Diluted Magnetic Semimetals - Beyond Heisenberg Coupling

Abstract

The sp-d coupling between localized (d) spins, S, and the spin o of conduction (sp) electrons usually is described by the symmetric Kondo Hamiltonian , α+k' ά-σS, or ,equivalently, by the Heisenberg form of the spin Hamiltonian, Jsp-dσS. This approximation is suffIcient for a description of most basic effects, which are caused by sp-d coupling. Such effects are, e.g., spinflip scattering and the Knight-like g-shift of the impurity resonance. Spin flip scattering causes a spin polarization of the conduction band electrons (CE) which, within second order perturbation, leads to the indirect d-sp-d (RKKY) exchange coupling among the impurity spins. The character of the spin polarization is different in semiconductors and in semimetals. In semimetals, the spin polarization is localized in the vicinity of the localized d-state and decreases with a decay length (2kF) -1 , as described by the Ruderman-Kittel (RK) function. The spatial integral of spin polarization yields the magnetic moment induced in the conduction electron gas by the local spin: σind = (3/16)(Jsp-dn0/EF)(nCE/n0)S, where EF is the Fermi energy, n 0 is concentration of crystal sites and n CE — that of the CE. The sum of the induced magnetic moments determines the magnetization of electron gas caused by the presence of the local spins. The resulting magnetization value is , however, only half of the value obtained within the one-electron approach, commonly used for semiconductors. Within the latter approach, the spin polarization of the CE is assumed to be homogeneously distributed in space and it causes an effective g-factor enhancement [1].