Phase transition and magnetic coupling in NbOI$_2$ monolayer

The NbOI$_2$ monolayer has been obtained recently through mechanical exfoliation and exhibits highly in-plane anisotropic electrical and optical properties [1]. It is also found to be a ferroelectric material with ultra-strong second-harmonic generation [2] and huge piezoelectric responses [3]. To further promote the application of two-dimensional NbOI$_2$, we investigate the structural phase transition dynamics and the resulting changes in ferroelectric and magnetic properties. The NbOI$_2$ monolayer possesses a small Young's modulus of ~80 N/m and an in-plane Poisson's ratio less than 0.1. There exists a structural transition along with the transition from a non-magnetic state to an antiferromagnetic state under the uniaxial strain. Based on the anisotropic Heisenberg model, the Néel temperature of the monolayer NbOI$_2$ is predicted to be 43 K, and the magnetic susceptibility has a valley at 10 K. The anisotropy of magnetic exchange-coupling strength along two orthogonal lattice vectors is further analyzed, and we provide a clear physical picture to understand these phenomena. This work elucidates the microcosmic mechanisms in the NbOI$_2$ monolayer and promotes its applications in future flexible electronics and multiferroics-based memory devices.