Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2)...

Amorphous films, Magneto-optical films and magnetic simeconductor films

(1) Amorphous films(2) magneto-optical effect and Materials(3) dilute semiconductor

Preparation of amorphous filmsRapid cooling via Vacuum evaporation, Sputtering

Many elements (ribbons FeNiPB, FeCoSiB, CoSiB….)Size difference (GdCo, TbFe, YFe….)Cooling the substrate

Characters: x-ray, conductivity, phase transition……

Chaudhari et al., APL(1973)202

Tc increases with the increasing Co contentTc decreases from Gd, Tb, Dy, Ho……

GdCoMoMean Field Theory

Suzuki et al., JAP 83(1988)3633

Single ion model

Moorjani and Coey Magnetic glasses p201

Shang and Wang et al PRL 63(1989)449; Wang and Kleemann PRB 44(1991)5132

Wang and Kleemann PRB 44(1991)5132

The potential energy of the system is

U= - (1/2)(M1xH1x+M1yH1y+ M2xH2x+M2yH2y)

= - (M1M2/4πμor123) (2cosθ1cosθ2 - sinθ1sinθ2)

If the two dipoles have the same magnetic moment, M1=M2=M and if

they are always parallel to each other, that is θ1=θ2=θ, the above expres

sion because

U= - [ 3M2/(4πμor123) ](cos2θ-1/3)

In the general case the potential energy is given by

U = (1/(4πμor123)) [(M1•M2) - 3/r2 (M1•r)( M2•r)]

M2

M1

x

y

rr12

θ2 θ1

(a) (b)

Atom pair model

The total dipolar energy for AA, BB and AB pairs can be expressed interms of probability functions PAA (r ), PBB (r ), and PAB (r ) . The average dipolar

energy associated with AA pairs, per A atom, is given by

The anisotropic probability functions may be expressed using spherical harmonics as follows

N total number of atoms per unit volume, Nj the number of j type anisotropy in alignment of ij atom pair

Cargill et al., JAP 49(1978)1753, 50(1979)3570

PRL 66(1991)1086, 69(1992)1939, 87(2001)067207 Pair model

Gd0.11Co0.67Mo0.16Ar0.06

Harris et al., PRL 69(1992)1939

Tb0.26Fe0.74 amorphous film

Magneto-optical Effect

The three types of geometries of the Kerr effect

1876 John Kerr

Magneto-optical Effect

θ k is defined as the main polarization plans is tilted over a small angle;εk = arctan(b/a).

The arrangement of the magnetization M and wave vectork in the local coordination employed in the derivation of the p-MOKE equation for Normal incidence.

Definition

The dielectric tensor has the following form

The normal model solution to the Fresnel Eq.

and the corresponding electric field model are

(1)

(2)

(3)

The definition of Kerr rotation and Kerr ellipticity

Kerr rotation and ellipticity are expressed by the component of conductivity sensor

θk = -Im [(n+ -n-)/( n+n- -1)]

εk = -Re[(n+ -n-)/( n+n- -1)]

n+ = n+ -ik+, n- = n- -ik-r+ - =(n+ - -1)/( n+- +1)

E (refl) / E (inc) = r(ω) = ρ(ω)exp[iθ(ω)]

r(ω) = (n+ik-1)/(n+ik+1)

R = E*(refl)E(refl)/E*(inc)E(inc) = r*r = ρ2

ε(ω)1/2 = n(ω) + ik(ω)

Once we know both R(ω) and θ(ω), we can obtain n(ω) and k(ω), then to getε(ω)= ε’(ω) +iε’’(ω)

Kittel Introduction to solid state physics, chapter 11: optical process and excitons

The off-diagonal terms σxy are proportional to M and describe the MOKE.

Both diagonal and off-diagonal terms are complex quantities,

σij =σ1ij +i σ2ij

The absorptive component of diagonal terms σ1xx is proportional to the sum

of absorption of left and right circularly polarized light (RCP and LCP). the absorptive component off-diagonal term σ2xy is proportional to the difference

in absorption of LCP and RCP components.

Erskine and Stern PRB 12(1975)5016

微观理论

在铁磁性金属物质中的磁光效应源于带内 (intraband) 和带间 (interband) 电子跃迁。前者局限于低能量端的跃迁，而后者发生在高能量区，常见的在可见光范围。磁光效应与电导张量非对角元密切相关。微观上，这一非对角元由自旋取向向上和向下两部分各自的跃迁之和来表示。

σ2xy=σ2xy↑(ω)+ σ2xy↓(ω)

  在自旋向上或向下的各自的初终态 α 和 β 之间的跃迁贡献为

σ2xy=(2πe2/4hm2Vω) Σαβ[(|<β↑|π-|α↑>|)2 + (|<β↓|π-|α↓>|)2

-(|<β↑|π+|α↑>|)2 - (|<β↓|π+|α↓>|)2 ] δ(ωαβ –ω) (5-10)

这里 , π± =πx ±iπy 为运动量矩算符，定义为： π=p(h/8πmc2)S×▽V(r), p 是动量矩算符， S

×▽V( r ) 描写自旋轨道耦合， v为总的体积 ,

h ωαβ =εβ -εα

显然 ,式 5-10 可视为一个光子的吸收过程，即一个电子从初态占有初态 α 到非占有终态 β 间的跃迁。 δ(ωαβ-ω) 表示为跃迁过程中的能量守恒 .矩阵元 (α|π+|β) 和 (α|π-|β) 相应于右园和左园偏振的跃迁 .因此 σ2xy 比例于右园和左园偏振光吸收概率之差 .从理论计算可以推得 σ1xx (ω) 比例于平均吸收 ,非对角元色散部分 σ2xx (ω) 和 σ1xy (ω) 可以通过 Kramers 关系推得 .

上述跃迁必需满足 Δl=±1, Δml =±1

第一选择定则表明，跃迁只能发生在 s和 p能级间或 p和 d能间间，第二选择定则表明，右园和左园偏振跃迁需分别满足 Δml =-1 和 Δml =+1.

Double Layers

MO layerReflector

rⅡ± rⅠ

±

Reim and Weller IEEE Trans on Mag., 25(1989(3752

Bennett and Stern PR 137(1965)A448

Faraday Effect

Petros N. Argyres, Theory of the Faraday and Kerr effect in ferromagnets, PR 97(1955)334,P.M. Oppeneer, Magneto-optical Kerr spectra in Handerbook of Magnetic Materials,Edited by Buschow (Vol.13), Physical Review B, 45(1992)10924.

From Oppeneer Magneto-optical Kerr spectra in Hanbook of magnetic

Materials, Edited by Buschow (Vol.13)

Experimental pola Kerr ritation an undoped MnBi sample (Di et al. 1992)

and Al-doped MnBi sample at room ) temperature (Shang et al., 1997).

Diluted Magnetic Semiconductors

• The charge of electrons in Semiconductor (Integrated circuits, devices);

• Spin of electrons in data storage (hard disc, tapes, magneto-optical disks)

May we be able to use the capability of mass storage andprocessing of information at the same time ? If both the charge and spin of electrons can be used to further enhance the performance of devices.

Three types of semiconductors: (A) a magnetic semiconductor, (B) a diluted magnetic semiconductor, an alloy between nonmagneticsemiconductor and magnetic element; and (c) a nonmagnetic semi-conductor.

wide band gap - , - Ⅲ Ⅴ Ⅱ Ⅵ as host

Mn(Fe)GaAsCo(Fe,Ni,V,Cr)+Ti02(ZnO)MnAs/ZnSeOthers (ZnMnO)

For most doped DMS Tc<room temperatureCo-Ti02 Tc ～ 400KZnMnO room T

Lattice constant a vs Mn composition x in (Ga1-x, Mnx)As films.a was determined by XRD at room temperature (Ohno et al.,APL 69(1996)363.

GaMnAs

Magnetic field dependence of magnetization M at 5K for a (Ga, Mn)As film with xMn=0.035. The field was applied parallelto the sample surface (Ohno et al., APL 69(1996)363).

Room temperature longitudinal MOKE responses for ferromagneticMnAs on ZnSe: (a) a single phase MnAs/ZnSe (b) a dual phase MnAs/ZnAs heterostructure (Berry et al., APL 77(2000)3812).

GaAs(001)/200nmZnSe/170nmMnAs

MnAs/ZnSe

ZnCoAl

XRD patterns and VSM curves of the thin films deposited at 400 oC at oxygen pressure 5x10-5 Pa(Yan et al., JAP 96(2004)508).

Co doped TiO2

An XRD pattern of a Co doped TiO2 film(x=0.08) showing (004) and (008) peaksof anatase( 锐钛矿 ) without any impurity peaks.

Atomic resolution TEM image. No segregation of impurity phase wasobserved.

Matsumoto et al., Science 291(2001)854

Images taken at 3K for anatase thin films with different Co contents on a combinatorial chip. (a) x=0, (b) 0.02, (c) 0.03, (d) 0.06. Magnetic domain were observed in all doped film.

A series of scanning SQUID microscope images

200 µm x 200 µm

(a) an M-H curve of an x=0.07 film on SrTiO3 taken at room temperature.(b) M-T curve in a field of 20 mT parallel to the surface. Tc > 400K.

PRL 90(2003)017401

Ti0.99Co0.01O2-δ

Small Clusters of Co results in Ferromagnetism in Co doped TiO2 ( 金红石 )

APL 86(2005)222503

Co 2+ or Co clusters

Zn1-xMnxO

Source ?

(1) Zener Model(2) RKKY interaction (H.Ohno Science 281(1998)951);(3) Forming resonant states (J.Inoue et al., PRL 85(2000) 4610;(4) Clusters of Co in Co-doped anatase TiO2 thin film (J.K. Kim et al., PRL 90(2003)017401.

Science 287(2000)1019

Fig. Normalized ferromagnetic temperature as a function ofHole concentrations

Driven by exchange Between carriers andLocalized spin(PR 81(1950)440)

AF is Fermi parameter, xeff is the effective spin magnitude,

β is p(carriers)-d exchange integral, No is the concentration of the cation sites,

Tc = TF – TAF, TFnor is normalized ferromagnetic temperature

Tc is determined by Eq.(2)

Tc(x) = Tcnor (F)(x) - Tc (AF) (x)

Fig.2, Curie temperature Tc in Zn1-xMnxTeN for various Mn contents x and hole concentrations

ρ deduced from the Hall resistance at 300 K. Theoretical predictions areindicated by the red mesh.

RKKY

B (T)

(Mn1-x Gax)As 200nm thick

(F.Matsukura et al., PRB 57(1998)R2037)

(Mn1-x Gax)As