Low-temperature magnetization of (Ga,Mn)As semiconductors

Abstract

We report on a comprehensive study of the ferromagnetic moment per Mn atom in (Ga,Mn)As ferromagnetic semiconductors. Theoretical discussion is based on microscopic calculations and on an effective model of Mn local moments antiferromagnetically coupled to valence band hole spins. The validity of the effective model over the range of doping studied is assessed by comparing with microscopic tight-binding/coherent-potential approximation calculations. Using the virtual crystal $\mathbf{k}∙\mathbf{p}$ model for hole states, we evaluate the zero-temperature mean-field contributions to the magnetization from the hole kinetic and exchange energies, and magnetization suppression due to quantum fluctuations of Mn moment orientations around their mean-field ground state values. Experimental low-temperature ferromagnetic moments per Mn are obtained by superconducting quantum interference device and x-ray magnetic circular dichroism measurements in a series of (Ga,Mn)As semiconductors with nominal Mn doping ranging from $\ensuremath{\sim}2$ to 8%. Hall measurements in as-grown and annealed samples are used to estimate the number of uncompensated substitutional Mn moments. Based on our comparison between experiment and theory we conclude that all these Mn moments in high quality (Ga,Mn)As materials have nearly parallel ground state alignment.