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Observation of spin splitting torque in a collinear antiferromagnet RuO2

Current-induced spin torques provide efficient data writing approaches for magnetic memories. Recently, the spin splitting torque (SST) was theoretically predicted (R. Gonz\'alez-Hern\'andez et al. Phys. Rev. Lett. 126, 127701 (2021)), which combines advantages of conventional spin transfer torque (STT) and spin-orbit torque (SOT) as well as enables controllable spin polarization. Here we provide the experimental evidence of SST in collinear antiferromagnet RuO2 films. The spin current direction is found to be correlated to the crystal orientation of RuO2 and the spin polarization direction is dependent on (parallel to) the N\'eel vector. These features are quite characteristic for the predicted SST. Our finding not only present a new member for the spin torques besides traditional STT and SOT, but also proposes a promising spin source RuO2 for spintronics.

RuO2 was commonly considered as a paramagnet, until the recent finding of itinerant antiferromagnetism, with the Néel temperature above 300 K and the Néel vector aligned along [001]-axis [22,23]. The crystal and magnetic structure of RuO2 is shown in Fig. 1(a). RuO2 is a rutile oxide with the P42/mnm space group, where Ru atoms occupy the center of stretched oxygen octahedrons [24]. Consequently, Ru atoms suffer from the octahedral crystal field, giving rise to anisotropic electronic structure and elliptical Fermi circles at kz=0 [12], as illustrated in Fig. 1(b). Note that Ru atoms of opposite magnetic sublattices are surrounded by different directional oxygen octahedrons (with 90º rotation). Such a sublattice rotation in real space results in anisotropic spin band splitting in momentum space [ Fig. 1(b)], ensuring RuO2 an efficient spin splitter to generate spin current. Two typical configurations to generate spin current were proposed in Ref. [12]. For the (100)-oriented RuO2 film, charge current applied along [01 ̅ 0]-axis can induce a transversal -odd spin current flowing along [100] direction (out-of-plane), and the spin polarization direction is parallel to the Néel vector ([001]-axis), as illustrated in Fig. 1(c). When the RuO2(100) film is adjacent to a ferromagnetic layer, the transversal spin current will induce the spin splitting torque. Differently, for the (110)-oriented RuO2 film, charge current applied along [11 ̅ 0]-axis produces only longitudinal spin polarized current, the transversal spin current is forbidden due to the symmetry, as displayed in Fig. 1(d) [25]. As a result, SST is absent for this case.
To probe SST experimentally, we deposited 12 nm thick (100)-and (110)-oriented RuO2 films onto (100)-oriented yttria-stabilized zirconia (YSZ) and (100)-oriented MgO substrates, respectively. Then 8 nm thick ferromagnetic permalloy (Py) layer and 2 nm thick Al capping layer were in-situ deposited on the RuO2 films. After fabricating into the device, we performed spin torque-ferromagnetic resonance 5 (ST-FMR) measurements [25], which is a standard technique to detect spin current and spin torque. Note that ST-FMR is widely used to calibrate the spin current strength and distinguish the spin polarization direction [18,20,21,26], which makes it pretty suitable for detecting SST. Compared to other detection techniques of charge-to-spin conversion, such as the harmonic Hall measurement, ST-FMR has the advantage of simplicity and large signal intensity [27]. In this work, two key parameters (spin torque efficiency SH eff and spin torque conductivity SH eff ) are extracted from the ST-FMR signals to calibrate the charge-to-spin conversion efficiency. Herein, SH eff refers to the spin current density per unit current density, and SH eff represents the angular momentum absorbed by the magnet per second per unit interface area per applied electric field. The detailed analysis methods of the ST-FMR signals are presented in the supplemental material [25].
Then we turn to the experimental results. We show in Fig. 2(c) and 2(d) the ST-FMR spectra of RuO2/Py samples measured at φ=45°, which can be decomposed into symmetric (VS) and antisymmetric components (VA). The angle between the charge current and the external magnetic field is termed as φ. Note that the RF current IRF was estimated by calibrating the reflection coefficient (S11) of the ST-FMR device, by which we conclude that VA of the ST-FMR data mainly arises from the Oersted field [25]. As a result, the ratio of VS/VA is proportional to the spin torque efficiency [26]. In order to quantitatively compare the spin torque efficiency of the two samples, frequency. For the RuO2(100) film SH eff is about 0.08, which is much larger than that of RuO2(110) film ( SH eff~0 .02) and is comparable to that of the typical heavy metal Pt [26]. Similar crystal orientation-dependent SH eff was observed in rutile paramagnetic IrO2 [28]. Furthermore, the effective spin torque conductivity ( SH eff ) is calculated for the two samples by estimating the RF current [25]. Corresponding data are plotted in Fig. 2(f). For the (100)-oriented RuO2 film, SH eff is up to 4 × 10 4 ℏ /2e Ω -1 m -1 , which is around three times as large as that of the (110)-oriented RuO2 film. Note that we calibrated the interfacial spin transparencies of these two samples by the ferromagnetic resonance measurement, the effective spin mixing conductance ↑↓ of them are comparable [25], thereby the enhanced spin torque efficiency in RuO2(100) sample can be ascribed to an extra spin current generation mechanism in addition to SHE. The generation of SST due to the anisotropic spin band splitting is a reasonable explanation, which is also in agreement with the theoretical prediction [12]. When the charge current is at an angle β to HFA, spin polarization generated by ASSE has both x-axis and y-axis components [ Fig. 3(e)], giving rise to β-dependent ratio of eff / eff . As analyzed in Fig. S16, | eff / eff |~|cosβ/(sinβ+C)|, where the constant C represents the ratio of SHE eff / ASSE eff [25]. Here, SHE eff and ASSE eff represent the spin torque efficiency induced by SHE and ASSE, respectively. We plot in Fig.   3(f) the experimental ratios of | eff / eff | at different β, which can be well fitted by the equation above. This result further supports the conclusion that SST exists in RuO2(100) films. The minimum of the fitting line deviates slightly from 90°, which is ascribed to the fitting error and the angle error in the device fabrication. Note that Vz,FL term with angular dependence ~sin2φ (green line) appears in Fig. 3(d), which could originate from the spin precession [19][20][21]30]. Angle-dependent ST-FMR measurements were also carried out in RuO2(110)/Py sample with magnetic field annealing. In this case, is negligible, which is consistent with the theoretical analysis [12,25]. which demonstrates that the RuO2 bulk dominates the generation of SST. This conclusion is supported by the angle-dependent ST-FMR measurements [25]. We point out that the slight reduction of SH eff compared to the counterpart without Cu insertion is reasonable because the additional interface and Cu spacer may increase the spin loss.
Based on the clues described above (i.e., crystal orientation dependent spin torque efficiency, Néel vector dependent spin polarization direction and bulk dominant contribution), we claim that SST is observed in the RuO2(100)/Py sample. Then we tend to compare the present ASSE and previous AFM-SHE [21]. Phenomenologically, ASSE-induced spin current generation in antiferromagnetic RuO2 is the AFM-SHE-like behavior, because both of them show Néel vector dependent charge-spin conversion. Nevertheless, strictly speaking, ASSE in RuO2 is different from AFM-SHE due to the former is dependent on nonrelativistic crystal structure (spin band) rather than the relativistic spin-orbit coupling.
In summary, we provide experimental evidences for the observation of spin can generate out-of-plane spin polarization [44]. In this work, we mainly focus on the spin splitting torque generated in (100)-oriented RuO2.