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

Monolayer (ML) NiCl 2 exhibits a strong biquadratic exchange interaction between the first neighboring magnetic atoms ( B 1 ), 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 NiCl 2 . However, they neither point out the role of B 1 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 B 1 is equivalent to half of J 3 in Heisenberg linear interactions and that the positive B 1 partially counteracts the negative J 3 's impact on the spin spiral to make the ML NiCl 2 ferromagnetic. The comparatively small J 3 + 1/2 B 1 from the spin spiral led us to believe that J 3 could be substituted by B 1 , 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.