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Page 1: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

Amorphous films, Magneto-optical films and magnetic simeconductor films

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

Page 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……

Page 3: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

Chaudhari et al., APL(1973)202

Page 4: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

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

Page 5: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor
Page 6: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

GdCoMoMean Field Theory

Page 7: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor
Page 8: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

Suzuki et al., JAP 83(1988)3633

Single ion model

Moorjani and Coey Magnetic glasses p201

Page 9: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

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

Page 10: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

Wang and Kleemann PRB 44(1991)5132

Page 11: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

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

Page 12: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

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

Page 13: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

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

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

Page 14: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

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

Page 15: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

Harris et al., PRL 69(1992)1939

Tb0.26Fe0.74 amorphous film

Page 16: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

Magneto-optical Effect

The three types of geometries of the Kerr effect

1876 John Kerr

Page 17: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

Magneto-optical Effect

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

Page 18: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

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

Page 19: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

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)

Page 20: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

The definition of Kerr rotation and Kerr ellipticity

Page 21: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

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)

Page 22: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

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

Page 23: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

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.

Page 24: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

Erskine and Stern PRB 12(1975)5016

Page 25: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor
Page 26: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

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.

Page 27: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

Double Layers

MO layerReflector

rⅡ± rⅠ

±

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

Page 28: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor
Page 29: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor
Page 30: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

Bennett and Stern PR 137(1965)A448

Faraday Effect

Page 31: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor
Page 32: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor
Page 33: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor
Page 34: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

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.

Page 35: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

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).

Page 36: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

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.

Page 37: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

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.

Page 38: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

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

Page 39: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

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

Page 40: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

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).

Page 41: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

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

Page 42: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

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).

Page 43: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

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

Page 44: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

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

Page 45: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

(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.

Page 46: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

PRL 90(2003)017401

Page 47: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

Ti0.99Co0.01O2-δ

Page 48: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor
Page 49: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

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

APL 86(2005)222503

Page 50: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

Co 2+ or Co clusters

Page 51: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

Zn1-xMnxO

Page 52: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

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.

Page 53: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

Science 287(2000)1019

Fig. Normalized ferromagnetic temperature as a function ofHole concentrations

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

Page 54: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor
Page 55: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

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)

Page 56: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

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.

Page 57: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor
Page 58: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

RKKY

B (T)

(Mn1-x Gax)As 200nm thick

Page 59: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

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

Page 60: Amorphous films, Magneto-optical films and magnetic simeconductor films (1) Amorphous films (2) magneto-optical effect and Materials (3) dilute semiconductor

(Mn1-x Gax)As