Same effect of biquadratic exchange interaction and Heisenberg linear interaction in a spin spiral.

Abstract

Monolayer (ML) NiCl2 exhibits a strong biquadratic exchange interaction between the first neighboring magnetic atoms (B1), as demonstrated by the spin spiral model in J. Ni et al., Phys. Rev. Lett., 2021, 127, 247204. This interaction is crucial for stabilizing the ferromagnetic collinear order within the ML NiCl2. However, they neither point out the role of B1 nor discuss the dispersion relation from spin orbit coupling (SOC) in the spin spiral. As we have done in this work, these parameters might theoretically potentially be derived directly by fitting the calculated spin spiral dispersion relation. Here, we draw attention to the fact that B1 is equivalent to half of J3 in Heisenberg linear interactions and that the positive B1 partially counteracts the negative J3's impact on the spin spiral to make the ML NiCl2 ferromagnetic. The comparatively small J3 + 1/2B1 from the spin spiral led us to believe that J3 could be substituted by B1, yet it still exists and plays a crucial function in magnetic semiconductors or insulators. The dispersion relation, which we also obtain from SOC, displays weak antiferromagnetic behavior in the spin spiral.