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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