Calculation of the magnetization of the layered III-VI diluted magnetic semiconductorGa1−xMnxS

Abstract

The magnetization of a compound belonging to a new class of diluted magnetic semiconductors (DMS) was calculated. The magnetization of the III-VI DMS, Gay 1 - x Mn x S, was found for the small x regime. The Hamiltonian usedto model the incomplete shell of 3d 4 electrons in the transition-metal manganese atom consists of the crystal field, spin-orbit, spin-spin, and the Zeeman terms. The 25×25 Hamiltonian matrix was found by usting an uncoupled angular momentum basis set and diagonalized numerically. The structure of the field-dependent energy levels is shown. The energy eigenvalues were used to compute the magnetization of the system. For a sample with x = 6.6% at temperatures from 50 to 400 K and fields up to 7 T agreement with experiment was excellent with only one adjustable parameter, the spin-orbit coupling constant, λ. At low temperatures the interaction of the Mn atoms lowers the magnetization of the system relative to the singlet model that does not incorporate these interactions. For temperatures <50 K we modeled the Mn pair interactions by introducing a nearest-neighbor antiferromagnetic exchange interaction with an effective exchange coefficient: this brings the agreement with experiment down to about 20 K. For temperatures below 20 K the spin-glass-like cusp in the experimental data at 11 K suggests that the longer-range Mn interactions become significant. The good agreement of our results with experiment over a wide region of parameter space is a significant step toward understanding the magnetic properties of this new class of DMS.