Principal spectra describing magnetooptic permittivity tensor in cubic crystals

TL;DR

This paper introduces a unified phenomenological framework using principal spectra to describe magnetooptic permittivity tensors in cubic crystals, supported by ab-initio calculations across various materials and energy ranges.

Contribution

It presents a novel, simplified method to determine magnetooptic effects in cubic crystals using only four principal spectra, applicable to any magnetization and surface orientation.

Findings

Principal spectra accurately describe permittivity tensor elements.

Method applies to bcc Fe, fcc Co, and fcc Ni across optical and x-ray ranges.

Analytical expressions derived using modified Kubo formula.

Abstract

We provide unified phenomenological description of magnetooptic effects being linear and quadratic in magnetization. The description is based on few principal spectra, describing elements of permittivity tensor up to the second order in magnetization. Each permittivity tensor element for any magnetization direction and any sample surface orientation is simply determined by weighted summation of the principal spectra, where weights are given by crystallographic and magnetization orientations. The number of principal spectra depends on the symmetry of the crystal. In cubic crystals owning point symmetry we need only four principal spectra. Here, the principal spectra are expressed by ab-initio calculations for bcc Fe, fcc Co and fcc Ni in optical range as well as in hard and soft x-ray energy range, i.e. at the 2p- and 3p-edges. We also express principal spectra analytically using modified Kubo formula.