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

TL;DR

This paper develops and benchmarks beyond-linear-spin-wave approaches for computing critical temperatures in 2D magnets with single-$Q$ order, focusing on single-ion anisotropy. It extends Holstein–Primakoff and Green's function formalisms, and introduces Callen decoupling (CD) for the anisotropy sector, yielding a hybrid RPA+CD method that preserves isotropic invariance and correctly handles $S= frac{1}{2}$ limits. Applied to CrI$_3$, NiPS$_3$, MnPS$_3$, FePS$_3$, and CrSBr with INS-derived exchange constants, RPA+CD generally yields the best agreement with experimental $T_c$ and magnon dispersions, especially when anisotropy is significant. The framework accommodates dipolar interactions and general spin interactions, providing a reliable route to predict thermal properties of 2D magnets and to improve material screening for spintronic applications.

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.

Figures (3)

• Figure 1: The magnon dispersion of monolayer CrI$_3$ calculated using bulk INS parameters from Ref. Chen-2021-cri3. A DM interaction of 0.09 meV in the out-of-plane direction opens a topological gap at the high symmetry point $\textrm{K}$. The inset shows the magnetic lattice of CrI$_3$.
• Figure 2: The magnon dispersion relations of monolayer MPS$_3$ (M=Ni, Fe, Mn) anti-ferromagnets with Heisenberg parameters taken from INS Wildes2018. The inset shows the magnetic lattices with the corresponding ground state magnetic order.
• Figure 3: The magnon dispersion of CrSBr calculated from the experimental parameters listed in tab. \ref{['table:2-J_n']}. The inset shows the real space arrangement of magnetic atoms.