Exchange constants and spin waves of the orbital ordered, non-collinear spinel MnV$_2$O$_4$

TL;DR

This paper investigates the magnetic interactions and spin wave excitations in the orbital ordered, non-collinear spinel MnV$_2$O$_4$, using density functional theory and experimental data to identify the correct orbital order.

Contribution

The study combines first-principles calculations with spin-wave modeling to determine the orbital order and magnetic properties of MnV$_2$O$_4$, providing a comprehensive analysis of its magnetic excitations.

Findings

Good agreement with experimental spin waves for one orbital order

Identification of the correct orbital order among various proposals

Quantitative exchange constants and anisotropy parameters obtained

Abstract

We study the exchange constants of MnV$_2$O$_4$ using magnetic force theorem and local spin density approximation of density functional theory supplemented with a correction due to on-site Hubbard interaction U. We obtain the exchanges for three different orbital orderings of the Vanadium atoms of the spinel. We then map the exchange constants to a Heisenberg model with single-ion anisotropy and solve for the spin-wave excitations in the non-collinear, low temperature phase of the spinel. The single-ion anisotropy parameters are obtained from an atomic multiplet exact-diagonalization program, taking into effect the crystal-field splitting and the spin-orbit coupling. We find good agreement between the spin waves of one of our orbital ordered setups with previously reported experimental spin waves as determined by neutron scattering. We can therefore determine the correct orbital order from various proposals that exist in the literature.