Efficient Spin-to-Charge Conversion via Altermagnetic Spin Splitting Effect in Antiferromagnet ${\mathrm{RuO}}_2$

The relativistic spin Hall effect and inverse spin Hall effect enable the efficient generation and detection of spin current. Recently, a nonrelativistic altermagnetic spin splitting effect (ASSE) has been theoretically and experimentally reported to generate time-reversal-odd spin current with controllable spin polarization in antiferromagnet ${\mathrm{RuO}}_2$. The inverse effect, electrical detection of spin current via ASSE, still remains elusive. Here we show the spin-to-charge conversion stemming from ASSE in ${\mathrm{RuO}}_2$ by the spin Seebeck effect measurements. Unconventionally, the spin Seebeck voltage can be detected even when the injected spin current is polarized along the directions of either the voltage channel or the thermal gradient, indicating the successful conversion of $x$- and $z$-spin polarizations into the charge current. The crystal axes-dependent conversion efficiency further demonstrates that the nontrivial spin-to-charge conversion in ${\mathrm{RuO}}_2$ is ascribed to ASSE, which is distinct from the magnetic or antiferromagnetic inverse spin Hall effects. Our finding not only advances the emerging research landscape of altermagnetism, but also provides a promising pathway for the spin detection.

Figure 1

Charge-spin interconversion via ASSE in ${\mathrm{RuO}}_2$. (a) Anisotropic spin band splitting of ${\mathrm{RuO}}_2$ at equilibrium. (b) Schematic diagrams of charge-to-spin conversion and (c) spin-to-charge conversion via ASSE in ${\mathrm{RuO}}_2$ from the view of momentum space. (d) Schematic diagram of the spin-to-charge conversion via ASSE in the (101)-oriented ${\mathrm{RuO}}_2$ film.

Figure 2

Spin-to-charge conversion of ${\sigma }_{\mathrm{x}}$. (a) Schematic diagram of SSE measurement configuration for the ${\mathrm{RuO}}_2(101)/\mathrm{Py}$ sample. (b) Schematic diagram of SSE devices with different directional $V$. The direction of $V$ is the $x$ axis, and $\phi$ is the relative angle between $V$ and the [010] crystal axis of ${\mathrm{RuO}}_2$. (c) Thermal gradient-induced spin-dependent voltage for $I_{\mathrm{heat}}=+16\mathrm{mA}$ in the device with $\phi =60°$. (d) The dependence of $V_{\mathrm{odd}}$ on $H_{\mathrm{ext}}$ for various heating current ($I_{\mathrm{heat}}$) measured in the device with $\phi =60°$. The inset summarizes values of $V_{\mathrm{odd}}$ at different heating power ($P_{\mathrm{heat}}$). (e) The dependence of detected voltage $V$ on the angle $\gamma$ for $I_{\mathrm{heat}}=12\mathrm{mA}$ in the device with $\phi =60°$. The inset shows the definition of the angle $\gamma$. (f) The dependence of $V_{\mathrm{odd}}$ on $\phi$ for $P_{\mathrm{heat}}=1\mathrm{W}$. The values are extracted from linear fitting of $V_{\mathrm{odd}}$ at each $P_{\mathrm{heat}}$ for devices with different $\phi$. (g) Temperature-dependent $V_{\mathrm{odd}}$ for $P_{\mathrm{heat}}=1\mathrm{W}$ in devices with $\phi =60°$ and $\phi =90°$.

Figure 3

SSE of the ${\mathrm{RuO}}_2(100)/\mathrm{YIG}(111)$ sample. (a) Schematic diagram of SSE measurement configuration for the ${\mathrm{RuO}}_2(100)/\mathrm{YIG}(111)$ sample. (b) Thermal gradient-induced spin-dependent voltage for $I_{\mathrm{heat}}=\pm 16\mathrm{mA}$ in the device with voltage channel $V$ parallel to the direction of annealing field ($H_{\mathrm{FA}}$). (c) The dependence of $V_{\mathrm{odd}}$ on $H_{\mathrm{ext}}$ for various $I_{\mathrm{heat}}$. The inset summarizes values of $V_{\mathrm{odd}}$ at different heating power $P_{\mathrm{heat}}$. (d) The dependence of $V_{\mathrm{odd}}$ on $H_{\mathrm{ext}}$ for devices with $V//H_{\mathrm{FA}}$ and $V\perp H_{\mathrm{FA}}$.

Figure 4

Spin-to-charge conversion of ${\sigma }_{\mathrm{z}}$. (a) Schematic diagram of SSE measurement configuration for the ${\mathrm{RuO}}_2(101)/[\mathrm{Co}/\mathrm{Pt}]$ sample. (b) The dependence of the current-induced anomalous Hall resistance ($R_{\mathrm{H}}$) and the thermal gradient-induced spin Seebeck voltage ($V$) on $H_{\mathrm{ext}}$ in the device with $V//[010]$. (c) The dependence of $V$ on $H_{\mathrm{ext}}$ for various $I_{\mathrm{heat}}$ in the device with $V//[010]$. The inset summarizes values of $V$ at different $P_{\mathrm{heat}}$. (d) The dependence of $V$ on $H_{\mathrm{ext}}$ in the device with $V//[010]$ and $V//[\overline{1}01]$.