Adiabatic magnon spectra with and without constraining field: Benchmark against an exact magnon spectrum

TL;DR

This paper benchmarks two methods for calculating adiabatic magnon spectra against exact solutions, revealing their relative accuracies across different coupling strengths and energy regimes.

Contribution

It provides a comparative analysis of the magnetic force theorem and constraining field approaches for adiabatic magnon spectra, highlighting their respective validity domains.

Findings

Constraining field method outperforms MFT at high energies and strong coupling.

Both methods are valid in low-energy, weak coupling regimes.

Benchmark against an exactly solvable model confirms the relative accuracy of each approach.

Abstract

The spectrum of magnon excitations in magnetic materials can be obtained exactly from the transverse dynamic magnetic susceptibility, which is however in practice numerically expensive. Many ab initio approaches therefore consider instead the adiabatic magnon spectrum, which assumes a separation of time scales of magnons and electronic excitations. There exist two alternative implementations for adiabatic magnon spectra: one based on the magnetic force theorem (MFT) and the other with a constraining field that enforces static non-collinear spin configurations. We benchmark both implementations against the exact magnon spectrum of an exactly solvable mean-field model. While both adiabatic methods are equally valid in the low magnon energy and strong Stoner coupling limits, we find that the constraining field method performs better than the MFT in both the cases of strong Stoner coupling and high magnon energies,while the MFT performs better for combined weak coupling and low magnon energies.