Critical temperatures of two dimensional magnets beyond linear spin wave theory: application to CrI$_3$, MPS$_3$ (M=Ni, Mn, Fe) and CrSBr

Abstract

Magnetic anisotropy is crucial for sustaining long range magnetic order in two-dimensional materials (2D) and must be taken into account by any approximate scheme for calculating critical temperatures. While 2D ferromagnets have received significant attention with regard to predicting Curie temperatures, the treatment of 2D anti-ferromagnetism has largely been restricted to classical approaches, which typically underestimate Néel temperatures. The concept of anti-ferromagnetism can be regarded as a special case of single-$Q$ magnetic order, and for such systems the critical temperature can be calculated from the magnon dispersion using either Holstein-Primakoff (HP) bosonization or Green's function-based Random Phase Approximation (RPA). Here, we study the effects of single-ion anisotropy in general single-$Q$ systems in both the HP and RPA methods. In the case of RPA, we generalize the approach to include the Callen Decoupling (CD) correction, which has previously been shown to yield good agreement with experimental Curie temperatures for 2D ferromagnets. We compare the calculated critical temperatures of CrI$_3$ (uniaxial ferromagnet), MPS$_3$ (M=Ni, Mn, Fe) (uniaxial anti-ferromagnets) and CrSBr (triaxial ferromagnet) monolayers with experimental values and find that the Green's function-based methods are much more reliable than HP and that the CD decoupling appears to be more accurate than RPA if the single-ion anisotropy is large.