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

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.

Tuning the size of skyrmion by strain at the Co/Pt3 interfaces.

Based on density functional theory calculations, we elucidated the tunability of the atomic structures and magnetic interactions of Co/Pt3 interface (one layer of hcp(0001) Co and three layers of fcc(111) Pt) and thus the skyrmion sizes using strain. The dispersion relations of the spin spiral in the opposite directions, E(q) and E(-q), were evaluated based on generalized Bloch equations. Effective exchange coupling (EC) and Dzyaloshinsky-Moriya interaction (DMI) parameters between different neighbors J i and d i at different lattice constants were derived by fitting the resulting spin spiral dispersion E(q) to EC model with DMI and E(q)-E(-q) formula, respectively. We observed an increase in DMI and a significant decrease in EC with an increase in strain. Hence, the size of Néel-type skyrmions determined by the ratio of EC/DMI can be controlled by applying strain, leading to an effective approach to tailor the formation of skyrmion lattices by inducing slight structural modifications on the magnetic thin films.