Numerical analysis of XMCD sum rules at the $L$-edge: when do they fail?

TL;DR

This study assesses the accuracy of XMCD sum rules in ultrafast spin dynamics, finding they are valid under typical conditions but fail with intense or long pulses due to charge transfer effects.

Contribution

It provides a detailed numerical analysis of when XMCD sum rules are valid or fail during laser-induced spin dynamics using TD-DFT simulations.

Findings

XMCD sum rules agree with direct calculations for typical pump pulses

Sum rules fail with short, intense, or long-duration pulses

Failures occur when charge is excited out of the $d$-band, invalidating assumptions

Abstract

In the highly non-equilibrium conditions of laser induced spin dynamics magnetic moments can only be obtained from the spectral information, most commonly from the spectroscopy of semi-core states using the so-called x-ray magnetic circular dichroism (XMCD) sum rules. The validity of the these sum rules in tracking femtosecond spin dynamics remains, however, an open question. Employing the time dependent extension of density functional theory (TD-DFT) we compare spectroscopically obtained moments with those directly calculated from the TD-DFT densities. We find that for experimentally typical pump pulses these two very distinct routes to the spin moment are, for Co and Ni, in excellent agreement, validating the experimental approach. However, for short and intense pulses or high fluence pulses of long duration the XMCD sum rules fail, with errors exceeding 50\%. This failure persists only during the pulse and occurs when the pump pulse excites charge out of the $d$-band and into $sp$-character bands, invalidating the semi-core to $d$-state transitions assumed by the XMCD sum rules.