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

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.

💡 Research Summary

This paper presents a systematic benchmark of three state‑of‑the‑art first‑principles techniques for calculating magnetic exchange interactions and magnon dispersions in the prototypical transition‑metal oxides NiO and MnO. All calculations are performed on the same LSDA+U ground state, with Hubbard U parameters obtained self‑consistently from density‑functional perturbation theory (U = 6.26 eV for Ni 3d and 4.29 eV for Mn 3d). The three approaches are: (i) the four‑state energy‑mapping method (ΔE), which directly extracts isotropic exchange constants J₍ᵢⱼ₎ from total‑energy differences of four spin configurations in a supercell; (ii) the infinitesimal‑rotation method based on the magnetic force theorem (MFT or IRM), which computes J₍ᵢⱼ₎ from the response of the single‑particle Kohn‑Sham spectrum to infinitesimal spin rotations, using maximally‑localized Wannier functions to construct a tight‑binding Hamiltonian; and (iii) time‑dependent density‑functional perturbation theory with Hubbard U (TDDFPT+U), which evaluates the dynamical spin susceptibility via the Liouville‑Lanczos algorithm and obtains magnon energies directly, fitting them afterwards with linear spin‑wave theory (LSWT) to extract effective J₍ᵢⱼ₎.

Technical details are carefully aligned: Quantum ESPRESSO v7.2 is used for all ground‑state and ΔE/MFT calculations, with a 12 × 12 × 12 k‑point mesh for the four‑atom AF‑II rhombohedral cell, plane‑wave cutoffs of 80 Ry (wavefunctions) and 320 Ry (charge), and scalar‑relativistic norm‑conserving pseudopotentials. Structural relaxations include Hubbard‑force contributions, yielding lattice parameters a = 5.03 Å, α = 33.65° for NiO and a = 5.32 Å, α = 34.16° for MnO. For TDDFPT+U, a 12 × 12 × 12 k‑mesh is retained, and 8000 Lanczos iterations are performed to achieve convergence of the spin‑susceptibility spectra.

The ΔE method produces nearest‑neighbor exchange constants that, when inserted into a Heisenberg Hamiltonian and solved with LSWT, reproduce the experimental magnon branches measured by inelastic neutron scattering with high fidelity. In particular, the finite magnon gap at the Brillouin‑zone M point is accurately captured for both compounds, and the overall bandwidth matches the data within a few percent. The TDDFPT+U approach yields magnon dispersions that are virtually indistinguishable from the ΔE‑based LSWT results; fitting these spectra back to a Heisenberg model gives exchange parameters that differ by less than 5 % from the ΔE values, confirming the internal consistency of the susceptibility‑based method.

In contrast, the MFT‑derived exchange constants lead to magnon dispersions that systematically deviate from experiment: the bandwidth is underestimated for NiO and over‑estimated for MnO, and the M‑point gap is either too small or absent. The authors attribute these discrepancies to the sensitivity of the MFT implementation to the quality of the Wannier functions (centeredness, symmetry preservation) and to the inherent approximation of replacing the total‑energy change by the change in single‑particle eigenvalues. Recent literature has highlighted similar issues, suggesting that MFT can be unreliable for strongly correlated insulators unless the Wannier construction is meticulously controlled.

Overall, the study demonstrates that (1) when a consistent LSDA+U ground state is used, the ΔE energy‑mapping and TDDFPT+U susceptibility approaches provide quantitatively accurate exchange interactions and magnon spectra for NiO and MnO; (2) the MFT/IRM method, while computationally attractive, may suffer from implementation‑specific errors that limit its predictive power for such systems. The work thus establishes TDDFPT+U as a robust, fully first‑principles route to magnetic excitations in correlated oxides, and validates the traditional ΔE mapping as a reliable, low‑cost alternative. These findings are highly relevant for the design of spintronic and magnonic devices, where accurate prediction of spin‑wave properties is essential. Future extensions could incorporate spin‑orbit coupling, anisotropic exchange, and magnon‑phonon coupling, leveraging the same unified LSDA+U + TDDFPT framework.