Tuning magnetic anisotropy in a Fe5GeTe2 monolayer through doping and strain

Controlling magnetic anisotropy energy (MAE) in two-dimensional ferromagnetic materials is crucial for designing novel spintronic devices. Using first-principles calculations, we systematically investigate the magnetic properties of monolayer ${\mathrm{Fe}}_{5}{\mathrm{GeTe}}_{2}$ (F5GT) under two scenarios: (I) Co and Ni doping and (II) compressive and tensile strains. Our results show that the F5GT monolayer exhibits a weak in-plane MAE, which can be significantly enhanced by Co doping. Additionally, a $1%$ compressive strain switches the magnetic easy axis from in plane to out of plane, while $4%$ compressive strain can further enhance the out-of-plane MAE. Spin-orbit coupling matrix analysis reveals that the enhancement of in-plane MAE in Co-doped F5GT arises from changes in $\ensuremath{\langle}{\mathit{p}}_{x}|{L}_{z}|{\mathit{p}}_{y}\ensuremath{\rangle}$ of Te and $\ensuremath{\langle}{\mathit{d}}_{xy}|{L}_{z}|{\mathit{d}}_{{x}^{2}+{y}^{2}}\ensuremath{\rangle}$ of Fe(2) and Fe(3). The effect of compressive strain is primarily attributed to a substantial increase in the positive contribution from $\ensuremath{\langle}{\mathit{d}}_{xy}|{L}_{z}|{\mathit{d}}_{{x}^{2}+{y}^{2}}\ensuremath{\rangle}$ of Fe(1).