Exchange interactions of DMS alloys in the GW approximation*

Dilute Magnetic semiconductors are a new but little understood class of materials, and in particular the origin of ferromagnetism in these materials. As we will show, the LSDA combined with the rigid-spin approximation fails to predict the observed magnetism in many of these materials, and a key question is whether the failing is due to the approximations made, or is something else going on? The best understood of DMS is zincblende Mn$_x$Ga$_{1-x}$As, with $x\tilde{<}0.1$. Optimally grown thin films have been recently shown to exhibit conventional temperature-dependent magnetization behavior with $T_c\sim{}170$K. Using a standard LDA linear-response technique the LSDA total energy is mapped analytically onto a Heisenberg hamiltonian, which is analyzed for random and partially ordered structures. Temperature-dependent properties were investigated using a form of the Cluster Variation method for the Heisenberg model. The calculated $T_c$ is predicted to increase with $x$ to $x$=15\%, reaching $T_c\sim$250K. For still larger $x$, $T_c$ is predicted to fall and turn antiferromagnetic when $x${}$>$50\%. Clustering and spin-orbit coupling are both found to reduce $T_c$. Thus in this case the theory falls in good agreement with observed values for low concentration. An analysis shows the Mn $e_g$ levels are responsible for the antiferromagnetic contribution. We show that suitable short-period superlattices can minimize this contribution, thus signficantly enhancing $T_c$. Many other less well studied DMS alloys--particularly nitride and oxide compounds--have now been reported with $T_c$ exceeding 300K. Several of these cases were investigated, and the LSDA linear-response predicts low $T_c$, typically $T_c<100$K. Moreover, the LDA results for Mn$_x$Ga$_{1-x}$As at large $x$ are at variance, with observed ferromagnetism in a quantum dot of MnAs in the zincblende phase[1]. To address validity of the LSDA+rigid approximation, a we present results from a recent implementation of self-consistent {\em GW} calculation of the spin susceptibility. As will be described {\em GW} alters the exchange parameters in even in elemental transition metals, and the changes in transition metal compounds can be dramatic. $^1$K. Ono et al, J. Appl. Phys. {\bf 91}, 8088 (2002).