Observation of the Orbital Rashba-Edelstein Magnetoresistance

We report the observation of magnetoresistance (MR) that could originate from the orbital angular momentum (OAM) transport in a permalloy (Py)/oxidized Cu (${\mathrm{Cu}}^{*}$) heterostructure: the orbital Rashba-Edelstein magnetoresistance. The angular dependence of the MR depends on the relative angle between the induced OAM and the magnetization in a similar fashion as the spin Hall magnetoresistance. Despite the absence of elements with large spin-orbit coupling, we find a sizable MR ratio, which is in contrast to the conventional spin Hall magnetoresistance which requires heavy elements. Through Py thickness-dependence studies, we conclude another mechanism beyond the conventional spin-based scenario is responsible for the MR observed in $\mathrm{Py}/{\mathrm{Cu}}^{*}$ structures—originated in a sizable transport of OAM. Our findings not only suggest the current-induced torques without using any heavy elements via the OAM channel but also provide an important clue towards the microscopic understanding of the role that OAM transport can play for magnetization dynamics.

Figure 1

(a)–(c) The angular dependent MR measurements in $\mathrm{Py}(5)/{\mathrm{Cu}}^{*}(3)$ heterostructure at 300 K and 6 T in the three ${\mu }_0\mathit{H}$-rotation planes $(\alpha ,\beta ,\gamma )$. The schematics on the right show the sample Hall bar and the definition of the axes, angles, and measurement configuration. $\mathrm{\Delta }{\rho }_{xx}/{\rho }_{xx}$ is the MR ratio collected in different ${\mu }_0\mathit{H}$-rotation planes. The inset in (b) shows a zoom for the MR signal in the $yz$ plane.

Figure 2

Schematic illustration of the ORMR. As the charge current flows at the interface to the insulating ${\mathrm{CuO}}_x$ along $x$, the $y$ component of the OAM (blue circle with orange circular arrow) is induced by the orbital Rashba-Edelstein effect due to the inversion symmetry breaking caused by the oxygen gradient. (a) When the direction of the magnetization (green arrow) is perpendicular to the direction of the induced OAM, the OAM is absorbed by the FM (Py) as it exerts a torque on the magnetization via the SOC that entangles the OAM with the spin (magenta arrow). (b) When the magnetization direction is parallel to the direction of the OAM, the OAM is reflected from the interface. Therefore, (a) exhibits higher resistivity compared to (b).

Figure 3

(a) Angular dependence of the ORMR for $\mathrm{Py}(5)/{\mathrm{Cu}}^{*}(t_{{\mathrm{Cu}}^{*}})$ samples with different ${\mathrm{Cu}}^{*}$ layer thicknesses. (b) ORMR ratio $\mathrm{\Delta }{\rho }_{xx}/{\rho }_{xx}$ as a function of the thickness of ${\mathrm{Cu}}^{*}$. The MR ratio keeps nearly constant for $t_{{\mathrm{Cu}}^{*}}\le 5\mathrm{nm}$, indicating a typical interfacial mechanism. For $t_{{\mathrm{Cu}}^{*}}>5\mathrm{nm}$, the MR ratio decreases monotonically as the thickness of ${\mathrm{Cu}}^{*}$ increases.

Figure 4

(a) and (b) The ORMR measurements in the $\beta$ scan for $\mathrm{Py}(t_F)/\mathrm{Pt}(4)$ and $\mathrm{Py}(t_F)/{\mathrm{Cu}}^{*}(3)$ at 6 T. (c) and (d) The plots of the Py thickness dependence of the MR ratio $(\mathrm{\Delta }{\rho }_{xx}/{\rho }_{xx})$ taken from (a) and (b), respectively. The red curves are the fitting curves of the data. The green dashed curve in (d) is the fitting by forcing the effective relaxation length of Py to match the value taken from the $\mathrm{Py}/\mathrm{Pt}$ samples, which shows a significant deviation from the obtained data.