Intralayer antiferromagnetism in two-dimensional van der Waals magnet Fe$_3$GeTe$_2$

TL;DR

Fe$_3$GeTe$_2$ hosts competing magnetic interactions that challenge the simple ferromagnetic picture in two-dimensional vdW magnets. The study combines magnetization measurements, anomalous Hall effect in high-quality, inert-enviro encapsulated flakes, and first-principles DFT to map intralayer exchanges. It finds an intra-layer AFM coupling between Fe$^{+3}$–Fe$^{+3}$ moments and an FM coupling between Fe$^{+3}$–Fe$^{+2}$ moments, with a strong interlayer FM interaction, and explains two discrete magnetization-switching events observed in AHE through these sublattices. The extracted exchange constants, MAE, and the critical exponent $ eta = 0.316$ support a 3D Ising-like transition and reveal a nuanced, layer-resolved magnetic order that informs vdW spintronic device design.

Abstract

For the van der Waals magnet Fe$_3$GeTe$_2$, although a ferromagnetic ground state has been reported, there are also reports of complex magnetic behavior suggesting coexistence of ferromagnetism and antiferromagnetism due to the intricate interaction between Fe$^{+3}$ and Fe$^{+2}$ ions in this system. The exact nature of the interactions and the origin of antiferromagnetism are still under debate. Here, we report the observation of signature of ferromagnetic and antiferromagnetic couplings between different Fe-ions in the anomalous Hall effect measured for devices of mechanically exfoliated Fe$_3$GeTe$_2$ nano-flakes of thicknesses ranging from\,$\sim$\,15-20 layers. The temperature-dependent anomalous Hall effect data reveal two sharp step-like switchings at low temperature ($T\lesssim150\,$K). Our detailed analyses suggest the step-like sharp switchings in anomalous Hall resistance are due to the magnetization reversal behavior of different Fe-ions in individual layers of Fe$_3$GeTe$_2$. The experimental results can be explained by considering an intra-layer antiferromagnetic coupling between Fe$^{+3}$ and Fe$^{+3}$ ions, whereas intra-layer ferromagnetic coupling between Fe$^{+3}$ and Fe$^{+2}$ in the system. Our experimental results and the analyses are supported by the first-principles calculations for energetics and intralayer as well as interlayer exchange coupling constants.

Figures (7)

• Figure 1: Crystal structure and device fabrication of FGT-3. (a) The crystal structure of a bilayer FGT-3. Monolayer FGT-3 contains two types of Fe atoms, Fe$^{+3}$ and Fe$^{+2}$, at different sites. (b) The X-ray diffraction pattern of FGT-3 single crystal. (c) Schematic diagram of the device geometry (top panel). The optical micrograph of fabricated FGT-3/hBN device (bottom panel). (d) Raman spectra of FGT-3 single crystal (black) & the nanoflake of FGT-3 device (red).
• Figure 2: (a) The magnetization at different applied fields ranging from 5 mT to 100 mT showing the thermo-hysteresis between FCC & FCW curves. The top and bottom right insets indicate the zoomed $M$-$T$ curve at the field of 5 mT and the irreversibility temperature ($T_\mathrm{ir}$) at different applied fields, respectively. (b) ZFC curves at various applied magnetic fields showing a kink near 160 K. Inset shows the derivative of magnetization at 5 mT, indicating the $T_\mathrm{C}$ = 198.6 K.
• Figure 3: The magneto-transport behavior of FGT-3/hBN device. (a) M-H of few-layer flakes and bulk single crystal of FGT-3 at T = 2 K. (b) The temperature-dependent resistivity of a few-layer ($\sim$ 20 layers) FGT-3 device. (Inset) The derivative of the resistivity curve showing the $T_\mathrm{C}$ of 196 K. (c) Anomalous Hall effect of a $\sim$ 20 layers FGT-3 device at T = 2 K. (d) The temperature evolution of the anomalous Hall behavior of the FGT-3 device.
• Figure 4: (a) Temperature dependence of anomalous Hall resistance ($R_{\rm{xy}}$) at saturation field. The red curve is the critical exponent power law equation fit, where $\beta$ is the critical exponent. (b) $T$- dependence of the switching fields at first switching ($B_{\rm{SW1}}$) and second switching ($B_{\rm{SW2}}$). (Inset) $T$- dependence of the ratio $B_{\rm{SW1}}/B_{\rm{SW2}}$ (top) and r = $\Delta\,R_{\rm{xy}}\rm{(SW1)}/\Delta\,R_{\rm{xy}}\rm{(SW1)}$ (bottom). Here $\Delta R_\mathrm{{xy}(SW1,2)}$ represent the change in $R_\mathrm{xy}$ at SW1 and SW2, respectively.
• Figure 5: The spin polarized electronic band structure of Bulk FGT, (a) & (b) spin-up and spin-down channels, respectively. Panels (c) & (d) The atom-projected and orbital-projected density of states, respectively. The Fermi level is set to zero.