Tuning valley splitting and magnetic anisotropy of multiferroic CuMP2X6 (M=Cr,V;X=S,Se) monolayer

Abstract

Monolayer $\mathrm{Cu}M{\mathrm{P}}_{2}{X}_{6}$ $(M=\mathrm{Cr},\mathrm{V};X=\mathrm{S},\mathrm{Se})$ has been attracting increasing attention due to the ferromagnetism derived from the indirect exchange interaction between Cr (V) atoms and the ferroelectricity originating from the spontaneous displacement of Cu atoms. Using first-principles calculations, we predicted the intrinsic valley splittings and anomalous valley Hall effect in $\mathrm{Cu}M{\mathrm{P}}_{2}{X}_{6}$ monolayers. In addition, the valley splittings and Berry curvature are independent of the orientation of out of plane (OOP) ferroelectric polarization, which makes it a promising storage device with dual degrees of freedom in ferroelectric polarization and ferrovalleys. Due to the variations in the energy of the spin-dependent valence-band maximum (VBM) and orbital compositions of the valleys, the magnitude of valley splitting at VBM can be effectively tuned by the biaxial strain and external electric field. Large OOP magnetic anisotropy can be obtained by changing the energy and occupation (unoccupation) states of $d$ orbital compositions through strain and charge doping, respectively, and the magnetic anisotropy of $\mathrm{Cu}M{\mathrm{P}}_{2}{X}_{6}$ increases with increasing tensile biaxial strain from \ensuremath{-}5% to 5%. Our research results are expected to tune the valley splittings and magnetic anisotropy of $\mathrm{Cu}M{\mathrm{P}}_{2}{X}_{6}$ and to help understand the physical mechanism.