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 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 ( Δ E ), 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 , for comparison, via LSWT. Our results show that TDDFPT + U and the Heisenberg model based on Δ E -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.