Inducing out-of-plane magnetic anisotropy by chemical substitutions in the multiferroic CuCrP 2 S 6 monolayer

Perpendicular magnetic anisotropy (PMA) has emerged as a key focus in spintronics due to its inherent stability against thermal fluctuations, scalability, endurance, and low switching current density, causing an ongoing search for new ways to control PMA. In this study, we predict an in-plane to out-of-plane transition in magnetic anisotropy orientation in the two-dimensional (2D) multiferroic material ${\mathrm{CuCrP}}₂{\mathrm{S}}₆$ (CCPS) upon isovalent doping with indium, based on first-principles calculations. The transition is triggered by a quasilinear increase in magnetocrystalline anisotropy (MCA) energy with In concentration in the mixed ${\mathrm{CuCr}}_{1\ensuremath{-}x}{\mathrm{In}}_x{\mathrm{P}}₂{\mathrm{S}}₆$ layer. Our calculations show that this increase in MCA energy results from two distinct and equally important contributions. The first contribution is purely structural in nature. It is the effect of a biaxial tensile strain acting on the CCPS units of the film caused by the increased in-plane lattice parameter upon the addition of In. The second contribution is a ``chemical effect'' due to the chemical substitutions at fixed geometry. We find it to be related to the decrease in the near-valence-edge density of states of the in-plane majority-spin $d$ orbitals of Cr atoms through hybridization changes produced by isovalent doping with a nonmagnetic element. Based on the analysis of the underlying mechanisms, we extend our findings relative to the tuning of MCA energy towards more positive values to other nonmagnetic dopants, isovalent with ${\mathrm{Cr}}³⁺$ and of ionic radius larger than that of ${\mathrm{Cr}}³⁺$ in 2D CCPS and related metal thiophosphates.