Engineering of Orbital Hybridization: An Exotic Strategy to Manipulate Orbital Current

TL;DR

The study tackles the efficiency bottleneck of current-induced spin-orbit torque (SOT) by leveraging orbital mechanisms that operate without spin-orbit coupling (SOC). It combines density functional theory with systematic oxidation-state engineering of CuO_x to strengthen orbital hybridization and the orbital Rashba-Edelstein effect at CuO_x/Cu interfaces, achieving a torque efficiency up to $\xi_ ext{FMR} \,\approx\,0.22$ and a markedly reduced current density $J_c$ compared with conventional heavy metals. A key finding is that the Cu4O3/Cu interfacial region—not CuO/Cu—dominates the SOT enhancement, and redox cycling enables reversible switching between high- and low-torque states. The work provides a general, SOC-free strategy to engineer orbital currents in weak-SOC materials, with broad applicability to other 3d metals and oxide interfaces for next-generation spin-orbitronic devices.

Abstract

Current-induced spin-orbit torque (SOT) plays a crucial role in the next-generation spin-orbitronics. Enhancing its efficiency is both fundamentally and practically interesting and remains a challenge to date. Recently, orbital counterparts of spin effects that do not rely on the spin-orbit coupling (SOC) have been found as an alternative mechanism to realize it. This work highlights the engineering of copper oxidation states for manipulating the orbital current and its torque in the CuO$_x$-based heterostructures. The orbital hybridization and thus the orbital-Rashba-Edelstein effect at the CuO$_x$/Cu interfaces are significantly enhanced by increasing the copper oxidation state, yielding a torque efficiency that is almost ten times larger than the conventional heavy metals. The Cu$_4$O$_3$/Cu interface, rather than the widely accepted CuO/Cu interface, is revealed to account for the enhanced SOT performance in the CuO$_x$-based heterostructures. In addition, the torque efficiency can be alternatively switched between high and low thresholds through the redox reaction. The current results establish an exotic and robust strategy for engineering the orbital current and SOT for spin-orbitronics, which applies to other weak-SOC materials.

Figures (5)

• Figure 1: SOT properties of a variety of heterostructures and first-principles analysis of CuO$_x$/Cu interfaces. a) Schematic illustration of orbital-Hall effect or orbital-Rashba-Edelstein effect and orbital torque in Co/Pt/CuO$_x$ heterostructure. The orbital current is converted to a spin current through the SOC in Pt layer, and then exerts a torque on the Co moments. b,c) Torque efficiency (b) and critical current $J_c$ for magnetization switching versus the thickness of an oxide layer for a variety of heterostructures. For torque efficiency in panel (b), solid symbols represent the heterostructures with heavy metals (e.g., Pt, Ta), while open symbols denote the heterostructures with a light-metal oxide layer (e.g., CuO$_x$). For $J_c$ in panel (c), solid and open symbols represent the heterostructures with dominant SHE and OHE (or OREE) mechanisms, respectively. The star symbols represent the current work, while the data of other heterostructures were taken from Refs. zhang_role_2015cao_efficient_2022ding_observation_2022liu_spin-torque_2012hu_efficient_2022greening_current-induced_2020an_enhanced_2023an_electrical_2023ding_orbital_2024gao_intrinsic_2018an_spintorque_2016ding_unidirectional_2022tsai_electrical_2020zhang_electrical_2016husain_field-free_2024liu_current-induced_2012ding_harnessing_2020zheng_effective_2024xiao_enhancement_2022. The details are summarized in Table S1 in the Supporting Information. d-f) Density of states for the O-2$p$ and Cu-3$d$ orbitals at the interface of Cu$_2$O/Cu (d), Cu$_4$O$_3$/Cu (e), and CuO/Cu (f) heterostructures, respectively. Here, Cu$_2$O, Cu$_4$O$_3$, and CuO denote three different oxidation states of Cu ions. Their crystal structural information can be found in Table S2 in the Supporting Information. g) Charge-density distributions at the Cu$_2$O/Cu, Cu$_4$O$_3$/Cu, and CuO/Cu interfaces. Yellow and blue regions indicate charge accumulation and depletion, respectively. h) Spin-orbit coupling energy $E_\mathrm{SOC}$ for Cu$_2$O/Cu, Cu$_4$O$_3$/Cu, and CuO/Cu heterostructures. Blue and red bars represent the averaged $E_\mathrm{SOC}$ of Cu atoms at the CuO$_x$/Cu interfaces and at the vacuum-facing surfaces, respectively. The $E_\mathrm{SOC}$ of each Cu atoms is listed in Table S3 in the Supporting Information. The optimized CuO$_x$/Cu heterostructures are shown in Figure S1 in the Supporting Information, and $E_\mathrm{SOC}$ of Cu$_2$O/Cu with two sets of different lattice constants are exceptionally discussed in Note S1 in the Supporting Information. i-k) SOC matrix elements for different 3$d$ orbitals of Cu atoms in the Cu$_2$O/Cu (i), Cu$_4$O$_3$/Cu (j), and CuO/Cu (k) heterostructures.
• Figure 2: Current-induced magnetization switching and ST-FMR. a) Evolution of longitudinal electrical resistance $R_\mathrm{xx}$ with natural oxidation time for the PCP/CuO$_x$ heterostructures. The resistance increases with the natural oxidation time and starts to saturate after 24 hours of exposure in air. The inset shows the field-dependent anomalous Hall resistance $R_\mathrm{xy}(H)$ after 24 hours of natural oxidation. For the $R_\mathrm{xy}$ measurements, the magnetic field was applied perpendicular to the film plane (i.e., $H_z$). b,c) Current-induced magnetization switching loops measured under various in-plane magnetic fields $H_x$ applied along the $x$-axis for PCP/CuO$_x$ (b) and PCP (c) heterostructures. The clockwise and anticlockwise $R_\mathrm{xy}$--$J$ loops were obtained by applying magnetic fields antiparallel (-$H_x$) or parallel ($H_x$) to the current direction, respectively. Field and current directions are indicated in Figure S2 in the Supporting Information. For the PCP/CuO$_x$ heterostructures, the asymmetric magnetization switching loops for the positive and negative in-plane fields are due to the presence of out-of-plane spin polarization, which is induced by the oxidation gradient in the CuO$_x$ layer. d) Magnetization switching ratio as a function of $H_x$ for PCP/CuO$_x$ and PCP heterostructures. The magnetization switching ratio is defined as the ratio between the saturated Hall resistance in the $R_\mathrm{xy}$-$J$ and $R_\mathrm{xy}$-$H$ loops. The ratio saturates to $\sim$80% when $H_x$ exceeds 7 mT for both heterostructures (see Figure S4, Supporting Information). Note that field-free magnetization switching was observed in PCP/CuO$_x$, while it is absent in the PCP heterostructure. e,f) ST-FMR spectra measured at 7 GHz for Py/Pt/CuO$_x$ (e) and Py/Pt (f) heterostructures. The Py (i.e., Ni$_{81}$Fe$_{19}$) layer offers an in-plane magnetic anisotropy for such measurements. Symbols are experimental data; solid lines represent fits to Equation \ref{['eq:ST-FMR']}. The dashed- and dash-dotted lines represent the symmetric ($V_\mathrm{S}$) and antisymmetric ($V_\mathrm{A}$) components of the resonance amplitude, respectively. The torque efficiency $\xi_\mathrm{FMR}$ can be obtained from the ratio between the magnitude of the symmetric $V_\mathrm{S}$ and antisymmetric component $V_\mathrm{A}$ of the spectra (see Equation \ref{['eq:efficiency']} in the Experimental Section). For these ST-FMR measurements, as indicated by the arrows in the insets, the angle $\phi_\mathrm{H}$ between the field $H$ and current $I_\mathrm{rf}$ directions was fixed at 30$^\circ$ and 210$^\circ$, respectively. By reversing the external magnetic field direction, the sign of $\tilde{V}_{\mathrm{mix}}$ also changes, as expected for the voltage generated by the ST-FMR. g) Angular dependence of the antisymmetric resonance amplitude $V_\mathrm{A}$ for the Py/Pt/CuO$_x$ heterostructure. The black line ($\sigma^\mathrm{total}$) is a fit to Equation S1 in the Supporting Information, while red and green lines represent the contributions with spin polarization along the $y$- ($\sigma^y$) and $z$-axis ($\sigma^z$), respectively. Note that the contribution with $\sigma^x$ (i.e., spin polarization along current direction) is negligible.
• Figure 3: Characterization of perpendicular magnetic anisotropy and oxidation states. a) Field-dependent Hall resistance $R_\mathrm{xy}(H)$ for PCP/CuO$_x$ heterostructures annealed at different temperatures up to 873 K in the air atmosphere. Except for 300 K (i.e., natural oxidation), the PCP/CuO$_x$ heterostructures were annealed at each temperature for half an hour. For $R_\mathrm{xy}$ measurements, the magnetic field was applied along $z$-axis (i.e., perpendicular to the film plane). b) X-ray photoelectron spectra of the Cu-2$p$ core-level of the PCP/CuO$_x$ heterostructures annealed at various temperatures. Solid black lines represent the fits including the contributions of Cu-2$p$ core-level of Cu$^{2+}$ (blue areas) and Cu/Cu$^{1+}$ (red areas). Multiple Gaussian distribution functions were used to fit the XPS spectra and to characterize the oxidation states of CuO$_x$ layer on the basis of Cu/Cu$^{1+}$ (933.5 eV and 953.4 eV) and Cu$^{2+}$ (934.4 eV and 954.3 eV) peaks. The full XPS spectra, including the Cu$^{2+}$ satellite peaks, are presented in Figure S8 in the Supporting Information. c) The peak-area ratio $\Gamma$ (left axis) versus the annealing temperature for PCP/CuO$_x$ heterostructures. The torque efficiency $\xi_{\mathrm{FMR}}$ of Py/Pt/CuO$_x$ heterostructures annealed at different temperatures are also summarized in panel (c) (right axis). Note that, as the annealing temperature increases above 450 K, the contact electrodes (i.e., Ti/Cu) of SOT devices become fully oxidized and insulating, hindering further ST-FMR measurements. Inset shows the linear correlation between $\xi_{\mathrm{FMR}}$ and $\Gamma$ ratio, which suggests that $\xi_\mathrm{FMR}$ could be enhanced further if a proper electrode or FM layer is chosen. The ST-FMR spectra of these heterostructures are summarized in Figure S9 in the Supporting Information. d) Electrical resistance $R_\mathrm{xx}$ and coercive field $H_\mathrm{c}$ (right-axis) for the PCP/CuO$_x$ heterostructures as a function of annealing temperature. The background color represents the magnitude of Hall resistance $R_\mathrm{xy}(H)$ of the PCP/CuO$_x$ heterostructures annealed at various temperatures. Here, the $R_\mathrm{xy}$ data collected from 100 to 0 mT are solely presented. Note the significant suppression of spontaneous anomalous Hall resistance and thus of the PMA in PCP/CuO$_x$ heterostructures when the annealing temperature is higher than 423 K, as indicated by the dashed line. All the XPS, ST-FMR, $R_\mathrm{xx}$ and $R_\mathrm{xy}$ measurements were carried out at room temperature.
• Figure 4: Spin-orbit torque efficiency and critical current for magnetization switching. a) Representative ST-FMR spectra for Py/Pt/CuO$_x$ heterostructures annealed at 373 K in the air atmosphere for 0, 1.5, and 2.5 hours, respectively. Solid lines are fits to Equation \ref{['eq:First-order derivative of ST-FMR']}, while dashed- and dash-dotted lines represent the symmetric and antisymmetric components of the corresponding spectra. b) Field-free current-induced magnetization switching for PCP/CuO$_x$ heterostructures annealed at 373 K in the air atmosphere for different times up to 2.5 hours. The results obtained by applying an in-plane magnetic field of 10 mT are summarized in Fig. S14 in the Supporting Information. c) The magnetization switching ratio (left axis) and the critical electric current density $J_c$ (right axis) versus the annealing time for PCP/CuO$_x$ heterostructures. d) Spin-Hall angle $\theta_\mathrm{SH}$ and SOT efficiency $\xi_\mathrm{FMR}$ as a function of peak-area ratio $\Gamma$ (see definition in Figure \ref{['fig:XPS']}). $\theta_\mathrm{SH}$ was obtained by harmonic-Hall measurements on PCP/CuO$_x$ heterostructures annealed at 373 K for different times, while the $\xi_\mathrm{FMR}$ was derived from ST-FMR measurements on Py/Pt/CuO$_x$ heterostructures. e) In-plane ($\xi_\mathrm{DL}^y$, left axis) and out-of-plane ($\xi_\mathrm{DL}^z$, right axis) damping-like SOT efficiencies versus $\Gamma$ for PCP/CuO$_x$ heterostructures annealed at 373 K for different times. Note that $\xi_\mathrm{DL}^z$ is smaller than $\xi_\mathrm{DL}^y$ by almost a factor of 100. Both $\xi_\mathrm{DL}^y$ and $\xi_\mathrm{DL}^z$ were determined through the angular-dependent ST-FMR spectra (see Figure S18 and Note 2, Supporting Information). The results of Py/CuO$_x$ in panels (d) and (e) were taken from Refs. an_electrical_2023kageyama_spin-orbit_2019gao_intrinsic_2018. The torque efficiencies of Py/CuO$_x$ heterostructures are relatively small due to the lack of SOC layer, which is crucial to convert the orbital current into spin current (Figure \ref{['fig:DFT']}a). f) Torque "switch". SOT efficiency $\xi_\mathrm{FMR}$ for Py/Pt/CuO$_x$ heterostructures annealed alternatively in the air (2.5 hours) and Ar(95%)/H$_2$(5%) (80 hours) atmospheres at 373 K. The oxidation states in the CuO$_x$ layer can be controlled by the redox cycle, and the cycle number indicates the sequence of annealing treatments. The ST-FMR spectra and magnetic properties of these heterostructures are presented in Figure S20 and Table S4 in the Supporting Information.
• Figure 5: Evidence of different oxidation states and their distributions in the CuO$_x$ layer. a) A representative optical image of the micro-fabricated PCP/CuO$_x$ heterostructure with a Hall-bar geometry, which was annealed at 373 K for 2 hours and was used for the TEM measurements. The dashed line indicates the cut direction by using a focused ion beam. The determined $\Gamma$ ratio is close to 50% (Figure S15, Supporting Information) for this device. b) Cross-sectional HAADF-STEM image with EELS elemental maps. The distributions of different elements including O (red), Cu (blue), Pt (purple), Co (cyan), and Si (green) are present. The fast Fourier transform images of PCP and CuO$_x$ layers are presented in Figure S22, Supporting Information. c) Cross-sectional SEM image. The arrows mark the scanning paths (I, II, and III) of the EELS measurements. Paths I (points 1-7) and II (points 8-14) scan from SiO$_2$/CuO$_x$ to CuO$_x$/Pt interfaces near the edge and in the center of the cut PCP/CuO$_x$ heterostructure, while the path III (points 15-21) scans from the edge to the center within the CuO$_x$ layer. d-f) The $\Gamma$ ratios (see definition in Figure \ref{['fig:XPS']}) as determined from EELS spectra collected along paths I (d), II (e), and III (f) at different positions marked in panel (c). Path I (blue arrow) and path II (red arrow) are close to the edge and center of the Hall bar, respectively, and EELS spectra were collected from the top to the bottom of CuO$_x$ layer; Path III is near the CuO$_x$/Pt interface, and EELS spectra were collected from the edge to the center of the Hall bar. Similar to the XPS spectra (Figure \ref{['fig:XPS']}b), the peaks at energies of 933.5 eV and 934.4 eV in the EELS spectra are attributed to the Cu $L$-edge for Cu/Cu$^{1+}$ and Cu$^{2+}$ oxidation states, respectively. The EELS spectra fitted with multiple Gaussian distribution functions are summarized in Figure S23, Supporting Information. g) Schematic plot of the CuO$_x$ layer demonstrating the distributions of Cu$^{2+}$, Cu$^{1+}$, and Cu. The arrows mark the same paths as in panel (c). h,i) Atomic-resolution HAADF-STEM images and the corresponding crystal models for Cu$_2$O (h) and Cu$_4$O$_3$ (i), which are oriented along [110] and [011] directions, respectively. Blue and red spheres represent Cu and O atoms, respectively. The Cu$_2$O and Cu$_4$O$_3$ crystallize in cubic ($Pn3m$) and tetragonal ($I4_1$/$amd$) crystal structures (see crystallographic information in Supporting Information Table S2). No CuO nanoparticles could be identified in the CuO$_x$ layer, consistent with x-ray diffraction measurements (see Figures S25 and S26, Supporting Information). j,k) HR-TEM image of the PCP/CuO$_x$ heterostructure annealed at 373 K for 2 hours. Both Cu$_4$O$_3$/Cu and Cu$_2$O/Cu interfaces can be clearly tracked. l) Crystal structures of Cu$_4$O$_3$ (top) viewed along the [111], Cu$_2$O (middle) viewed along the [110], and Cu (bottom) viewed along the [110] zone axis, respectively. Here, only the Cu atoms are presented. The crystal structures and atomic distances match the HR-TEM image very well, confirming the presence of both Cu$_4$O$_3$/Cu and Cu$_2$O/Cu interfaces.