The Faraday effect in magnetic semiconductors (abstract)

Abstract

In n-type ferromagnetic semiconductors, both bound electrons and free carriers make contributions to the Faraday effect. The spin-orbital interaction of bound electrons, and the spin-spin exchange interaction between bound electrons and between bound electrons and free electrons exist. Thus, the Faraday rotation θ has been deduced as follows: θ=(eμ0/mc)∑∞l=1blλ2lL (He+ν′M)+(eμ0/mc) ∑∞n=1(an/λ2n) L[He+(ν+ν′)M] =θS+θF, where L is the thickness, He the external field, M the magnetization, ν′M the effective field related to the exchange interaction between bound electrons and free electrons, νM the effective field related to the spin-orbital interaction of bound electrons and so on, an and bl the constants related to the concentration N1 of free electrons and the concentration N2 of bound electrons, respectively. While λ>λ0, the wavelength at θ=0, or N1>N0∼1022/m3, θS>θF. Conversely, θS<θF. When θS≪θF, θ∼(a1/λ2+a2/λ4+...). The temperature behavior of θ mainly depends on that of M. θ tends to saturation with M. When θS≫θF, θ∼(b1λ2+b2λ4+⋅⋅⋅). θ is directly proportional to approximately He. The calculations are confirmed by the experimental results in CdCr2S4, etc.