The intrinsic ferromagnetism of two-dimensional (2D) MnO$_2$ revisited: A many-body Quantum Monte Carlo and DFT+U study

Monolayer MnO$_2$ is one of the few predicted two-dimensional (2D) ferromagnets that has been experimentally synthesized and is commercially available. The Mermin-Wagner theorem states that magnetic order in a 2D material cannot persist unless magnetic anisotropy (MA) is present and perpendicular to the plane, which permits a finite critical temperature. Previous computational studies have predicted the magnetic ordering and Curie temperature of 2D MnO$_2$ with DFT+U (Density Funtional Theory + Hubbard U correction), with the results having a strong dependence on the Hubbard U parameter. Diffusion Monte Carlo (DMC) is a correlated electronic structure method that has had demonstrated success for the electronic and magnetic properties of a variety of 2D and bulk systems since it has a weaker dependence on the starting Hubbard parameter and density functional. In this study, we used DMC and DFT+U to calculate the magnetic properties of monolayer MnO$_2$. We found that the ferromagnetic ordering is more favorable than antiferromagnetic and determined a statistical bound on the magnetic exchange parameter ($J$). In addition, we performed spin-orbit MA energy calculations using DFT+U and using our DMC and DFT+U parameters along with the analytical model of Torelli and Olsen, we estimated an upper bound of 28.8 K for the critical temperature of MnO$_2$. These QMC results intend to serve as an accurate theoretical benchmark, necessary for the realization and development of future 2D magnetic devices. These results also demonstrate the need for accurate methodologies to predict magnetic properties of correlated 2D materials.