Energy Eigenstates of Electrons, Magnons and Phonons in Fe$_3$O$_4$ (magnetite), MnFe$_2$O$_4$ (jacobsite), and mixed Mn-Zn ferrites

TL;DR

This study uses first-principles calculations to analyze the electronic, magnetic, and vibrational properties of various ferrite materials, providing a comprehensive computational approach for their characterization.

Contribution

It introduces a self-consistent DFT+U+J methodology combined with spin-wave theory to accurately predict excitation spectra in ferrites with different compositions and cation arrangements.

Findings

Computed electronic structures and magnetic exchange parameters.

Predicted magnon dispersion relations and densities of states.

Generated phonon spectra and vibrational densities of states.

Abstract

We report first-principles calculations of the electronic structure, magnon excitations, and phonons in magnetite (Fe$_3$O$_4$), jacobsite (MnFe$_2$O$_4$), and mixed manganese-zinc ferrites (Mn$_{x}$,Zn$_{1-x}$)Fe$_2$O$_4$ for representative compositions ($0\le x \le 1$) and A/B-site cation arrangements. Electronic structures are computed using density functional theory (DFT) augmented by rotationally invariant DFT+U+J, with on-site Hubbard and Hund's parameters, $U$ and $J$, respectively, determined self-consistently by spin-polarized linear-response perturbations of the chosen correlated subspaces (including, where applied, the ligand $2p$ subspace). A classical Heisenberg spin Hamiltonian is parameterized by mapping DFT+U+J total energies for multiple collinear spin configurations onto nearest-neighbor exchange couplings, which are then used to obtain magnon dispersions and magnon densities of states within linear spin-wave theory. Phonon spectra and densities of states are obtained from finite-displacement force constants and dynamical matrices computed on the same DFT+U+J-relaxed structures. Overall, the workflow provides a consistent, composition- and configuration-aware route to electronic, vibrational, and magnetic excitation spectra across the Mn/Zn ferrite space.