What is the valence of Mn in Ga$_{1-x}$Mn$_x$N?

TL;DR

This study clarifies the Mn valence in Ga$_{1-x}$Mn$_x$N as close to 2+ and introduces two effective low-energy models that capture the dual nature of doped holes, advancing understanding of its magnetic properties.

Contribution

The paper provides the first first-principles derivation of two low-energy models for Mn-doped GaN, resolving a key controversy about Mn valence and highlighting the dual nature of doped holes.

Findings

Mn valence is close to 2+ ($d^5$) with a mixed spin state.

Two effective models ($d^4$ and $d^5$) describe local and extended properties.

Revealed novel physical effects in the extended $d^5$ picture.

Abstract

We investigate the current debate on the Mn valence in Ga$_{1-x}$Mn$_x$N, a diluted magnetic semiconductor (DMSs) with a potentially high Curie temperature. From a first-principles Wannier-function analysis, we unambiguously find the Mn valence to be close to $2+$ ($d^5$), but in a mixed spin configuration with average magnetic moments of 4$\mu_B$. By integrating out high-energy degrees of freedom differently, we further derive for the first time from first-principles two low-energy pictures that reflect the intrinsic dual nature of the doped holes in the DMS: 1) an effective $d^4$ picture ideal for local physics, and 2) an effective $d^5$ picture suitable for extended properties. In the latter, our results further reveal a few novel physical effects, and pave the way for future realistic studies of magnetism. Our study not only resolves one of the outstanding key controversies of the field, but also exemplifies the general need for multiple effective descriptions to account for the rich low-energy physics in many-body systems in general.