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Monolayer MnO$_2$ is one of the few predicted two-dimensional (2D)ferromagnets that has been experimentally synthesized and is commerciallyavailable. The Mermin-Wagner theorem states that magnetic order in a 2Dmaterial cannot persist unless magnetic anisotropy (MA) is present andperpendicular to the plane, which permits a finite critical temperature.Previous computational studies have predicted the magnetic ordering and Curietemperature of 2D MnO$_2$ with DFT+U (Density Funtional Theory + Hubbard Ucorrection), with the results having a strong dependence on the Hubbard Uparameter. Diffusion Monte Carlo (DMC) is a correlated electronic structuremethod that has had demonstrated success for the electronic and magneticproperties of a variety of 2D and bulk systems since it has a weaker dependenceon the starting Hubbard parameter and density functional. In this study, weused DMC and DFT+U to calculate the magnetic properties of monolayer MnO$_2$.We found that the ferromagnetic ordering is more favorable thanantiferromagnetic and determined a statistical bound on the magnetic exchangeparameter ($J$). In addition, we performed spin-orbit MA energy calculationsusing DFT+U and using our DMC and DFT+U parameters along with the analyticalmodel of Torelli and Olsen, we estimated an upper bound of 28.8 K for thecritical temperature of MnO$_2$. These QMC results intend to serve as anaccurate theoretical benchmark, necessary for the realization and developmentof future 2D magnetic devices. These results also demonstrate the need foraccurate methodologies to predict magnetic properties of correlated 2Dmaterials.

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