Spin to Charge Conversion at Room Temperature by Spin Pumping into a New Type of Topological Insulator: $\alpha$-Sn Films

We present results on spin to charge current conversion in experiments of resonant spin pumping into the Dirac cone with helical spin polarization of the elemental topological insulator (TI) $\alpha$-Sn. By angle-resolved photoelectron spectroscopy (ARPES), we first check that the Dirac cone (DC) at the $\alpha$-Sn (0 0 1) surface subsists after covering Sn with Ag. Then we show that resonant spin pumping at room temperature from Fe through Ag into $\alpha$-Sn layers induces a lateral charge current that can be ascribed to the inverse Edelstein effect by the DC states. Our observation of an inverse Edelstein effect length much longer than those generally found for Rashba interfaces demonstrates the potential of TIs for the conversion between spin and charge in spintronic devices. By comparing our results with data on the relaxation time of TI free surface states from time-resolved ARPES, we can anticipate the ultimate potential of the TI for spin to charge conversion and the conditions to reach it.

Figure 1

Edelstein and inverse Edelstein effect. (a),(b) Top: Energy dispersion surfaces of the 2D states at a Rashba interface (a) and Dirac dispersion cone of the surface or interface states of a topological insulator (b). Bottom: Fermi contours of Rashba states (a) with two contours with helical spin configurations of opposite chirality and TI surface or interface states (b). (c),(d) Edelstein effect: A flow of electrons along $x$ (${j_C}^{2\mathrm{D}(x)}<0$ in the figure) in Rashba (c) or TI (d) 2DEGs is associated with shifts $\mathrm{\Delta }k$ of the Fermi contours generating an extra population of spin along the $y$ direction (for Rashba there is a partial compensation of the contributions of the two contours). (e),(f) Inverse Edelstein effect: Injection of a spin current density spin polarized along $y$ (${j_{S(y)}}^{3\mathrm{D}}<0$ in the figure) into Rashba (e) or TI (f) 2DEGs induces an extra population on one of the sides of the Fermi contour (along the $x$ direction), a depletion on the other side, and therefore a charge current density ${j_C}^{2\mathrm{D}(x)}$ ($<0$ in the figure). ${j_{S(y)}}^{3\mathrm{D}}$ and ${j_C}^{2\mathrm{D}(x)}$ of this figure can be seen as carried by the electrons of the wave vector (wavy arrow) and spin (straight arrow) in the schematic at the bottom of (a) and (b). For a circular Fermi contour, the expressions of the IEE length ${\lambda }_{\mathrm{IEE}}$ are given in the bottom right of the figure as a function of the relaxation time of the topological states and Rashba coefficient ${\alpha }_R$ or Fermi velocity $v_F$ of the DC. All the figures are drawn for electron-type conduction in the 2D states.

Figure 2

ARPES characterization of the interfaces states of $\alpha$-Sn (0 0 1) films covered by Fe or Ag. Top: ARPES intensity plots of the DC along [100] or [110] on the free surface of $\alpha$-Sn (approximately 30 ML thick). Below: ARPES plots after covering by 0.9 or 1.8 Å of Fe (left) and 4.3 or 12 Å of Ag (right). The intensity is color coded with the same color scale in each panel (arbitrary units).The DC subsists if $\alpha$-Sn is covered by Ag, and it can still be seen when the $\mathrm{Sn}|\mathrm{Ag}$ interface is buried below 12 Å of Ag. It disappears after covering by Fe, but the overlap with the high intensity of the Fe $3d$ band dispersion at the Fermi level precludes definitive conclusions on the complete suppression of the DC.

Figure 3

Spin to charge current conversion by spin pumping into the topological states of $\alpha$-Sn (0 0 1). (a) Experimental setup for spin pumping into $\alpha$-Sn by ferromagnetic resonance (FMR) of a Fe layer [24]. (b) Broadband frequency dependence of the peak-to-peak FMR linewidth when the magnetic field $H$ is applied along the [1 0 0] direction of the InSb substrate for $\mathrm{InSb}|\mathrm{Fe}|\mathrm{Au}$ (reference for the Fe layer), $\mathrm{InSb}|\alpha \text{−}\mathrm{Sn}|\mathrm{Fe}|\mathrm{Au}$, and $\mathrm{InSb}|\alpha \text{−}\mathrm{Sn}|\mathrm{Ag}|\mathrm{Fe}|\mathrm{Au}$ samples. The effective damping coefficient of Fe, proportional to the slopes, is definitely larger with the Ag interface ($\alpha =0.028$ compared to 0.008 and 0.006 for the two other structures), which shows the strong spin absorption by the $\alpha \text{−}\mathrm{Sn}|\mathrm{Ag}$ interface. (c) FMR and dc charge current signals from measurements in a cylindrical $X$-band resonant cavity on $\mathrm{InSb}|\mathrm{Fe}|\mathrm{Au}$, $\mathrm{InSb}|\alpha \text{−}\mathrm{Sn}|\mathrm{Fe}|\mathrm{Au}$, and $\mathrm{InSb}|\alpha \text{−}\mathrm{Sn}|\mathrm{Ag}|\mathrm{Fe}|\mathrm{Au}$ samples. Only the third sample shows a dc current signal in agreement with the observation of a Dirac cone at only the $\alpha \text{−}\mathrm{Sn}|\mathrm{Ag}$ interface.