Germanene-Based Two-Dimensional Magnet with Tunable Properties

Abstract

Magnetic order engineering in two-dimensional Dirac systems is of great interest for theoretical and technological exploration. Up to now, the experimental advances in this field mostly concerned graphene monolayers. Here, we report a comprehensive study of a monolayer-thick germanene-like sheet in contact with gadolinium atoms. Direct observations supported by first-principles calculations reveal the fingerprints of the Dirac fermions in the electronic structure and noncollinear antiferromagnetism. The hybridization of the germanene layer with Gd atoms leads to a large and tunable gap in the Dirac states that carry a nonzero spin-Berry curvature. We discovered that cesium-induced controlled electron doping can switch the system into a ferromagnetic state and then back to the antiferromagnetism at saturated cesium monolayer limit. We explain these reversible magnetic transitions by the oscillatory behavior of the Ruderman-Kittel-Kasuya-Yosida interaction and suggest that this system could find application in magnetoelectronics and spintronics.

Keywords: 2D materials; ARPES; DFT; germanene; reversible AFM-FM transition.

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Electronic and topological properties of the GdGe₂monolayer. (a) Atomic structure of the GdGe₂ monolayer on the Ge(111) substrate in top and side view and its (b) LEED pattern with 1 × 1 reflexes marked by arrows. (c) ARPES spectrum along M̅-Γ̅-K̅-M̅-K̅′ high-symmetry directions taken at 14 K with 35 eV photon energy. (d) Calculated spectra of nonmagnetic phase of GdGe₂/Ge­(111). Size of blue circles corresponds to the weight of the states localized in the GdGe₂ layer. (e) ARPES spectrum along p(Γ̅-K̅). (f) Constant energy map taken at a binding energy of 1.7 eV. (g) Evolution of the constant energy map close to the K̅-M̅-K̅′ line as a function of the binding energy. The dashed lines highlight the contours of the π and π* bands. Details of the K̅ point Dirac state with (h) orbital and (i) out-of-plane (S _z ) spin projections. (j) Calculated spin Berry curvature (in logarithmic scale) in the vicinity of K̅ and K̅′ for equilibrium (low-buckled) and buckled germanene (as it separated from the GdGe₂) and substrate-supported GdGe₂ monolayer. (k) Spin-Berry curvature map around K̅-M̅-K̅′ path, assuming the E _F within the local K̅ gap.

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(a) ARPES spectra along K̅-M̅ as a function of the Cs doping with a focus on the Dirac cone and vHS. The data are shown as the second derivative of the photoemission intensity with respect to the energy. (b) ARPES spectra along M̅-Γ̅ (top row) and corresponding Fermi surfaces (bottom row) as a function of Cs doping. Horizontal dashed blue lines in the rightmost subpanels (1 ML Cs) mark the π*−σ* indirect gap (blue arrow); the dashed red lines and arrow show the hybridization gap at Γ̅. k _F marks the Fermi vector of the electron pocket related to the band. All ARPES data are taken at 14 K with 35 eV photon energy. (c) DFT spectrum of the nonmagnetic GdGe₂/Ge­(111) case with Cs on the surface. Gray color shows predominantly the Ge substrate bands, and the gradient lines changing a color from yellow to violet exhibit relative weights of GdGe₂ and Cs orbitals, respectively. Dashed blue line shows the low-energy band of the spectrum of the free-standing Cs monolayer. Dashed-line gray rectangles highlight the E(k _∥) areas shown in ARPES panels.

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(a) Magnetization curves measured at the Gd M₅ edge (1188.9 eV) with grazing (green) and normal (violet) incident light at 1.8 K, showing the absence of hysteresis. (b) Inverse magnetic susceptibility χ^–1 vs temperature T, extracted from XMCD data at magnetic field H = 0.3 T. (c) Energy splitting of the electron band at M̅ as a function of Cs coverage at 14 K. (d) Calculated relative energy difference of the Cs/GdGe₂/Ge­(111)- $(\sqrt{3}\times \sqrt{3})$ structures between noncollinear antiferromagnetic (ncl-AFM) and ferromagnetic (FM) coupling on the Gd sublattice with Cs coverage $\mathrm{\Theta }=0,\frac{1}{3},\frac{2}{3}$ , and 1 ML. (e) ARPES data for 0.85 ML Cs/GdGe₂ film (e) at 14 K and (f) at 55 K along M̅ – Γ̅. The data are shown as the second derivative of the photoemission intensity with respect to the energy. The inset shows the zoom on Γ̅ for prisine data. (g) Energy splitting of the electron band at M̅ as a function of temperature for 0.85 ML Cs/GdGe₂. (h) DFT spectrum for the FM_∥ state with 0.66 ML of Cs on the surface (two Cs atoms per $(\sqrt{3}\times \sqrt{3})$ cell) unfolded onto the (1 × 1) surface Brillouin zone of GdGe₂. (i) The same as (h) for nonmagnetic case. Gray arrows point spin splitting in (e) and (h) and its missing in (f) and (i). (j) Element-resolved DOS for nonmagnetic calculation. Blue dashed line in (i) and (j) marks the position of the experimental E _F. (k) Oscillatory term of the RKKY interaction as a function of Fermi vector.