Large spin-charge interconversion induced by interfacial spin-orbit coupling in a highly conducting all-metallic system

Spin-charge interconversion in systems with spin-orbit coupling has provided a new route for the generation and detection of spin currents in functional devices for memory and logic such as spin-orbit torque switching in magnetic memories or magnetic-state reading in spin-based logic. Disentangling the bulk (spin Hall effect) from the interfacial (inverse spin galvanic effect) contribution has been a common issue to properly quantify the spin-charge interconversion in these systems, being the case of Au paradigmatic. Here, we obtain a large spin-charge interconversion at a highly conducting Au/Cu interface which is experimentally shown to arise from the inverse spin galvanic effect of the interface and not from the spin Hall effect of bulk Au. We use two parameters independent of the microscopic details to properly quantify the spin-charge interconversion and the spin losses due to the interfacial spin-orbit coupling, providing an adequate benchmarking to compare with any spin-charge interconversion system. The good performance of this metallic interface, not based in Bi, opens the path to the use of much simpler light/heavy-metal systems.

Figure 1

Spin absorption and SC conversion experiments. (a) SEM image of device D1 with two NiFe/Cu LSVs. The left one is a reference and the right one includes a Au/Cu wire between the two NiFe electrodes. The nonlocal measurement configurations (red and blue circuits correspond to the reference and spin absorption, respectively), the direction of the applied magnetic field ($B$), and the materials (NiFe, Cu. and Au) are shown. (b) Nonlocal resistance ($R_{\mathrm{NL}}$) as a function of $B_y$ (trace and retrace) measured in device D1 at $I_{\mathrm{app}}=200\mu \mathrm{A}$ and 10 K from the reference (blue squares) and the spin absorption (red spheres) configurations. From these measurements, we extract the spin signals $2\mathrm{\Delta }{R}_{\mathrm{NL}}^{\mathrm{ref}}$ and $2\mathrm{\Delta }{R}_{\mathrm{NL}}^{\mathrm{abs}}$. (c) Sketch of the SC conversion measurement configuration. The direction of $B$ and the materials (NiFe, Cu, and Au) are shown. (d) Spin-to-charge resistance ($R_{\mathrm{SC}}$) as a function of $B_x$ (trace and retrace) measured in device D1 at $I_{\mathrm{app}}=200\mu \mathrm{A}$ and 10 K. Each curve is an average of six sweeps. From this measurement, we extract the SC signal ($2\mathrm{\Delta }{R}_{\mathrm{SC}}$).

Figure 2

CS conversion and its interfacial SOC origin. (a) Charge-to-spin resistance ($R_{\mathrm{CS}}$) as a function of $B_x$ (trace and retrace) measured in device D1 at $I_{\mathrm{app}}=150\mu \mathrm{A}$ and 10 K. Each curve is an average of three sweeps. From this measurement, we extract the CS signal ($2\mathrm{\Delta }{R}_{\mathrm{CS}}$). Top-right inset: sketch of CS conversion measurement configuration. Bottom-left inset: sketch of the charge current flowing in plane at the Au/Cu interface. (b) Same measurement as panel (a), taken at 300 K. Each curve is an average of eight sweeps. (c) $R_{\mathrm{CS}}$ as a function of $B_x$ measured at $I_{\mathrm{app}}=150\mu \mathrm{A}$ and 10 K in a control device with bare Cu (no Au layer on top of the vertical Cu wire). Each curve is an average of five sweeps. Inset: sketch of the charge current flowing along the vertical Cu wire (in plane with the Cu surface). (d) $R_{\mathrm{CS}}$ as a function of $B_x$ measured at $I_{\mathrm{app}}=150\mu \mathrm{A}$ and 10 K in a control device with a Cu/Au/Cu stack at the vertical wire. Each curve is an average of five sweeps. Inset: sketch of the charge current flowing in plane at the Cu/Au/Cu double interface.

Figure 3

Temperature dependence of the spin absorption and SC conversion. (a) Spin absorption ratio ($\eta$) as a function of temperature obtained from the measured nonlocal signals for different devices. (b) SC signal as a function of temperature for different devices. The negative SC signal at the Au/Cu system is reproduced in three different devices (D1, D2, D3) fabricated in two different substrates. (c) Effective spin Hall angle (${\theta }_{\mathrm{SH}}^{\mathrm{eff}}$) of our Au/Cu system as a function of temperature, obtained from data in panels (a) and (b) and modeling the interface by FEM with an effective thickness $t_{\mathrm{int}}=3\mathrm{nm}$. (d) Inverse Edelstein length (${\lambda }_{\mathrm{IEE}}$), (e) interfacial spin-loss conductance ($G_{\parallel }$), and (f) interfacial spin-to-charge/charge-to-spin conductivity (${\sigma }_{\mathrm{sc}/\mathrm{cs}}$) of our Au/Cu interface as function of temperature, extracted using the relations between the FEM and the boundary conditions models [see discussion above Eq. (3)].

Figure 4

(a) False-colored SEM image of device D1 after finishing the nanofabrication. (b) Sketch of the Cu and Au depositions performed at different angles, corresponding to the dashed area in panel (a), which shows how Au is deposited in the vertical wire of the Cu cross only. (c) y–z plane cut of the sketch in panel (b), showing the ZEP resist profile and the horizontal Cu wire. Blue arrow shows the direction of Au deposition. $d_{\mathrm{s}}$ is the shadow length that indicates the maximum width of the horizontal Cu wire that can be hidden by the shadow under the 45° angle deposition. (d) SEM image showing that the angle deposition works well in the nanodevice. The 80-nm-wide horizontal Cu wire is not covered by the deposited Au because $d_{\mathrm{s}}=236\mathrm{nm}$ in the experiment.

Figure 5

(a) Cross-sectional HAADF STEM image of Cu(80)/Au(3) bilayer and EDX map in the inset shows layers of Au (red), Cu (blue), and Pt protective layer (greenish). (b) Grazing incidence x-ray diffraction with $2\theta$ scan for a grazing incidence angle of $\varphi =0.5^{\circ }$ in a reference Cu(80)/Au(3) bilayer thin film. (c) High-resolution TEM image. (d) Map of the (111) lattice parameter obtained from panel (c).

Figure 6

(a) Resistance of Cu(10)/Au(3) (red) and $\mathrm{Cu}\left(10\right)/\mathrm{Si}{\mathrm{O}}_2\left(5\right)$ (blue) stacks shaped as double-Hall crosses with an identical lateral geometry, measured using the four-probe measurement. The extracted value for the resistance of 3-nm-thick Au is shown in green. (b) The calculated value of resistivity of the 3-nm-thick Au and 10-nm-thick Cu.

Figure 7

Resistivity of Cu channel of the LSV as a function of temperature.

Figure 8

(a) SEM image of the control device D4 showing the labeling of contacts used for the transport measurements. The device consists of two NiFe/Cu LSVs: the left one is a reference and the right one includes a Pt wire between the two NiFe electrodes. (b) Spin-to-charge resistance ($R_{\mathrm{SC}}$) as a function of $B_x$ (trace and retrace) measured at $I_{\mathrm{app}}=200\mu \mathrm{A}$ and 10 K for the Cu/Au (device D1) and Pt/Cu (device D4) systems. Each curve is an average of three sweeps for device D1. The same sign of the SC signals is obtained with the same measurement configuration and the opposite stacking order.

Figure 9

3D finite-elements method simulation. (a) Geometry and mesh of the 3D FEM model used for simulating the spin absorption and spin-to-charge conversion signals using the two-current drift-diffusion equations. Inset: zoom of the mesh presenting the method to simulate the interface. The Au wire is separated as two layers in the $z$ direction. The first layer is an effective interface with spin-orbit coupling (int, in blue) with the resistivity of Au, thickness $t_{\mathrm{int}}$, and two free parameters ${\lambda }_{\mathrm{int}}$ and ${\theta }_{\mathrm{SH}}^{\mathrm{eff}}$. The second layer is the rest of Au with the inputs of bulk Au parameters (${\lambda }_{\mathrm{s}}^{\mathrm{Au}}$ and ${\theta }_{\mathrm{SH}}^{\mathrm{Au}}$) based on its resistivity (see Refs. [35] and [36]). A current ($I_{\mathrm{app}}$) is applied from F3 to Cu to induce a spin accumulation. (b) Representation of the spin accumulation (${\mu }_{\mathrm{s}}^x)$ landscape, i.e., the difference of electrochemical potentials given by up-spin and down-spin electrons. A pure spin current ($I_{\mathrm{s}}$) is injected in the Cu channel in the $y$ direction. This $I_{\mathrm{s}}$ is relaxed and converted to a charge current due to spin Hall effect in both the interfacial and the Au layers. The SC signal amplitude is the difference between to electrical potentials at the ends of the wire and normalized to the applied current $[\mathrm{\Delta }{R}_{\mathrm{SC}}=\left(V_{\mathrm{SC}}^{+}-V_{\mathrm{SC}}^{-}\right)/I_{\mathrm{app}}]$. This corresponds to the experimental results in Fig. 3. The rest of $I_{\mathrm{s}}$ induces a spin accumulation at F3/Cu interface which is probed in the same way as $[\mathrm{\Delta }{R}_{\mathrm{NL}}^{\mathrm{abs}}=\left(V_{\mathrm{abs}}^{+}-V_{\mathrm{abs}}^{-}\right)/I_C]$. This value is fit with the spin absorption signal to extract ${\lambda }_{\mathrm{int}}$. Since all equations used for the simulations are linear, $I_{\mathrm{app}}$ has been set to 1 A. (c) Black spheres are the effective spin Hall angle ${\theta }_{\mathrm{SH}}^{\mathrm{eff}}$ obtained for each thickness $t_{\mathrm{int}}$ in the FEM model to match the experiment results. The red curve is the fit to Eq. (3).

Figure 10

Effective spin-diffusion length ${\lambda }_{\mathrm{int}}$ as a function of temperature. The values are extracted by modeling the spin absorption results with the FEM simulation using $t_{\mathrm{int}}=3\mathrm{nm}$.