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Amorphous films, Magneto-optical films and magnetic simeconductor films

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## Amorphous films, Magneto-optical films and magnetic simeconductor films

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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 films**Rapid 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……**Tc increases with the increasing Co content**Tc decreases from Gd, Tb, Dy, Ho……**Mean Field Theory**GdCoMo**Single ion model**Moorjani and Coey Magnetic glasses p201 Suzuki et al., JAP 83(1988)3633**Shang and Wang et al PRL 63(1989)449; Wang and Kleemann PRB**44(1991)5132**y**Atom pair model θ2 θ1 x r r 12 (a) (b) M M 1 2 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 expression 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)]**The total dipolar energy for AA, BB and AB pairs can be**expressed in terms 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**Tb0.26Fe0.74amorphous film**Harris et al., PRL 69(1992)1939**Magneto-optical Effect**1876 John Kerr The three types of geometries of the Kerr effect**Magneto-optical Effect**θ k is defined as the main polarization plans is tilted over a small angle; εk= arctan(b/a).**Definition**The arrangement of the magnetization M and wave vector k in the local coordination employed in the derivation of the p- MOKE equation for Normal incidence.**The dielectric tensor has the following form**(1) The normal model solution to the Fresnel Eq. (2) and the corresponding electric field model are (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)**Kittel Introduction to solid state physics, chapter 11:**optical process and excitons 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)**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.**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**rⅠ± rⅡ± MO layer Reflector Reim and Weller IEEE Trans on Mag., 25(1989(3752**Faraday Effect**Bennett and Stern PR 137(1965)A448**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 and processing 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 nonmagnetic semiconductor and magnetic element; and (c) a nonmagnetic semi- conductor.**wide band gap Ⅲ-Ⅴ,Ⅱ-Ⅵ as host**Mn(Fe)GaAs Co(Fe,Ni,V,Cr)+Ti02(ZnO) MnAs/ZnSe Others (ZnMnO) For most doped DMS Tc<room temperature Co-Ti02 Tc ～400K ZnMnO room T**GaMnAs**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.**Magnetic field dependence of magnetization M at 5K for a**(Ga, Mn)As film with xMn=0.035. The field was applied parallel to the sample surface (Ohno et al., APL 69(1996)363).**MnAs/ZnSe**GaAs(001)/200nmZnSe/170nmMnAs Room temperature longitudinal MOKE responses for ferromagnetic MnAs on ZnSe: (a) a single phase MnAs/ZnSe (b) a dual phase MnAs/ZnAs heterostructure (Berry et al., APL 77(2000)3812).**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**Matsumoto et al., Science 291(2001)854 Atomic resolution TEM image. No segregation of impurity phase was observed. An XRD pattern of a Co doped TiO2 film (x=0.08) showing (004) and (008) peaks of anatase(锐钛矿) without any impurity peaks.**A series of scanning SQUID microscope images**200 µm x 200 µm 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) 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.**Small Clusters of Co results in Ferromagnetism in Co doped**TiO2 (金红石) APL 86(2005)222503