size can bean underestimation, as structural disorder as well asrandom internal stresses would also contribute to the linewidth. With increasing annealing temperature the HCP(0 0 2) peak grows in intensity, which suggests that filmdevelops a texture along HCP (0 0 2) direction. The widthof the peak also decreases indicating grain growth.Annealing temperature dependence of the grain size ascalculated from the width of the HCP (0 0 2) peak is shownin Fig. 3. After annealing at 350 1C an additional peak at2y�51.01 appears which is close to the (2 0 0) reflection ofFCC cobalt phase. With increasing annealing temperature,this peak becomes more clear and shifts to 2y�51.61, whichexactly matches with the position of the FCC (0 0 2) peak.This shows that above 350 1C the HCP phase graduallytransforms into FCC phase. Initially, it is not possible toseparate the FCC (1 1 1) reflection from HCP (0 0 2)reflection due to the broad nature of the peaks; however,at temperatures of 400 1C and above, it is possible to fitreliably the peak around 46.71 as a combination of HCP(0 0 2) and FCC (1 1 1) reflections. The width of the FCC(1 1 1) peak is used to obtain the grain size of this phase andis also presented in Fig. 3. One may note that the averagegrain size of the two phases is comparable.

Several studies in the literature have examined thermalstability of the FCC phase in thin films [1,13–17]. In somestudies, the stabilisation of this metastable phase at roomtemperature has been attributed to rapid cooling from hightemperatures [14,15]. In some other theoretical studies, it is

0 100 200 300 400 500 600

0

5

10

15

20

25

Annealing Temperature (°C)

Par

tical

Siz

e (n

m)

hcp002

fcc111

Fig. 3. Particle size corresponding to HCP and FCC phases as a function

of annealing temperature.

(c)x 0.500 µm/div z 25.000 µm/div

1.0

1.5

2.0

Fig. 4. AFM pictures of the (a) as-prepared Co film, as well as after

annealing the film at (b) 200 1C and (c) 500 1C.

suggested that contribution from surface energy canstabilise the FCC phase below a critical size of about20 nm diameter [16]. In the present case, the FCC phase isstabilised at room temperature, although no rapid coolingis involved. However, the maximum grain size of the FCCphase is around 20 nm, and thus, in agreement with Ref.[16], the surface energy may be the cause of stabilisation ofFCC phase in the present case.The surface morphology of the film in different states

(as-prepared, annealed at 200 and 500 1C) was imaged byAFM. Fig. 4 gives the AFM pictures of the film in as-prepared state as well as after annealing at 200 and 500 1C.

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ARTICLE IN PRESSD. Kumar, A. Gupta / Journal of Magnetism and Magnetic Materials 308 (2007) 318–324 321

AFM image of the film surface in as-prepared state showsisland like features with wide distribution of the sizes andseparation. In the as-prepared film, the size of their featuresis about 100.0 nm, which increases about 500.0 nm afterannealing at 500 1C. However, the contrast betweennanograins is not visible in the AFM pictures. Asillustrated in Fig. 4b and c, the average size and separationof these features increased with annealing at 200 and500 1C, respectively. The rms roughness has been calculatedby taking the average over at least five regions of area of2� 2 mm and is also shown in Fig. 4. One may note thatannealing results in an increase in rms roughness of the filmsurface, and may be associated with the grain growth andstructural transformation from HCP to FCC phase.

Fig. 5(a) gives the MOKE pattern of the as-preparedsample as a function of azimuthal angle. There is a strongvariation in the shape of the hysteresis curve with angle.For applied magnetic field in the direction of easy axis ofmagnetisation, the hysteresis curve is a perfect squaresuggesting that the magnetisation takes place purelythrough domain wall motion. With increasing azimuthalangle, the rounding off of the hysteresis curve indicatesincreasing contribution of the rotation of domain magne-

(a)

(b)

Fig. 5. (a) Some representative longitudinal MOKE hysteresis loops of the

as-prepared film at different azimuthal angles; (b) the azimuthal angle

dependence of coercivity fitted with Ha and Hcw as fitting parameters.

tisation. The observed angular dependence of the coercivityof this sample is shown in Fig. 5(b), which shows thatsample posses a uniaxial magnetic anisotropy. Since thegrains are expected to be oriented randomly, the origin ofthe observed anisotropy cannot be the magneto-crystallineanisotropy of HCP phase. Such induced anisotropy in thinfilms have also been observed in crystalline [18] as well asamorphous [19] phases, and may be attributed to the long-range stresses developed in the film during deposition. Thedirection of the easy axis had a definite relationship withthe direction of the ion-beam used for sputtering. Similarbehaviour of the magnetic anisotropy was also observed inamorphous magnetic thin films [19], and therefore isexpected to be related to anisotropic ejection of thesputtered atoms relative to the direction of the ion beam[20]. However, the exact origin of this anisotropy is notclear and is the subject of further investigation. In case ofuniaxial anisotropy, it has been shown that the azimuthalangle dependence of the coercivity can be written as [18]

Hc ¼ Ha cos2 y0 þ ðH2

cw �H2a cos

2 y0 sin2 y0Þ

1=2, (1)

where Ha is the magnetic anisotropic field, Hcw is domain-wall pinning coercivity and y0 is the angle between theapplied field and easy axis of the magnetisation. Theazimuthal angle dependence of coercivity in Fig. 5(b) hasbeen fitted with the above equation taking Ha and Hcw asfitting parameters. One may note that fit to the data is goodand yields the magnetic anisotropy field as well as pinningcoercivity.Angular dependence of coercivity as obtained from

MOKE measurement after annealing at different tempera-tures is shown in Fig. 6. For each annealing temperature,the data was fitted with Eq. (1) to yield the values ofanisotropy field and pinning coercivity. Fig. 7 shows theannealing temperature dependence of these two quantities.One may note that with increasing annealing temperature,the magnitude of anisotropy initially increases and reachesa maximum value around the annealing temperature of300 1C. Beyond this temperature, the anisotropy startsdecreasing and around the temperature of 550 1C itcompletely disappears. Fig. 7 also displays the annealingtemperature dependence of the pinning coercive field Hcw.Coercivity exhibits a slow non-monotonous variation up toa temperature of 500 1C. The observed behaviour may beattributed to a combined effect of increase in surfaceroughness and decrease in internal stresses. With increasingannealing temperature, the surface roughness increases,which is expected to result in an increase in the coercivity[18,21,22]. A decrease in coercivity on going from 400 to450 1C may be attributed to a rapid relaxation of internalstresses as evidenced from a rapid decrease in the magneticanisotropy. A sudden increase in the coercivity uponannealing at 550 1C for 5 h may be related to thetransformation from HCP to FCC phase.In case of ideal uniaxial anisotropy the observed

dependence of the shape of magnetisation curve on theangle between the applied field and the easy axis can be

Page 5: Evolution of structural and magnetic properties of sputtered nanocrystalline Co thin films with thermal annealing

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Fig. 6. Azimuthal angle dependence of coercivity (Hc) at some repre-

sentative annealing temperatures. The corresponding hysteresis loop along

easy direction (y0 ¼ 01) and hard direction (y0 ¼ 901) are also shown.

°

Fig. 7. The variation of the pinning coercivity (Hcw) and anisotropy field

(Ha) as a function of annealing temperature.

D. Kumar, A. Gupta / Journal of Magnetism and Magnetic Materials 308 (2007) 318–324322

understood in terms of the Stoner–Wohlfarth model [23].The free energy of the system in the presence of an appliedfield H making an angle y0 from the easy axis can bewritten as [23]

F ¼ �Ku cos2ðy� y0Þ �HMs cos y, (2)

where Ku is the anisotropy constant and y is the anglebetween the magnetisation and the applied field. The fielddependence of the magnetisation can be obtained by

minimising the free energy with respect to y, which givesthe well-known Stoner–Wohlfarth solution as

2mð1�m2Þ1=2 cos 2y0 þ sin 2y0ð1� 2m2Þ

� 2hð1�m2Þ1=2¼ 0, ð3Þ

where h ¼ H=Ha is the reduced field and m ¼M=Ms is thereduced magnetisation.The solutions of this equation for different values of y0

are shown in Fig. 8(a). For y0 ¼ 01, the hystersis curve is aperfact square shape with coercivity equal to Ha, while fory0 ¼ 901 the curve is linear with zero coercivity andsaturates at field H ¼ Ha. For an intermediate value ofy0, theory predicts that the applied field needed to saturatethe magnetisation significantly higher as compared to thatneeded to saturate the magnetisation for y0 ¼ 901.A comparison of angular dependence of the shape of

hystersis curve for the film annealed at different tempera-ture shows that the film annealed at 300 1C exhibitshystersis curves, which are closer to the shape predictedby the Stoner–Wohlfarth model. For comparison, thehysteresis loops for the sample y0 ¼ 01, 601 and 901 areshown in Fig. 8(b). Close to the theoretical predictions, thecoercivity at y0 ¼ 901 is very small and the magnetisationsaturates at HEHa. At y0 ¼ 601, the field needed tosaturate the magnetisation is significantly higher than Ha.In contrast to this, in the as-prepared sample as well as thesample annealed at lower temperatures, even for y0 ¼ 901coercivity is significantly large and also the magnetisationsaturates at an applied field which is much larger than Ha.The observed annealing temperature dependence of uni-axial anisotropy as well as the shape of the hystersis curvecan be understood if one conjectures that as-prepared filmcontains both long-range as well as short-range stresses.The long-range stresses give rise to the uniaxial anisotropy,while short-range stresses are random in direction. Becauseof these random stresses, the applied field needed tosaturate the magnetisation would exceed Ha. It may be

Page 6: Evolution of structural and magnetic properties of sputtered nanocrystalline Co thin films with thermal annealing

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(a)

(b)

Fig. 8. (a) Simulated M–H curves for the different values of angle between

easy axis and applied field on the basis of Stoner–Wohlfarth model; (b) the

corresponding data for film annealed at 300 1C.

D. Kumar, A. Gupta / Journal of Magnetism and Magnetic Materials 308 (2007) 318–324 323

noted that according to Stoner–Wohlfarth model, it ismore difficult to fully saturate the magnetisation for y0values intermediate between 01 and 901, because theapplied field is working against a torque �dfa/dy [23]. Thistorque vanishes as y approaches 901, but for theintermediate values of y torque does not vanish as M

aligns with the field. Because of random stresses there willbe regions with their easy axis pointing in the directionsdifferent form the easy direction of the bulk of the sample.In these regions, even for y0 ¼ 901, the angle between theapplied field and the local easy direction will not be 901.Therefore, a field greater than Ha is needed to saturate themagnetisation.

With thermal annealing, first the short-range stresses willstart relaxing. As a result, the effective uniaxial anisotropyalong the direction defined by the long-range stresses willincrease, and also the field needed to saturate themagnetisation for y0 ¼ 901 will decrease and approach anideal value of Ha.

Beyond 300 1C, even the long-range stresses startrelaxing giving rise to decrease in uniaxial anisotropy.From the XRD results we find that the significant graingrowth starts taking place above 300 1C only. Since graingrowth requires long-range movement of the atoms, therelaxation of the long-range stresses is also associated with

such atomic movements. On the other hand, relaxation ofshort-range stresses is associated with annihilation ofdefects, which involves only short-range movements ofthe atoms and can occur at lower temperatures.

4. Conclusion

Thin film of HCP cobalt with ultrafine grain size hasbeen prepared using ion-beam sputtering. Evolution ofstructural as well as magnetic properties of the film as afunction of thermal annealing has been studied. Up to anannealing temperature of 300 1C the film exhibits slowgrain growth, however, beyond this temperature the rate ofgrain growth increases rapidly and structural transforma-tion from HCP to FCC phase is also observed. As-prepared film exhibits a uniaxial anisotropy, which may beattributed to long-range stresses in the film. With increas-ing annealing temperature, the magnitude of anisotropyinitially increases gradually and reaches a maximum valuearound the annealing temperature of 300 1C, which may beattributed to annealing out of short-range stresses that arerandom in direction. Beyond this temperature, it shows arapid decrease, concurrent with relaxation of long-rangstresses as well as HCP to FCC transformation. Theobserved variation in the pinning coercivity with annealingtemperature can be understood in terms of variations in thesurface roughness, internal stresses and grain structure.After annealing at 550 1C for 5 h the dominant phase isFCC Co with only a small fraction of HCP phase present.The present study shows that even in polycrystalline films,the FCC phase can be stabilised by thermal annealing andslow cooling.

Acknowledgements

The authors thank Mr. S. Potdar for the help in thedeposition of Co film. One of the authors Mr. DileepKumar is thankful to CSIR, India, for Senior ResearchFellowship.

References

[1] H.T. Shi, D. Lederman, Phys. Rev. B 58 (1998) 1778.

[2] Y.Z. Wu, H.F. Ding, C. Jing, D. Wu, G.L. Liu, V. Gordon, G.S.

Dong, X.F. Jing, S. Zhu, K. Sun, Phys. Rev. B 57 (1998) 11935.

[3] A. Kharmouche, S.-M. Cherif, A. Bourzami, A. Layadi, G.

Schmerber, J. Phys. D: Appl. Phys. 37 (2004) 2583.

[4] H. Xu, A.C.H. Huana, T. Andrew, S. Weea, D.M. Tong, Solid State

Commun. 126 (2003) 659.

[5] S.J. Oh, W. Kim, W. Kim, B.H. Choi, J.-Y. Kim, H. Koh, H.J. Kim,

J.H. Park, Appl. Surf. Sci. 169–170 (2001) 127.

[6] W. Weber, C.H. Back, A. Bischof, Ch. Wursch, R. Allenspach, Phys.

Rev. Lett. 76 (1996) 1940.

[7] W. Wulfhekel, T. Gutjahr-Loser, F. Zavaliche, D. Sander,

J. Kirschner, Phys. Rev. B 64 (2001) 144422.

[8] X.Q. Zhao, S. Veintemillas-Verdaguer, O. Bomati-Miguel, M.P.

Morales, H.B. Xu, Phys. Rev. B 71 (2005) 024106.

[9] V.F. Puntes, K.M. Krishnan, A.P. Alivisatos, Science 291 (2001)

2115.

Page 7: Evolution of structural and magnetic properties of sputtered nanocrystalline Co thin films with thermal annealing

ARTICLE IN PRESSD. Kumar, A. Gupta / Journal of Magnetism and Magnetic Materials 308 (2007) 318–324324

[10] V. Skumryev, S. Stoyanov, Y. Zhang, G. Hadipanayis, D. Givord,

J. Nogues, Nature (London) 423 (2003) 850.

[11] P.C. Riedi, T. Dumelow, M. Rubinstein, G.A. Prinz, S.B. Qadri,

Phys. Rev. B 36 (1987) 4595.

[12] L.G. Parratt, Phys. Rev. 95 (1954) 359.

[13] H. Shi, D. Lederman, J. Appl. Phys. 87 (2000) 6095.

[14] W. Gong, H. Li, Z. Zhao, J. Chen, J. Appl. Phys. 69 (1993) 5119.

[15] K. Zhang., R. Gupta, K.P. Lieb, Y. Luo, G.A. Muller, P. Schaaf, M.

Uhrmacher, Europhys. Lett. 64 (2003) 668.

[16] O. Kitakami, H. Sato, Y. Shimada, F. Sato, M. Tanaka, Phys. Rev. B

56 (1997) 13849.

[17] O. Kitakami, T. Sakurai, Y. Miyashita, Y. Takano, Y. Shimada, H.

Takano, H. Awano, K. Ando, Y. Sugita, Jpn. J. Appl. Phys. 35

(1996) 1724.

[18] M. Li, Y.P. Zhao, G.-C. Wang, H.-G. Min, J. Appl. Phys. 83 (1998)

6287.

[19] P. Sharma, A. Gupta, J. Magn. Magn. Mater. 288 (2005) 347.

[20] Y. Nagal, A. Tago, K. Yanagisawa, T. Toshima, J. Appl. Phys. 8

(1987) 3843.

[21] Q. Jiang, H.-N. Yang, G.-C. Wang, Surf. Sci. 373 (1997) 181.

[22] J.-H. Kim, S.-C. Shin, Jpn. J. Appl. Phys. 35 (1996) 342.

[23] R.C. O’Handley, Modern Magnetic Materials: Principles and

Applications, Wiley-Interscience Publication, New York, 2000.