Dynamical response of noncollinear spin systems at constrained magnetic moments

TL;DR

This paper introduces a new linear-response framework for controlling local spin moments in noncollinear magnetic systems within time-dependent DFT, improving accuracy and efficiency in describing low-lying spin excitations.

Contribution

It develops a general methodological approach using Legendre transforms to parametrize and relate magnetic functionals at the linear-response level, enhancing response function calculations.

Findings

Identifies a correction to adiabatic formulations involving electron inertia effects.

Demonstrates the method on bulk CrI₃ and Cr₂O₃, revealing hybrid electro-magnon contributions.

Improves understanding of spin-lattice interactions in noncollinear magnets.

Abstract

Noncollinear magnets are notoriously difficult to describe within first-principles approaches based on density-functional theory (DFT) because of the presence of low-lying spin excitations. At the level of ground-state calculations, several methods exist to constrain the magnetic moments to a predetermined configuration, and thereby accelerate convergence towards self-consistency. Their use in a perturbative context, however, remains very limited. Here we present a general methodological framework to achieve parametric control over the local spin moments at the linear-response level. Our strategy builds on the concept of Legendre transform to switch between various flavors of magnetic functionals, and to relate their second derivatives via simple linear-algebra operations. Thereby, we can address an arbitrary response function at the time-dependent DFT level of theory with optimal accuracy and minimal computational effort. In the low frequency limit, we identify the leading correction to the existing adiabatic formulation of the problem [S. Ren \emph{et al.}, Phys. Rev. X {\bf 14}, 011041 (2024)], consisting in a renormalization of the phonon and magnon masses due to electron inertia. As a demonstration, we apply our methodology to the THz optical response of bulk CrI$_3$ and Cr$_2$O$_3$, where we identify contributions from hybrid (electro)magnons with mixed spin-lattice character.