Abstract
In a recent article [Resta, Phys. Rev. Research 2, 023139 (2020)] it is argued, based on the dichroic sum rules derived from the modern theory of orbital magnetization, that the x-ray magnetic circular dichroism (XMCD) orbital magnetization sum rule is not providing an expectation value of the orbital angular momentum and of the orbital part of the magnetic moment, but a different quantity, also related to the breakdown of time-reversal invariance, but different. In this Comment, it is shown that this conclusion is incorrect, and that the XMCD sum rule, within its assumptions, delivers an essentially exact expectation value of the orbital angular momentum and of the orbital moment.
Highlights
In a recent publication [1], an interesting discussion is provided about the relationship between the orbital sum rule for XMCD (x-ray magnetic circular dichroism) [2,3], and the expression derived some years ago for the orbital magnetization of an independent-electron solid and some related sum rules [4]
This is highly relevant, as both results had considerable impact, well documented in the literature: the XMCD sum rule is very often applied to x-ray dichroic spectra of ferro- and paramagnetic systems, in order to extract element-specific orbital magnetic information, hardly obtainable by other means; and the modern theory of orbital magnetization is remarkable for its deep connections to geometrical and topological aspects of Bloch band theory
In the rest of this Comment, it is argued that the results of Ref. [1] have no bearing on the XMCD orbital sum rule, and, in particular, the claim that the XMCD orbital sum rule does not, even in principle, determine the orbital magnetization is not valid. It is based on the unjustified assumption that the XMCD sum rule is an approximation to the dichroic sum rules, as given by Souza and Vanderbilt, obtained by restricting the range of integration to a finite interval, or by considering only the contribution of a single band
Summary
In a recent publication [1], an interesting discussion is provided about the relationship between the orbital sum rule for XMCD (x-ray magnetic circular dichroism) [2,3], and the expression derived some years ago for the orbital magnetization of an independent-electron solid (the so-called modern theory of orbital magnetization) and some related sum rules [4].
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