Comparative study of magnetic exchange parameters and magnon dispersions in NiO and MnO from first principles

TL;DR

This work addresses reliable first-principles modeling of spin-wave excitations in NiO and MnO by benchmarking three approaches—$\Delta E$, IRM via MFT, and TDDFPT+$U$—on a common DFT+$U$ ground state with ab initio $U$ values. The study demonstrates that TDDFPT+$U$ and LSWT with $\Delta E$-derived exchange parameters reproduce neutron-scattering magnons well, while LSWT from MFT-derived parameters significantly overestimates energies, especially for MnO. A consistent inclusion of rhombohedral distortion and long-range couplings up to the fifth nearest neighbor is shown to be essential for stable and accurate magnon spectra. The results provide guidance on selecting and combining first-principles methods for reliable spin-wave predictions in transition-metal oxides, and lay groundwork for broader benchmarking across magnetic materials.

Abstract

Spin-wave excitations are fundamental to understanding the behavior of magnetic materials and hold promise for future information and communication technologies. Yet, modeling these accurately in transition-metal compounds remains challenging, starting from the self-interaction errors affecting localized and partially filled $d$-orbitals in density-functional theory (DFT) with (semi-)local functionals. In this work, we compare three advanced first-principles approaches for computing magnetic exchange parameters and magnon dispersions in NiO and MnO, all based on a common DFT+$U$ ground state with ab initio Hubbard $U$ values obtained from density-functional perturbation theory. Two methods extract exchange parameters directly: one via total-energy differences using the four-state mapping ($ΔE$), and the other via the magnetic force theorem (MFT) using infinitesimal spin rotations. Magnon dispersions are then obtained from a Heisenberg Hamiltonian through linear spin-wave theory (LSWT). The third approach, time-dependent density-functional perturbation theory with $U$ (TDDFPT+$U$), yields magnon dispersions directly from the dynamical spin susceptibility, with exchange parameters fitted a posteriori, for comparison, via LSWT. Our results show that TDDFPT+$U$ and the Heisenberg model based on $ΔE$-derived parameters align well with experimental neutron scattering data, whereas the MFT-based approach shows larger discrepancies, possibly due to some inherent approximations and limitations of the particular implementation used. This study benchmarks the accuracy of state-of-the-art first-principles techniques for spin-wave modeling and contributes to advancing reliable computational tools for the study and design of magnetic materials.

Figures (4)

• Figure 1: Face-centered cubic conventional unit cell of NiO and MnO with the AFII magnetic order. Transition-metal elements (Ni in NiO, or Mn in MnO) and O atoms are shown in purple and grey, respectively. Yellow and blue vertical thick arrows centered on atoms indicate the direction of the spin. The ferromagnetic (111) planes are depicted in transparent blue and yellow color. The Heisenberg exchange interaction parameters $J_1^+$, $J_1^-$, and $J_2$ are highlighted for selected atoms, with thin red arrows showing the atom pairs involved in these interactions. Rendered using VESTAMomma:2008.
• Figure 2: Magnon dispersions for (a) NiO and (b) MnO computed using LSWT with Heisenberg exchange parameters from MFT and $\Delta E$ are shown as blue and red solid lines, respectively (see Table \ref{['tab:exchange_param_from_DFT']} and Eq. \ref{['eq:heisenberg_hamiltonian_0']}). The TDDFPT+$U$ magnons dispersions are computed directly from the dynamical spin susceptibility and are shown as green dots. Experimental magnon dispersions, shown as black dots, are taken from inelastic neutron scattering measurements reported in Refs. Hutchings:1972Pepy:1974. The green and black dashed lines represent LSWT fits to the TDDFPT+$U$ and experimental data, respectively, based on the effective Heisenberg Hamiltonian of Eq. \ref{['eq:heisenberg_hamiltonian']}. All theoretical results are based on the same DFT+$U$ ground state.
• Figure 3: Effective exchange parameters for NiO within the minimal Heisenberg model [Eq. \ref{['eq:heisenberg_hamiltonian']}]: (a) $\mathcal{J}_1^+$, (b) $\mathcal{J}_1^-$, and (c) $\mathcal{J}_2$, all in meV, extracted by fitting magnon dispersions using the analytical LSWT expression (see Sec. S3 in the SM SupplementalMaterial) for four data sets: $(i)$ LSWT dispersions with MFT-derived $J_1$--$J_5$ values, $(ii)$ LSWT dispersions with $\Delta E$-derived $J_1$--$J_5$ values, $(iii)$ TDDFPT+$U$ magnon dispersions from the dynamical spin susceptibility, $(iv)$ Experimental data from Ref. Hutchings:1972. Theoretical results are shown as histograms, while experimental values are indicated by horizontal dashed lines. All theoretical results are based on the same DFT+$U$ ground state.
• Figure 4: Effective exchange parameters for MnO within the minimal Heisenberg model [Eq. \ref{['eq:heisenberg_hamiltonian']}]: (a) $\mathcal{J}_1^+$, (b) $\mathcal{J}_1^-$, and (c) $\mathcal{J}_2$, all in meV, extracted by fitting magnon dispersions using the analytical LSWT expression (see Sec. S3 in the SM SupplementalMaterial) for four data sets: $(i)$ LSWT dispersions with MFT-derived $J_1$--$J_5$ values, $(ii)$ LSWT dispersions with $\Delta E$-derived $J_1$--$J_5$ values, $(iii)$ TDDFPT+$U$ magnon dispersions from the dynamical spin susceptibility, $(iv)$ Experimental data from Ref. Pepy:1974. Theoretical results are shown as histograms, while experimental values are indicated by horizontal dashed lines. All theoretical results are based on the same DFT+$U$ ground state.