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Dynamical Response of Noncollinear Spin Systems at Constrained Magnetic Moments

Miquel Royo1,* and Massimiliano Stengel1,2,†

  • *Contact author: mroyo@icmab.es
  • †Contact author: mstengel@icmab.es
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Phys. Rev. X 16, 011049 – Published 6 March, 2026

DOI: https://doi.org/10.1103/c68v-8tkb

Abstract

Noncollinear magnets are notoriously difficult to describe within first-principles approaches based on density-functional theory 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 toward 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 density-functional 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 et al., Phys. Rev. X 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 terahertz optical response of bulk CrI3 and Cr2O3, where we identify contributions from hybrid (electro)magnons with mixed spin-lattice character.

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Popular Summary

Accurately modeling the interactions between magnons, atomic vibrations, and electromagnetic fields is a significant challenge because the strong response of magnets at low energies often causes numerical instabilities in standard first-principles calculations. We addressed this by developing a theoretical framework that constrains local magnetic moments during the evaluation of a magnet’s linear response to external fields. This method eliminates problematic low-energy resonances and allows for fast, stable simulations, while exact mathematical relations are used to recover the physical behavior of the unconstrained system. We applied this approach to prototypical ferromagnetic and antiferromagnetic insulators, revealing how hybrid spin-lattice excitations determine their optical response in the terahertz and far-infrared regimes. Our findings provide a unified, nonadiabatic description of coupled spin and lattice dynamics that consistently accounts for magnetic effects from the electronic to the vibrational level. These results establish an efficient path for the predictive modeling of complex magnetic materials and the development of technologies based on ultrafast spin control.

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Phys. Rev. X 16, 011049– Published 6 March, 2026
  • Received 22 January 2025
  • Revised 5 December 2025
  • Accepted 27 January 2026
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