Suppression of local magnetic moment formation and paramagnetic exchange interactions in monolayer Fe$_3$GeTe$_2$

Abstract

We study the electronic and magnetic properties of monolayer Fe$_3$GeTe$_2$ within the DFT+DMFT approach in the paramagnetic phase. We argue that this compound is sufficiently far from the local magnetic moment limit, demonstrating non-linear temperature dependencies of the partial inverse local and uniform magnetic susceptibilities in a broad temperature range. We find that in the regime of moderate Coulomb interactions ($U=3-4$ eV), the iron atoms located above and below the Ge plane carry a substantial local magnetic moment ($μ\gtrsim 4.5 μ_B$), while the iron atom located within the Ge plane does not exhibit any pronounced magnetic moment. At the same time, the RKKY-type exchange interactions between these two symmetry-nonequivalent types of atoms turn out to be crucial for stabilizing long-range ferromagnetic order in Fe$_3$GeTe$_2$. The estimated spin-wave stiffness and Curie temperature are in good agreement with the experimental data, indicating that a dynamical treatment of electron correlations in Fe$_3$GeTe$_2$ is essential to properly describe its partially itinerant magnetic behavior.

Figures (7)

• Figure 1: Frequency dependence of partial densities of $d$ states of iron and p states of tellurium calculated within the DFT+DMFT approach at $\beta=10$ eV$^{-1}$ and $U=2$ eV and $4$ eV. The inset shows the crystal structure of Fe$_3$GeTe$_2$, numbers $r=1..3$ correspond to Fe$_r$ atoms in the unit cell.
• Figure 2: Frequency dependence of the imaginary parts of the electronic self-energies, corresponding to various $d$-orbital states at Fe$_{1,2}$ atoms (circles) and Fe$_3$ atoms (diamonds) calculated within the DFT+DMFT approach at $\beta=10$ eV$^{-1}$ and $U=2$ eV (a), $U=4$ eV (b).
• Figure 3: Temperature dependence of the inverse local susceptibilities of Fe$_{1,2}$ (left axis) and Fe$_3$ (right axis) atoms calculated within the DFT+DMFT approach. Dashed lines show the result of extrapolation.
• Figure 4: Temperature dependence of the inverse partial (open and closed symbols) and total (crossed symbols) uniform spin susceptibilities of Fe atoms calcualted within the DFT+DMFT approach with $U=2$ eV (squares) and $U=4$ eV (circles). Solid lines show the result of interpolation.
• Figure 5: (a) Momentum dependence of inequivalent exchange interactions $J_{\mathbf q}^{rr'}$ between various iron atoms $r,r'=1..3$ and (b) magnon dispersions $E_i(q)$ at $\beta=10$ eV$^{-1}$ and various values of the on-site Coulomb interaction $U$.