A deep investigation of NiO and MnO through the first principle calculations and Monte Carlo simulations

TL;DR

This paper combines first-principles DFT+$U$ calculations and Monte Carlo simulations to investigate the magnetic properties of NiO and MnO, focusing on exchange interactions and temperature-dependent behaviors.

Contribution

It introduces a method to accurately estimate exchange and biquadratic interactions from DFT+$U$ and demonstrates the importance of quantum corrections in MC simulations.

Findings

Biquadratic interactions modify the order parameter but not the Néel temperature.

At least twice as many magnetic configurations are needed to accurately estimate exchange parameters.

Quantum corrections are necessary for fair comparison between classical MC and experimental results.

Abstract

In this study, we use Hubbard-Corrected density functional theory (DFT+$U$) to derive spin model Hamiltonians consisting of Heisenberg exchange interactions up to the fourth nearest neighbors and bi-quadratic interactions. We map the DFT+$U$ results of several magnetic configurations to the Heisenberg spin model Hamiltonian to estimate Heisenberg exchanges. We demonstrate that the number of magnetic configurations should be at least twice the number of exchange parameters to estimate exchange parameters correctly. To calculate biquadratic interaction, we propose specific non-collinear magnetic configurations that do not change the energy of the Heisenberg spin model. We use classical Monte Carlo (MC) simulations to evaluate DFT+$U$ results. We obtain the temperature dependence of magnetic susceptibility and specific heat to determine the Curie-Weiss and N\'eel temperatures. The MC simulations reveal that although the biquadratic interaction can not change the N\'eel temperature, it modifies the order parameter. We indicate that for a fair comparison between classical MC simulations and experiments, we need to consider the quantum effect by applying $(S+1)/S$ correction in classical MC simulations.