First-principles investigation of the assumptions underlying model-Hamiltonian approaches to ferromagnetism of 3d impurities in III-V semiconductors

Abstract

We use first-principles calculations for transition-metal impurities V, Cr, Mn, Fe, Co, and Ni in GaAs, as well as Cr and Mn in GaN, GaP, and GaSb, to identify the basic features of the electronic structures of these systems. The microscopic details of the hole state such as the symmetry and the orbital character, as well as the nature of the coupling between the hole and the transition-metal impurity, are determined. This could help in the construction of model Hamiltonians to obtain a description of various properties beyond what current first-principles methods are capable of. We find that the introduction of a transition-metal impurity in III-V semiconductor introduces a pair of levels with t₂ symmetry—one localized primarily on the transition-metal atom, referred to as crystal-field resonance (CFR), and the other localized primarily on the neighboring anions, referred to as the dangling bond hybrid (DBH). In addition, a set of nonbonding states with e symmetry, localized on the transition-metal atom, are also introduced. Each of the levels is also spin split. Considering Mn in the host crystal series GaN→GaP→GaAs→GaSb, we find that while in GaN the hole resides in the tCFR level deep in the band gap, in GaAs and GaSb it resides in the t^DBH level located just above the valence-band maximum. Thus, a DBH-CFR level anticrossing exists along this host-crystal series. A similar anticrossing occurs for a fixed host crystal (e.g., GaAs) and changing the 3d impurity along the 3d series: V in GaAs represents a DBH-below-CFR limit, whereas Mn corresponds to the DBH-above-CFR case. Consequently, the identity of the hole-carrying orbital changes. The symmetry (e vs t₂) and the character (DBH vs CFR), as well as the occupancy of the gap level, determine the magnetic ground state favored by the transition-metal impurity. LDA+U calculations are used to model the effect of pushing the occupied Mn states deeper into the valence band by varying U. We find that this makes the DBH state more hostlike, and at the same time diminishes ferromagnetism. While the spin-splitting of the host valence band in the presence of the impurity has been used to estimate the exchange coupling between the hole and the transition-metal impurity, we show how using this would result in a gross underestimation of the coupling.