Effect of biquadratic magnetic exchange interaction in the 2D antiferromagnets MPS₃ (M = Mn, Fe, Co, Ni)

The two-dimensional van der Waals (vdW) materials MPS₃ (M = Mn, Fe, Co, Ni) display antiferromagnetic ordering of the magnetic moments at the transition metal ions. The possibility to exfoliate thin layers that preserve the magnetic order makes these materials interesting for numerous applications in devices that require integration of flexible patches of magnetic materials, e. g. in antiferromagnetic spintronics. Hence, an improved understanding of their magnetic properties is desirable. Here, we parameterize spin Hamiltonians for a monolayer of all four materials of this class using density functional theory plus Hubbard U calculations. We provide a step-by-step guide for calculating the magnetic exchange interactions and magnetic anisotropy energy using the (non-) collinear DFT+U (+ SOC) approach with a suitably chosen U for each material. It is found that the biquadratic interactions gain in importance while moving through the 3d series. Retaining the leading terms of a Holstein-Primakoff-transformed spin Hamiltonian, the magnon spectra are calculated. While MnPS₃ is found to be an almost isotropic antiferromagnet with a tiny gap, the biquadratic interaction opens an increasingly wider gap for FePS₃, CoPS₃ and NiPS₃. In line with this observation, Monte Carlo simulations demonstrate that the biquadratic interactions contribute to a systematic rise in the Neel temperature from FePS₃ to NiPS₃.