Wannier-based calculation of the orbital magnetization in crystals

TL;DR

This paper introduces a first-principles Wannier-based method to accurately and efficiently compute the orbital magnetization in magnetic crystals, even with complex Fermi surfaces, by interpolating k-space quantities.

Contribution

The paper develops a gauge-invariant Wannier interpolation scheme for orbital magnetization, improving computational efficiency and accuracy over previous methods.

Findings

Successfully applied to bcc Fe, hcp Co, and fcc Ni.

Reproduces experimental orbital magnetization ordering.

Efficient interpolation with few Wannier functions.

Abstract

We present a first-principles scheme that allows the orbital magnetization of a magnetic crystal to be evaluated accurately and efficiently even in the presence of complex Fermi surfaces. Starting from an initial electronic-structure calculation with a coarse ab initio k-point mesh, maximally localized Wannier functions are constructed and used to interpolate the necessary k-space quantities on a fine mesh, in parallel to a previously-developed formalism for the anomalous Hall conductivity [X.Wang, J. Yates, I. Souza, and D. Vanderbilt, Phys. Rev. B 74, 195118 (2006)]. We formulate our new approach in a manifestly gauge-invariant manner, expressing the orbital magnetization in terms of traces over matrices in Wannier space. Since only a few (e.g., of the order of 20) Wannier functions are typically needed to describe the occupied and partially occupied bands, these Wannier matrices are small, which makes the interpolation itself very efficient. The method has been used to calculate the orbital magnetization of bcc Fe, hcp Co, and fcc Ni. Unlike an approximate calculation based on integrating orbital currents inside atomic spheres, our results nicely reproduce the experimentally measured ordering of the orbital magnetization in these three materials.