Evaluation of spin diffusion length and spin Hall angle of the antiferromagnetic Weyl semimetal ${\mathrm{Mn}}_3\mathrm{Sn}$

The antiferromagnetic Weyl semimetal ${\mathrm{Mn}}_3\mathrm{Sn}$ has been shown to generate strong intrinsic anomalous Hall effect (AHE) at room temperature, due to large momentum-space Berry curvature from the time-reversal symmetry-breaking electronic bands of the Kagome planes. This prompts us to investigate intrinsic spin Hall effect, a transverse phenomenon with identical origin as the intrinsic AHE. We report inverse spin Hall effect experiments in nanocrystalline ${\mathrm{Mn}}_3\mathrm{Sn}$ nanowires at room temperature using spin absorption method, which enables us to quantitatively derive both the spin diffusion length and the spin Hall angle in the same device. We observed clear absorption of the spin current in the ${\mathrm{Mn}}_3\mathrm{Sn}$ nanowires when kept in contact with the spin transport channel of a lateral spin-valve device. We estimate spin diffusion length ${\lambda }_{s\left({\text{Mn}}_3\text{Sn}\right)}\sim 0.75$ $\pm$ 0.67 nm from the comparison of spin signal of an identical reference lateral spin valve without ${\mathrm{Mn}}_3\mathrm{Sn}$ nanowire. From inverse spin Hall measurements, we evaluate spin Hall angle ${\theta }_{\text{SH}}\sim 5.3$ $\pm$ 2.4 $\%$ and spin Hall conductivity ${\sigma }_{\text{SH}}\sim 46.99$ $\pm$ 20.63 $\left(\frac{\hslash }{e}\right){\left(\mathrm{\Omega }\mathrm{cm}\right)}^{-1}$. The estimated spin Hall conductivity agrees with both in sign and magnitude to the theoretically predicted intrinsic ${\sigma }_{\text{SH}}^{\text{int}}\sim 36$-96 ($\hslash /e$) (${\mathrm{\Omega }\mathrm{cm})}^{-1}$. We also observed anomalous Hall effect at room temperature in nano-Hall bars prepared at the same time as the spin Hall devices. Large anomalous Hall conductivity along with adequate spin Hall conductivity makes ${\mathrm{Mn}}_3\mathrm{Sn}$ a promising material for ultrafast and ultrahigh-density spintronics devices.

Figure 1

Magnetic field dependence of the anomalous Hall conductivity(${\sigma }_{xy}^{\text{AHE}}=-\frac{{\rho }_{xy}}{{\rho }_{xx}^2}$) measured at various temperatures between 150 to 300 K. Inset shows SEM picture of a ${\mathrm{Mn}}_3\mathrm{Sn}$ nano-Hall bar (width = 500 nm, thickness = 70 nm, length = 3900 nm) with measurement configuration.

Figure 2

Scanning electron microscopy (SEM) image of (a) spin Hall device (SHD) and (b) reference lateral spin valve device. The nonlocal and spin Hall measurement configuration are shown. In nonlocal measurement configuration, magnetic field ($H$) is applied in plane along the long easy axis of Py while in spin Hall measurement configuration $H$ is directed perpendicular (inplane) to it. (c) Resistivity of ${\mathrm{Mn}}_3\mathrm{Sn}$ nanowire in the spin Hall device as a function of temperature. (d) Nonlocal resistance $R_{\text{NL}}$ as a function of magnetic field for reference and spin Hall device measured at room temperature.

Figure 3

(a) Magnetic field dependence of Inverse spin Hall resistance $R_{\text{ISHE}}$ measured at room temperature. The inverse spin Hall resistance $R_{\text{ISHE}}$ saturates above $\pm 3000$ Oe when Py magnetization is aligned along applied magnetic field. The difference between positive and negative saturated $R_{\text{ISHE}}$ is called inverse spin Hall signal $2\mathrm{\Delta }{R}_{\text{ISHE}}$. (b) Anisotropic magnetoresistance (AMR) of the Py nanowire in the same device. The spin polarization direction $\vec{s}$ of the spin current $\overrightarrow{I_s}$ is determined by the magnetization direction of Py injector electrode.

Figure 4

X-ray diffraction scan of 50-nm ${\mathrm{Mn}}_3\mathrm{Sn}$ thin film with 2-nm-Ru seed layer (red) and bare Si/${\mathrm{SiO}}_2$ substrate (black). Bottom panel shows simulated x-ray diffraction pattern of ${\mathrm{Mn}}_3\mathrm{Sn}$ with all possible peaks indexed.

Figure 5

(a) Temperature dependence of resistance of ${\mathrm{Mn}}_3\mathrm{Sn}$ nanowire without postannealing. Nano-Hall bar prepared together with this nanowire did not show AHE at room temperature. (b)–(d) Temperature dependence of resistance of different types of nanowires obtained after annealing at 450 ${}^{\circ }\mathrm{C}$ and 500 ${}^{\circ }\mathrm{C}$ for 1 h. Nano-Hall bars prepared together with these nanowires showed AHE at room temperature.

Figure 6

COMSOL simulation result of current density in the shunt device. To determine $x, I$ = 500 $\mu A$ was passed through the ${\mathrm{Mn}}_3\mathrm{Sn}$ nanowire and voltages $V_w$ and $V_{wo}$ were measured from the simulation.

Figure 7

Variation of (a) spin Hall angle ${\theta }_{\text{SH}}$ and (b) spin Hall conductivity ${\sigma }_{\text{SH}}$ with shunting factor $x$ in the range 0.01 to 0.1. Note that $x$ = 0.1 is the maximum value of shunting factor reported [65] experimentally in these devices, with resistivity of spin Hall material of the order of $\sim 900$ $\mu \mathrm{\Omega }$ cm.