Magnetic Anisotropy of Cubic Iron-Based Diluted Magnetic Semiconductors

Iron-based diluted magnetic semiconductors having the cubic zinc-blende structure display unusual responces to external magnetic fields. For low fields, B, the magnetic susceptibility is isotropic as expected for cubic crystals. However, when the magnetic field is sufficiently high so that the Zeeman energy cannot be neglected in comparison to the spacing of the low lying levels of Fe²⁺ (owing to the spin orbit interaction), the nonlinear magnetization exhibits a striking anisotropy. This phenomenon is related to the Van Vleck paramagnetism primarily due to the nature of the ground state of the (3d)⁶ configuration of Fe²⁺, namely a singlet in the crystal field of tetrahedrally coordinated semiconductors. We are concerned with Fe²⁺ in a tetrahedral environment and the concomitant Van Vleck type of paramagnetism. We present an analytic investigation of the magnetic moment of a Fe²⁺ ion in a T_d field. In this approach the spin-orbit interaction and the Zeeman energy are treated as small compared to the crystal field spitting but are themselves viewed as of comparable magnitudes. We obtain expressions for the effective number of Bohr magnetons per ion for B along the ⟨001⟩, ⟨111⟩ and ⟨110⟩ directions. The anisotropy of this quantity is of the order of 15% at liquid helium temperatures in a magnetic field of 150 kG. Corrections proportional to the ratio of the spin-orbit interaction and the crystal field spiltting are also evaluated in first order.