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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi>d</a:mi> </a:math> 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 <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mi>DFT</b:mi> <b:mo>+</b:mo> <b:mi>U</b:mi> </b:mrow> </b:math> ground state with Hubbard <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mi>U</c:mi> </c:math> values obtained from density-functional perturbation theory. Two methods extract exchange parameters directly: one via total-energy differences using the four-state mapping ( <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mi mathvariant="normal">Δ</d:mi> <d:mi>E</d:mi> </d:mrow> </d:math> ), 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 <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mi>U</f:mi> </f:math> ( <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:mi>TDDFPT</g:mi> <g:mo>+</g:mo> <g:mi>U</g:mi> </g:mrow> </g:math> ), yields magnon dispersions directly from the dynamical spin susceptibility, with exchange parameters fitted , for comparison, via LSWT. Our results show that <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mrow> <h:mi>TDDFPT</h:mi> <h:mo>+</h:mo> <h:mi>U</h:mi> </h:mrow> </h:math> and the Heisenberg model based on <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mrow> <i:mi mathvariant="normal">Δ</i:mi> <i:mi>E</i:mi> </i:mrow> </i:math> -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.