Absorption of diffusive spin current in surface and bulk states of a topological insulator

We report the absorption of a diffusive spin current in a bulk-carrier compensated topological insulator: ${\mathrm{Sn}}_{0.02}-{\mathrm{Bi}}_{1.08}{\mathrm{Sb}}_{0.9}{\mathrm{Te}}_2\mathrm{S}$ (Sn-BSTS). By injecting spins into a Sn-BSTS crystal from a ferromagnetic metal using spin pumping, we found that the magnetic damping of the ferromagnetic layer is enhanced due to the absorption of the spin current in the surface and bulk states of the topological insulator. We found that the damping enhancement depends critically on temperature, which allows us to disentangle the spin absorption in the surface and bulk states, owing to the nearly perfect carrier compensation in the bulk part at low temperature. Our results show that the absorption of the spin current is dominated by the surface state of the Sn-BSTS crystal at low temperature, whereas the spin absorption in the surface state is comparable to that in the bulk state near room temperature. The coexistence of the spin absorption in the surface and bulk states has been demonstrated in two different systems, where the surface state is coupled with the dynamical magnetization through the diffusive spin current or exchange coupling. These results will be essential for quantitative understanding of the spin absorption and spin-charge conversion due to the spin-momentum locked surface state of topological insulators.

Figure 1

(a) Temperature ($T$) dependence of the in-plane resistivity (${\rho }_{\text{in}}$) for the ${\mathrm{Sn}}_{0.02}-{\mathrm{Bi}}_{1.08}{\mathrm{Sb}}_{0.9}{\mathrm{Te}}_2\mathrm{S}$ (Sn-BSTS) samples with different thicknesses $t$. The thickness $t$ of the samples are $62\mu \mathrm{m}$ (red), $21\mu \mathrm{m}$ (blue), $8\mu \mathrm{m}$ (black). (b) A schematic illustration of the Py/Cu/Sn-BSTS heterostructure. The size of the Sn-BSTS crystal is $2\text{mm}\times 4\text{mm}$ and that of the Py/Cu layer is $1\text{mm}\times 3\text{mm}$. (c) A schematic illustration of the experimental setup. The sample was placed on the coplanar waveguide for the microwave absorption measurement. The sample and waveguide are electrically disconnected by the insulating sheet.

Figure 2

(a) Magnetic field $H$ dependence of microwave transmittance ${\left|S_{21}\right|}^2$ for the Py/Cu/Sn-BSTS layer at the microwave frequency of $f=6.0$ GHz at various temperatures. The red colored areas represent FMR. (b) Microwave excitation frequency $f$ dependence of the half maximum half width field $\mathrm{\Delta }H$ at $T=60\mathrm{K}$. The red solid circles are the experimental data for the Py/Cu/Sn-BSTS layer and the blue solid circles are the experimental data for the Py layer. The red and blue solid lines are the linear fit to the experimental data.

Figure 3

(a) $T$ dependence of the magnetic damping constant $\alpha$ for the Py/Cu/Sn-BSTS heterostructure (red solid circles) and the Py layer (blue solid circles). (b) $T$ dependence of the additional damping constant $\mathrm{\Delta }\alpha$ for the Py/Cu/Sn-BSTS and Py/Sn-BSTS heterostructures. The solid circles are the experimental data of the additional damping constant $\mathrm{\Delta }\alpha ={\alpha }_{\mathrm{F}}/\mathrm{N}/\mathrm{TI}-{\alpha }_{\mathrm{F}}$, where ${\alpha }_{\mathrm{F}}/\mathrm{N}/\mathrm{TI}$ and ${\alpha }_{\mathrm{F}}$ are the magnetic damping constant for the Py/Cu/Sn-BSTS heterostructure and the Py film, respectively. The open circles are the experimental data of the additional damping constant $\mathrm{\Delta }\alpha ={\alpha }_{\mathrm{F}}/\mathrm{TI}-{\alpha }_{\mathrm{F}}$, where ${\alpha }_{\mathrm{F}}/\mathrm{TI}$ is the magnetic damping constant for the Py/Sn-BSTS heterostructure. (c) $T$ dependence of the magnetic damping constant $\alpha$ for the Py/Sn-BSTS heterostructure (red solid circles) and the Py layer (blue solid circles).