Spin Hall effect in van der Waals ferromagnet Fe$_{5}$GeTe$_{2}$

Abstract

We investigate the spin Hall effect (SHE) in a van der Waals (vdW) ferromagnet Fe$_{5}$GeTe$_{2}$ (FGT) with a Curie temperature $T_{\rm C}$ of 310 K utilizing the spin-torque ferromagnetic resonance method. In synchronization with the emergence of the ferromagnetic phase resulting in the anomalous Hall effect (AHE), a noticeable enhancement in the SHE was observed below $T_{\rm C}$. On the other hand, the SHE shows a different temperature dependence from the AHE: the effective spin Hall conductivity is clearly enhanced with decreasing temperature unlike the anomalous Hall conductivity, reflecting the variation of band-structure accompanied by the complicated magnetic ordering of the FGT. The results provide a deep understanding of the SHE in magnetic materials to open a new route for novel functionalities in vdW materials-based spintronic devices.

Figures (4)

• Figure 1: (a) Crystal structure of FGT depicted by VESTA vesta. The top and side views of the crystal are illustrated on the left and right, respectively. The gray rectangle in the right panel represents a unit cell. Fe1 and Ge sites are 50% occupied. (b) Optical microscope image of FGT device for the Hall measurement. A current is applied to the in-plane direction and a magnetic field is applied to the out-of-plane direction as shown in the image. The scale bar corresponds to 10 $\rm{\mu}$m. (c) Anomalous Hall effect at 50 K. The definition of the anomalous Hall resistivity is also indicated. (d) Temperature dependence of magnetization measurement of the bulk sample. Black and gray lines show the in-plane ($H//ab$) and the out-of-plane ($H//c$) magnetization. $H//c$ is multiplied by 5 for the clarity. The magnetic state of FGT changes depending on the temperature region. The FM and PM regions correspond to the ferromagnetic and paramagnetic phases, respectively, while the FM’ region is defined as the region where the in-plane magnetization decreases with decreasing temperature. (e) Temperature dependence of the longitudinal resistivity (left axis) and the anomalous Hall resistivity (right axis) obtained from the thin film sample.
• Figure 2: (a) Schematic of ST-FMR device consisting of FGT(70)/Cu(5)/Ni-Fe(10). Magnetization $M$ precession of Ni-Fe, external magnetic field $H\rm{_{ext}}$, rf current $J\rm{^{C}_{rf}}$, rf magnetic field $H\rm{_{rf}}$, and spin current generated by the SHE in FGT $J\rm{^{S}_{rf}}$ are illustrated as arrows. (b) Schematic of the circuit of the ST-FMR measurement setup. (c) FMR spectra obtained with FGT(70)/Cu(5)/Ni-Fe(10) device. The frequency range is from 6 to 15 GHz. (d) FMR spectrum at $T = 300$ K and $f = 9$ GHz. The black dotted line is the best fit with Eq. (1). The green and blue lines show the symmetric and antisymmetric components of the black dotted curve, respectively. The yellow line shows the contribution from the Ni-Fe single layer.
• Figure 3: (a) Temperature dependence of the anomalous Hall angle for FGT device A (70 nm) and device B (60 nm). The same data as shown in Fig. 1(e) are used for device A. (b) Temperature dependence of the effective spin Hall angle for FGT devices C-E (60-70 nm). The same data as shown in Fig. 2 are used for device C. (c), (d) Temperature dependence of the anomalous Hall conductivity (c) and the effective spin Hall conductivity (d). (e), (f) The anomalous Hall conductivity (e) and the effective spin Hall conductivity (f) as a function of the longitudinal conductivity. The dotted lines in all figures indicate zero value.
• Figure 4: Relation between electrical conductivity $\sigma_{xx}$ and the effective spin Hall angle |$\theta^{\rm{eff}}_{\rm{SH}}$| for various spin Hall materials. We plot the results of device C as the green symbols and also green shaded area. Red, black, and yellow symbols are the results of 4$d$ and 5$d$ transition metals liu_prl_2011pai_apl_2012liu_science_2012, 3$d$ ferromagnets omori_prb_2019, and 2D materials song_natmater_2020zhao_prr_2020. The grey dotted line represents a fixed effective spin Hall conductivity, which is written as the product of |$\theta^{\rm{eff}}_{\rm{SH}}$| and $\sigma_{xx}$.The dotted line used $(\rm{\Omega m)}^{-1}$ as a unit.