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

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.

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