Hematite is a canted antiferromagnetic insulator, promising for applications in spintronics.
Here we present ab initio calculations of the tensorial exchange interactions of hematite
and use them to understand its magnetic properties by parametrizing a semiclassical
Heisenberg spin model. Using atomistic spin dynamics simulations, we calculate the
equilibrium properties and phase transitions of hematite, most notably the Morin transition.
The computed isotropic and Dzyaloshinskii-Moriya interactions result in a Neel temperature
and weak ferromagnetic canting angle that are in good agreement with experimental
measurements. Our simulations show how dipoledipole interactions act in a delicate
balance with first and higher-order on-site anisotropies to determine the material's
magnetic phase. Comparison with spin-Hall magnetoresistance measurements on a hematite
single crystal reveals deviations of the critical behavior at low temperatures. Based
on a mean-field model, we argue that these differences result from the quantum nature
of the fluctuations that drive the phase transitions.
