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
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