Strong magneto-optical effect and anomalous transport in the two-dimensional van der Waals magnets FenGeTe2 ( n=3 , 4, 5)

Abstract

Two-dimensional ferromagnetic materials have recently been attracted much attention mainly due to their promising applications toward multifunctional devices, e.g., microelectronics, spintronics, and thermoelectric devices. Utilizing the first-principles calculations together with the group theory analysis, we systematically investigate the magnetocrystalline anisotropy energy, magneto-optical effect, and anomalous transport properties (including anomalous Hall, Nernst, and thermal Hall effects) of monolayer and bilayer ${\mathrm{Fe}}_{n}\mathrm{Ge}{\mathrm{Te}}_{2}$ ($n=3$, 4, 5). The monolayer ${\mathrm{Fe}}_{n}\mathrm{Ge}{\mathrm{Te}}_{2}$ ($n=3$, 4, 5) exhibits the out-of-plane, in-plane, and in-plane ferromagnetic orders with considerable magnetocrystalline anisotropy energies of $\ensuremath{-}3.17$, 4.42, and 0.58 meV/f.u., respectively. Ferromagnetic order is predicted in bilayer ${\mathrm{Fe}}_{4}\mathrm{Ge}{\mathrm{Te}}_{2}$ while antiferromagnetic order is preferred in bilayer ${\mathrm{Fe}}_{3}\mathrm{Ge}{\mathrm{Te}}_{2}$ and ${\mathrm{Fe}}_{5}\mathrm{Ge}{\mathrm{Te}}_{2}$. The group theory analysis reveals that in addition to monolayer ferromagnetic ${\mathrm{Fe}}_{n}\mathrm{Ge}{\mathrm{Te}}_{2}$ ($n=3$, 4, 5), the magneto-optical and anomalous transport phenomena surprisingly exist in bilayer antiferromagnetic ${\mathrm{Fe}}_{5}\mathrm{Ge}{\mathrm{Te}}_{2}$, which rare in realistic collinear antiferromagnets. If spin magnetic moments of monolayer and bilayer ${\mathrm{Fe}}_{n}\mathrm{Ge}{\mathrm{Te}}_{2}$ are reoriented from the in-plane to out-of-plane direction, then the magneto-optical and anomalous transport properties are enhanced significantly, presenting strong magnetic anisotropy. We also demonstrate that the anomalous Hall effect decreases with the temperature increases. The gigantic anomalous Nernst and thermal Hall effects are found in monolayer and bilayer ferromagnetic ${\mathrm{Fe}}_{n}\mathrm{Ge}{\mathrm{Te}}_{2}$, and the largest anomalous Nernst and thermal Hall conductivities, respectively, of $\ensuremath{-}3.31$ A/Km and 0.22 W/Km at 130 K are observed in bilayer ferromagnetic ${\mathrm{Fe}}_{4}\mathrm{Ge}{\mathrm{Te}}_{2}$. In particular, bilayer antiferromagnetic ${\mathrm{Fe}}_{5}\mathrm{Ge}{\mathrm{Te}}_{2}$ exhibits large zero-temperature anomalous Hall conductivity of 2.63 ${e}^{2}/h$ as well as anomalous Nernst and thermal Hall conductivities of 2.76 A/Km and 0.10 W/Km at 130 K, respectively. Our results suggest that two-dimensional van der Waals magnets ${\mathrm{Fe}}_{n}\mathrm{Ge}{\mathrm{Te}}_{2}$ ($n=3$, 4, 5) have great potential applications in magneto-optical devices, spintronics, and spin caloritronics.