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

Deepak Dhariwal, Michael R. von Spakovsky, William T. Reynolds

TL;DR

This work addresses how cation distribution in spinel ferrites tunes electronic, magnetic, and vibrational excitations by integrating ab initio electronic structure with effective spin Hamiltonians and lattice dynamics. Using self-consistent linear-response DFT+$U$+$J$ to obtain on-site interactions, the authors map DFT energies to NN Heisenberg exchange constants $J_{AB}$, $J_{AA}$, and $J_{BB}$ and compute magnon spectra via LSWT, complemented by Phonopy phonon calculations on the same relaxed structures. Across Fe$_{3}$O$_{4}$, MnFe$_{2}$O$_{4}$, and Mn–Zn ferrites with varying A/B distributions, A–B superexchange remains the dominant, antiferromagnetic channel, while inversion and Zn/Mn distribution reshape the magnon and phonon spectra and tend to suppress magnetite-like half-metallicity in the DOS. The resulting mutually self-consistent spectra provide a configuration-aware dataset for fundamental understanding and modeling of ferrite excitations and loss mechanisms in high-frequency applications.

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.

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 work addresses how cation distribution in spinel ferrites tunes electronic, magnetic, and vibrational excitations by integrating ab initio electronic structure with effective spin Hamiltonians and lattice dynamics. Using self-consistent linear-response DFT++ to obtain on-site interactions, the authors map DFT energies to NN Heisenberg exchange constants , , and and compute magnon spectra via LSWT, complemented by Phonopy phonon calculations on the same relaxed structures. Across FeO, MnFeO, and Mn–Zn ferrites with varying A/B distributions, A–B superexchange remains the dominant, antiferromagnetic channel, while inversion and Zn/Mn distribution reshape the magnon and phonon spectra and tend to suppress magnetite-like half-metallicity in the DOS. The resulting mutually self-consistent spectra provide a configuration-aware dataset for fundamental understanding and modeling of ferrite excitations and loss mechanisms in high-frequency applications.

Abstract

We report first-principles calculations of the electronic structure, magnon excitations, and phonons in magnetite (FeO), jacobsite (MnFeO), and mixed manganese-zinc ferrites (Mn,Zn)FeO for representative compositions () 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, and , respectively, determined self-consistently by spin-polarized linear-response perturbations of the chosen correlated subspaces (including, where applied, the ligand 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.
Paper Structure (18 sections, 25 equations, 5 figures, 3 tables)

This paper contains 18 sections, 25 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Computational Procedure
  3. The Hubbard functional for correlated electrons
  4. Spin-polarized linear response
  5. Calculation of U and J
  6. The Heisenberg model
  7. Determining the exchange coupling constants
  8. Nearest-neighbor Hamiltonian on the spinel lattice:
  9. Bond-weighted sums valid for Fe$_3$O$_4$, Mn ferrite, and Mn-Zn ferrite:
  10. Energy mapping and closed-form expressions for $J_{AB}$, $J_{AA}$, and $J_{BB}$:
  11. Magnon calculations
  12. Phonon calculations
  13. Discussion
  14. Structural properties
  15. Electron density of states
  16. ...and 3 more sections

Figures (5)

  • Figure 1: Full unit cell of a spinel ferrite. Tetrahedral cations are shown in blue, octahedral cations in gray, and oxygen anions in red. The atomic radii are not shown to scale. The glass bonds show the nearest neighbor interactions.
  • Figure 2: Pseudo-ternary map with markers indicating studied compositions. The dashed segments indicate directions toward the excluded ZnFe2O4 end member.
  • Figure 3: Electron DOS for spinel ferrites with different cationic composition and configuration. (a) archetypal Fe3O4, (b) MnFe2O4 Config. 1 where all Mn atoms occupy A-sites of the spinel structure, (c) MnFe2O4 Config. 2 where half of the Mn atoms occupy A-sites and the other half occupy B-sites, (d) (Mn_0.5,Zn_0.5)Fe2O4 Config. 1 where all Zn & Mn atoms occupy A-sites, (e) (Mn_0.5,Zn_0.5)Fe2O4 Config. 2 where all Zn atoms occupy A-sites & all Mn atoms occupy B-sites, (f) (Mn_0.5,Zn_0.5)Fe2O4 Config. 3 where all Zn atoms occupy A-sites & the Mn atoms occupy half A-sites and half B-sites.
  • Figure 4: Magnon DOS for spinel ferrites with different cationic composition and configuration. (a) archetypal Fe3O4, (b) MnFe2O4 Config. 1 where all Mn atoms occupy A-sites of the spinel structure, (c) MnFe2O4 Config. 2 where half of the Mn atoms occupy A-sites and the other half occupy B-sites, (d) (Mn_0.5,Zn_0.5)Fe2O4 Config. 1 where all Zn & all Mn atoms occupy A-sites, (e) (Mn_0.5,Zn_0.5)Fe2O4 Config. 2 where all Zn atoms occupy A-sites & all Mn atoms occupy B-sites, (f) (Mn_0.5,Zn_0.5)Fe2O4 Config. 3 where all Zn atoms occupy A-sites & the Mn atoms occupy half A-sites and half B-sites.
  • Figure 5: Phonon DOS for spinel ferrites with different cationic compositions and configurations. (a) archetypal Fe3O4, (b) MnFe2O4 Config. 1 where all Mn atoms occupy A-sites of the spinel structure, (c) MnFe2O4 Config. 2 where half of the Mn atoms occupy A-sites and the other half occupy B-sites, (d) (Mn_0.5,Zn_0.5)Fe2O4 Config. 1 where all Zn & Mn atoms occupy A-sites, (e) (Mn_0.5,Zn_0.5)Fe2O4 Config. 2 where all Zn atoms occupy A-sites & all Mn atoms occupy B-sites, (f) (Mn_0.5,Zn_0.5)Fe2O4 Config. 3 where all Zn atoms occupy A-sites & the Mn atoms occupy half A-sites and half B-sites.