Similar-Concept Interface in Spin-Orbit Devices

• SCI is an interface enabling efficient spin-charge interconversion via strong spin–orbit coupling, primarily through the Rashba–Edelstein effect at metal/oxide boundaries.
• Device studies reveal that engineered Cu/WOₓ interfaces achieve high spin-loss conductance and exceptional spin–charge conductivity, outperforming conventional systems.
• The SCI mechanism is critical for MESO logic devices, providing robust magnetic-state readout via optimized spin absorption and interconversion parameters.

A Similar-Concept Interface (SCI) in spin-orbitronic devices refers to an interface that facilitates efficient spin-charge interconversion (SCI) via interfacial spin–orbit coupling phenomena such as the Rashba–Edelstein effect. SCI plays a crucial role in devices that integrate nonvolatile memory and logic—especially in the context of magnetoelectric spin-orbit (MESO) logic—by enabling robust conversion between spin and charge currents. The efficiency of SCI is determined, both theoretically and experimentally, by interfacial transport coefficients that quantify spin absorption and spin–charge conversion, and by the underlying electronic and chemical structure at the interface, often involving ultrathin metal-oxide layers.

1. Theoretical Framework and Key Interfacial Coefficients

Interfacial SCI leverages two-dimensional spin–orbit coupling effects—primarily the Rashba–Edelstein effect—at normal metal (NM)/spin–orbit material (SOM) interfaces. The interface is characterized by two independent linear-response coefficients:

• Interfacial spin-loss conductance, $G_{||}$ ($\Omega^{-1} \mathrm{m}^{-2}$):

$G_{||}$ quantifies the absorption of interfacial spin accumulation $\mu^s$ as a transverse spin current $J^s_z$ into the spin-sink (SOM) side. In the 1D spin-diffusion formalism, the spin-current boundary condition at the interface ($z=0$) is

$$J^s_z\big|_\mathrm{NM\rightarrow SOM} = G_{||} \left[\mu^s_\mathrm{NM}(0) - \mu^s_\mathrm{SOM}(0)\right].$$

For the relevant device configuration, this corresponds to $G_{||} = (J^s_z) / (\mu^s/2)$ per unit area under the symmetric boundary condition $\mu^s_\mathrm{NM} = -\mu^s_\mathrm{SOM}$.

• Interfacial spin–charge conductivity, $\sigma_{SC}$ ($\Omega^{-1} \mathrm{m}^{-2}$0):

$\Omega^{-1} \mathrm{m}^{-2}$1 quantifies the generation of in-plane charge current $\Omega^{-1} \mathrm{m}^{-2}$2 from an interfacial spin accumulation (or, reciprocally, the injection of spin accumulation by an in-plane charge current). The relation at the interface ($\Omega^{-1} \mathrm{m}^{-2}$3) is

$\Omega^{-1} \mathrm{m}^{-2}$4

applicable for both charge-to-spin and spin-to-charge scenarios, related by Onsager reciprocity.

• Inverse Edelstein length, $\Omega^{-1} \mathrm{m}^{-2}$5 (nm):

Defined by

$\Omega^{-1} \mathrm{m}^{-2}$6

$\Omega^{-1} \mathrm{m}^{-2}$7 is the characteristic length for SCI, analogous to $\Omega^{-1} \mathrm{m}^{-2}$8 in bulk spin-Hall materials.

These coefficients form the quantitative foundation for assessing the SCI efficiency at metallic and oxide-metallic interfaces.

2. Device Fabrication, Interface Characterization, and Measurement Protocols

SCI in the archetypal lateral spin valve (LSV) geometry is studied using a Py/Cu/W device, wherein the specific interface of interest is between Cu and an unintentionally formed WO$\Omega^{-1} \mathrm{m}^{-2}$9 interlayer on W. The principal fabrication and characterization steps are as follows:

• Geometry:
  • Ferromagnetic Py (Ni$G_{||}$0Fe$G_{||}$1, FM$G_{||}$2 and FM$G_{||}$3) electrodes are patterned with $G_{||}$4500 nm edge-to-edge separation.
  • A 4.5 nm W strip (partly oxidized) resides centrally.
  • A 90 nm thick, 123 nm wide Cu channel transverses all electrodes.
  • All structures are defined by e-beam lithography, evaporation or sputtering, lift-off, and Ar-ion cleaning, followed by SiO$G_{||}$5 capping.
• Interface Structure:
  • Four-terminal nonlocal resistance measurements of the Cu/W junction exhibit an anomalously negative resistance, attributable to inhomogeneous current flow via an ultra-low impedance interfacial layer.
  • 3D finite-element simulations (Comsol) are employed to extract the resistivity $G_{||}$6 of the WO$G_{||}$7 layer by fitting device simulations to experimental $G_{||}$8.
  • Cross-sectional HAADF-STEM and EDX resolve a $G_{||}$91.5 nm WO$\mu^s$0 layer between the Cu (top) and W (bottom), with no detectable Cu present within the oxide.
• Spin-Absorption and Spin–Charge Measurements:
  • In spin-absorption mode, a DC current is injected from FM$\mu^s$1 into Cu, generating a spin accumulation that diffuses toward FM$\mu^s$2. The spin signal is probed via the nonlocal resistance difference for parallel and antiparallel FM alignments.
  • Spin absorption by the Cu/WO$\mu^s$3/W stack is quantified by the ratio $\mu^s$4, modeled with a 1D spin-diffusion equation. The analysis confirms that dominant spin-loss is interfacial, rather than bulk-like, at the Cu/WO$\mu^s$5 boundary.
  • For charge-to-spin and spin-to-charge conversion, current injection along the W/WO$\mu^s$6 interface induces an Edelstein-generated spin accumulation, producing a measurable nonlocal voltage via FM$\mu^s$7. Analysis with a combined spin-diffusion and Edelstein conversion model, adjusted for shunting effects determined by additional finite-element modeling, yields $\mu^s$8.

3. Quantitative SCI Parameters in Cu/WO$\mu^s$9

Experimental analysis at 10 K and 300 K yields:

Temperature (K)	$J^s_z$0 ($J^s_z$1)	$J^s_z$2 ($J^s_z$3)	$J^s_z$4 (nm)
10	21 $J^s_z$5 2	$J^s_z$6	$J^s_z$7
300	21 $J^s_z$8 2	$J^s_z$9	$z=0$0

$z=0$1 is temperature-independent, suggesting a robust, interface-dominated mechanism. $z=0$2 and $z=0$3 decline with increasing temperature but remain substantially larger than at typical metal/oxide interfaces. The magnitude and sign of these coefficients indicate a SCI process consistent with a strong Rashba-like mechanism at the Cu/WO$z=0$4 interface (Groen et al., 2022).

4. Comparative Analysis with Metal/Oxide and Bulk Spin-Hall Interfaces

A benchmarking of the Cu/WO$z=0$5 interface against other known SCI systems is summarized below (all values at 10 K):

Interface	$z=0$6 ($z=0$7)	$z=0$8 ($z=0$9)	$$J^s_z\big|_\mathrm{NM\rightarrow SOM} = G_{||} \left[\mu^s_\mathrm{NM}(0) - \mu^s_\mathrm{SOM}(0)\right].$$0 (nm)
Cu/BiO$$J^s_z\big|_\mathrm{NM\rightarrow SOM} = G_{||} \left[\mu^s_\mathrm{NM}(0) - \mu^s_\mathrm{SOM}(0)\right].$$1	2.8 $$J^s_z\big|_\mathrm{NM\rightarrow SOM} = G_{||} \left[\mu^s_\mathrm{NM}(0) - \mu^s_\mathrm{SOM}(0)\right].$$2 0.2	44 $$J^s_z\big|_\mathrm{NM\rightarrow SOM} = G_{||} \left[\mu^s_\mathrm{NM}(0) - \mu^s_\mathrm{SOM}(0)\right].$$3 8	0.16 $$J^s_z\big|_\mathrm{NM\rightarrow SOM} = G_{||} \left[\mu^s_\mathrm{NM}(0) - \mu^s_\mathrm{SOM}(0)\right].$$4 0.03
Cu/Au	7.6 $$J^s_z\big|_\mathrm{NM\rightarrow SOM} = G_{||} \left[\mu^s_\mathrm{NM}(0) - \mu^s_\mathrm{SOM}(0)\right].$$5 0.6	-127 $$J^s_z\big|_\mathrm{NM\rightarrow SOM} = G_{||} \left[\mu^s_\mathrm{NM}(0) - \mu^s_\mathrm{SOM}(0)\right].$$6 8	-0.17 $$J^s_z\big|_\mathrm{NM\rightarrow SOM} = G_{||} \left[\mu^s_\mathrm{NM}(0) - \mu^s_\mathrm{SOM}(0)\right].$$7 0.04
Cu/WO$$J^s_z\big|_\mathrm{NM\rightarrow SOM} = G_{||} \left[\mu^s_\mathrm{NM}(0) - \mu^s_\mathrm{SOM}(0)\right].$$8	21 $$J^s_z\big|_\mathrm{NM\rightarrow SOM} = G_{||} \left[\mu^s_\mathrm{NM}(0) - \mu^s_\mathrm{SOM}(0)\right].$$9 2	-1,610 $G_{||} = (J^s_z) / (\mu^s/2)$0 50	-0.76 $G_{||} = (J^s_z) / (\mu^s/2)$1 0.07

For comparison, bulk $G_{||} = (J^s_z) / (\mu^s/2)$2-W exhibits a bulk spin-Hall conductivity $G_{||} = (J^s_z) / (\mu^s/2)$3 and an effective $G_{||} = (J^s_z) / (\mu^s/2)$4–$G_{||} = (J^s_z) / (\mu^s/2)$5 nm, depending on $G_{||} = (J^s_z) / (\mu^s/2)$6 and $G_{||} = (J^s_z) / (\mu^s/2)$7 (Groen et al., 2022). The performance of the Cu/WO$G_{||} = (J^s_z) / (\mu^s/2)$8 interface matches or exceeds the best bulk values and far exceeds those of other all-metallic interfaces.

5. Role of the WO$G_{||} = (J^s_z) / (\mu^s/2)$9 Interlayer in SCI Enhancement

The WO$\mu^s_\mathrm{NM} = -\mu^s_\mathrm{SOM}$0 (thickness $\mu^s_\mathrm{NM} = -\mu^s_\mathrm{SOM}$11.5 nm, $\mu^s_\mathrm{NM} = -\mu^s_\mathrm{SOM}$2–$\mu^s_\mathrm{NM} = -\mu^s_\mathrm{SOM}$3) layer forms unintentionally during device processing, acting as a protective barrier for the W electrode and preventing further oxidation. This layer is highly resistive yet ultra-thin, resulting in negligible bulk spin loss. All significant spin absorption, and thus SCI, is confined to the Cu/WO$\mu^s_\mathrm{NM} = -\mu^s_\mathrm{SOM}$4 interface. The enhanced Rashba-like interfacial spin–orbit coupling (and possibly orbital Edelstein effects) at this boundary yields extremely high $\mu^s_\mathrm{NM} = -\mu^s_\mathrm{SOM}$5 and $\mu^s_\mathrm{NM} = -\mu^s_\mathrm{SOM}$6 values, among the largest reported for all-metallic systems (Groen et al., 2022).

6. Technological Implications for MESO Logic Devices

MESO logic devices require low-impedance, high-efficiency magnetic-state readout through robust spin-to-charge interconversion. The large interfacial $\mu^s_\mathrm{NM} = -\mu^s_\mathrm{SOM}$7 (–0.4 to –0.8 nm) and $\mu^s_\mathrm{NM} = -\mu^s_\mathrm{SOM}$8 demonstrated at the Cu/WO$\mu^s_\mathrm{NM} = -\mu^s_\mathrm{SOM}$9 interface indicate its suitability as a magnetic-state detector within MESO circuits. The unintentional yet beneficial formation of WO$\sigma_{SC}$0 suggests that rational design of engineered oxide/metal interfaces can further optimize SCI performance for device applications (Groen et al., 2022).