Electronic structure of Gd pnictides calculated within theLSDA+Uapproach

Abstract

A computational study of the electronic structure and magnetic properties of Gd pnictides is reported. The calculations were performed using a full-potential linear muffin-tin orbital method within the so-called $\mathrm{LSDA}+\mathrm{U}$ approach, which adds Hubbard-$U$ correlation effects to specified narrow bands in a mean-field approach to the local spin-density approximation (LSDA). Here both the $\mathrm{Gd}\phantom{\rule{0.3em}{0ex}}4f$ and 5$d$ states are subject to such corrections. The ${U}_{f}$ values were determined semiempirically by using photoemission and inverse photoemission data for $\mathrm{GdP}$, $\mathrm{GdAs}$, $\mathrm{GdSb}$, and $\mathrm{GdBi}$. In contrast to ${U}_{f}$ which represents narrow-band physics, ${U}_{d}$ represents a quasiparticle self-energy correction of the LSDA gap underestimate. The ${U}_{d}$ value was adjusted using optical-absorption data for semiconducting $\mathrm{GdN}$ above its Curie temperature. Below the Curie temperature, however, in the ferromagnetic state, the gap becomes almost zero. The other Gd pnictides are found to have a small overlap of the conduction band at the $X$ point and the valence band at the $\ensuremath{\Gamma}$ point in the majority-spin channel. A small gap opens in the spin-minority channel of $\mathrm{GdP}$ and $\mathrm{GdAs}$, which are thus half metallic. This spin-minority gap closes in semimetallic $\mathrm{GdSb}$ and $\mathrm{GdBi}$. While $\mathrm{GdN}$ is found to be ferromagnetic, the other Gd pnictides are found to be antiferromagnetic, with ordering along [111]. From calculations with different magnetic configurations, a Heisenberg model with first and second nearest-neighbor exchange parameters is extracted. The Heisenberg model is then used to predict Curie-Weiss and N\'eel temperatures and critical magnetic fields within mean field and compared with experimental data. The trends are found to be in good agreement with the experimental data.