Large magneto-optical effect and magnetic anisotropy energy in two-dimensional metallic ferromagnet Fe3GeTe2

The recent discovery of long-range magnetic orders in atomically thin semiconductors ${\mathrm{Cr}}_{2}{\mathrm{Ge}}_{2}{\mathrm{Te}}_{6}$ and $\mathrm{Cr}{\mathrm{I}}_{3}$ as well as metal ${\mathrm{Fe}}_{3}\mathrm{Ge}{\mathrm{Te}}_{2}$ has opened up exciting opportunities for fundamental physics of two-dimensional (2D) magnetism and also for technological applications based on 2D magnetic materials. To exploit these 2D metallic magnets, the mechanisms that control their physical properties should be well understood. In this paper, based on systematic first-principles density functional theory calculations, we study the magnetic anisotropy energy (MAE) and magneto-optical (MO) effects of ferromagnetic multilayers [mono-, bi-, tri-, tetra-, and pentalayer] and bulk ${\mathrm{Fe}}_{3}\mathrm{Ge}{\mathrm{Te}}_{2}$ as well as their connections with the underlying electronic structures of the materials. Firstly, all the considered ${\mathrm{Fe}}_{3}\mathrm{Ge}{\mathrm{Te}}_{2}$ structures are found to prefer the out-of-plane magnetization and have gigantic MAEs of $\ensuremath{\sim}3.0$ meV/f.u. This gigantic perpendicular anisotropy results from the large magnetocrystalline anisotropy energy (MCE), which is ten times larger than the competing magnetic dipolar anisotropy energy. The giant MCEs are attributed to the large Te ${p}_{x,y}$ orbital density of states near the Fermi level and also to the topological nodal point just below the Fermi level at the K points in the Brillouin zone. Secondly, 2D and bulk ${\mathrm{Fe}}_{3}\mathrm{Ge}{\mathrm{Te}}_{2}$ also exhibit strong MO effects with their Kerr and Faraday rotation angles being $\ensuremath{\sim}1.{0}^{\ensuremath{\circ}}$ and $\ensuremath{\sim}100 \mathrm{deg}/\ensuremath{\mu}\mathrm{m}$ in the visible-light frequency region, respectively. The strong MO Kerr and Faraday effects are found to result from the large MO conductivity (or strong magnetic circular dichroism) in these ferromagnetic materials. In particular, the calculated MO conductivity spectra are one order of magnitude larger than that of ${\mathrm{Y}}_{3}{\mathrm{Fe}}_{5}{\mathrm{O}}_{12}$. The calculated MO conductivity spectra are analysed in terms of the dipole-allowed optical transitions at high symmetry $\mathrm{\ensuremath{\Gamma}}$, K, and ${\mathrm{K}}^{\ensuremath{'}}$ points, which further indicate that atomically thin ${\mathrm{Fe}}_{3}\mathrm{Ge}{\mathrm{Te}}_{2}$ films with odd layer-number might exhibit anomalous ferrovalley Hall effect. All these interesting findings thus suggest that 2D and bulk ferromagnetic ${\mathrm{Fe}}_{3}\mathrm{Ge}{\mathrm{Te}}_{2}$ are promising materials for high-density MO and spintronic nanodevices.