Field-free coexistence of skyrmions and anti-skyrmions induced by higher-order interactions and biaxial strain in the NiI ₂ monolayer

The spin spiral (SS) state in monolayer (ML) NiI₂ presents a promising avenue for the exploration of two-dimensional multiferroics, but the mechanisms underlying this SS state and its effective modulation remain insufficiently understood. In this study, we employ first-principles calculations to reveal the major features and physical mechanisms governing the magnetism of ML-NiI₂ under in-plane strain, explicitly considering the effects of higher-order interactions (HOIs), which have been overlooked in prior research. Our findings identify the magnetic ground state of ML-NiI₂ as an SS state characterized by a propagation vector q = 0.23 and demonstrate that in-plane biaxial strain serves as an effective method for tuning the period and stability of the SS state, the frustrated ratio, magnetic anisotropy energy and the strength of HOIs. Notably, the strength of HOIs significantly increases under higher strain, particularly for the four-site-four-spin exchange interaction, which is substantial and crucial to the properties of ML-NiI₂. Additionally, through atomistic spin dynamics simulations, the coexistence of skyrmions and anti-skyrmions with diameters of at least 2 nm is achieved in ML-NiI₂via in-plane biaxial strain, without the necessity for an external magnetic field, which is more conducive to spintronic applications. The presented results establish ML-NiI₂ as a prospective candidate for next-generation spintronic devices and contribute to a deeper understanding of HOIs in two-dimensional magnets.