Rotational $g$ factors and Lorentz forces of molecules and solids from density-functional perturbation theory

TL;DR

This paper introduces a first-principles density-functional perturbation theory method to calculate gyromagnetic $g$ factors and Lorentz forces in molecules and solids, validated against experiments and applied to cubic SrTiO$_3$.

Contribution

It develops an efficient linear-response approach to compute magnetic coupling effects on atomic displacements in molecules and solids from first principles.

Findings

Accurately computed gyromagnetic $g$ factors for molecules, matching experimental data.

Demonstrated the method's application by calculating phonon mode splitting in SrTiO$_3$.

Validated the approach against previous theoretical and experimental results.

Abstract

Applied magnetic fields can couple to atomic displacements via generalized Lorentz forces, which are commonly expressed as gyromagnetic $g$ factors. We develop an efficient first-principles methodology based on density-functional perturbation theory to calculate this effect in both molecules and solids to linear order in the applied field. Our methodology is based on two linear-response quantities: the macroscopic polarization response to an atomic displacement (i.e., Born effective charge tensor), and the antisymmetric part of its first real-space moment (the symmetric part corresponding to the dynamical quadrupole tensor). The latter quantity is calculated via an analytical expansion of the current induced by a long-wavelength phonon perturbation, and compared to numerical derivatives of finite-wavevector calculations. We validate our methodology in finite systems by computing the gyromagnetic $g$ factor of several simple molecules, demonstrating excellent agreement with experiment and previous density-functional theory and quantum chemistry calculations. In addition, we demonstrate the utility of our method in extended systems by computing the energy splitting of the low-frequency transverse-optical phonon mode of cubic SrTiO$_3$ in the presence of a magnetic field.