It has been recently demonstrated that spin–orbit coupling in ferromagnetic metals can generate spin current with symmetries different from the conventional spin Hall effect in nonmagnetic metals. The generated spin current can induce a spin–orbit torque on a neighboring magnetic layer with spin rotation symmetry. In this paper, we introduce a set of tools to measure this effect in a perpendicularly magnetized film, by using the second-order planar Hall effect method and spin-torque ferromagnetic resonance spectroscopy. These results are comparable to those detected by the polar magneto-optic Kerr effect technique.

The spin Hall effect (SHE)1–3 enables conversion from an electric current into a spin current within a nonmagnet (NM). It exerts a spin–orbit torque (SOT)4,5 on a neighboring ferromagnet (FM), which can be used to switch magnetization,6,7 and drive motion of magnetic domain walls8,9 and skyrmions10,11 in applications of magnetic memories. The SHE has a symmetry such that the electric current, spin current, and spin direction are all orthogonal to each other. Limited by this symmetry, an in-plane electric current can only generate an out-of-plane spin current when the spin direction is within the film plane, which sets a constraint on practical applications. For example, to deterministically switch a perpendicularly magnetized film using an in-plane polarized spin current, an external magnetic field or equivalent field is often required.12–15 Thus, it is desirable to exploit unconventional spin–orbit coupling mechanisms that allow the manipulation of the spin direction.

Recent work has shown that the limitation of the conventional spin Hall symmetry can be lifted by breaking additional symmetry of spin current generators. MacNeil and Stiehl et al. have demonstrated that crystal symmetry can be used to control SOT directions in WTe2/FM bilayers.16 Taniguchi et al. have proposed to use a magnetic film with magnetization partially tilted out-of-plane.17 Due to the spin filtering effect, it is expected that the SHE from the magnetic film will generate a spin current with spin direction parallel to the magnetization. Humphries and Wang et al. have observed a spin-charge conversion with spin rotation symmetry in a magnetic film,18 in which an unconventional spin current is generated with spin direction perpendicular to both the magnetization and the spin direction due to the conventional SHE. Hereafter, we refer to the generation of spin current with spin rotation symmetry from a magnetic film as the spin rotation effect. It can be used to generate an out-of-plane polarized spin current,19 by using an in-plane magnetized film. Due to the simple device architecture and magnetization-dependent spin current generation, the spin rotation effect becomes a promising candidate for generating spin current with arbitrary spin direction.

While the spin rotation effect has been demonstrated by both experiments18,19 and first principles calculations,20 the underlying mechanisms for the spin rotation effect are still unsettled. Two different theories have been postulated that lead to the spin rotation effect, including the spin–orbit precession19,21 at the interface between the ferromagnetic and the neighboring nonmagnetic layer, and the spin swapping effect due to the extrinsic spin–orbit scattering in the bulk ferromagnet.22,23 In order to investigate different microscopic mechanisms and to search for magnetic material systems that exhibit efficient spin rotation effect, it is important to develop sensitive and convenient tools to quantify this effect.

A general device for studying the spin rotation effect is a FM1/NM/FM2 spin valve structure, where the FM1 layer is the ferromagnetic spin current generator. The spin current diffuses through the NM spacer layer and exerts a SOT on the FM2 layer, which serves as a spin detector of the spin current generated by the FM1 via the spin rotation effect.

In this paper, we develop and compare a series of experimental procedures to measure SOTs generated by the spin rotation effect in a perpendicularly magnetized film. We show that the second-order planar Hall effect (PHE),24,25 spin-torque ferromagnetic resonance (ST-FMR),26 and magneto-optic Kerr effect (MOKE),27,28 which were developed for studying regular SOTs with spin Hall symmetry in NM/FM bilayers, can be applied to study the SOTs with spin rotation symmetry.

Generally, the spin current is a tensor with two spatial indices, QαβvαSβ: subscript α specifies the spin current flow direction and superscript β specifies the spin direction, where vα is the spin velocity operator, Sβ is the Pauli spin matrix, and α,βx,y,z. In this paper, it is only the spin current flowing in the z-direction that is of interest, we can reduce the spin current tensor to a vector, Qz, in the notation of which the magnitude of the vector represents the magnitude of the spin current, and the direction represents the spin polarization orientation. As shown in Fig. 1(a), when applying an in-plane electric field E to a FM layer with perpendicular magnetization m, a spin current can be generated via spin–orbit coupling that flows out of plane which can be described as 29 

Qz=QSH+QSR=σSHẑ×E+σSRm×ẑ×E,
(1)

where m is the unit magnetization vector. In the rest of the paper, we refer to the first term on the right as the spin-Hall-spin current QSH, and the second term as the spin-rotation-spin current QSR, with σSH and σSR being the corresponding spin Hall conductivities. According to Eq. (1), the spin direction of QSH remains the same when the magnetization switches, while that of QSR reverses as m switches, as illustrated in Fig. 1(a). The different directions and dependences on the magnetization can be used to distinguish the spin Hall and spin rotation spin current components.

FIG. 1.

Spin-orbit effects with spin Hall and spin rotation symmetries. (a) Spin currents generated from a FM layer by an in-plane electrical field E. The gray arrows represent the conventional spin-Hall-spin current QSH, and the orange arrows denote the spin-rotation-spin current QSR, with their corresponding spin directions marked by red and blue colors, respectively. QSR depends on the orientation of the FM magnetization m, which is indicated by a black arrow. (b) The film stack of the Pt/Co/Cu/Py spin valve sample (Pt capping layer is not shown). (c) Out-of-plane hysteresis loop of the sample measured by the polar MOKE.

FIG. 1.

Spin-orbit effects with spin Hall and spin rotation symmetries. (a) Spin currents generated from a FM layer by an in-plane electrical field E. The gray arrows represent the conventional spin-Hall-spin current QSH, and the orange arrows denote the spin-rotation-spin current QSR, with their corresponding spin directions marked by red and blue colors, respectively. QSR depends on the orientation of the FM magnetization m, which is indicated by a black arrow. (b) The film stack of the Pt/Co/Cu/Py spin valve sample (Pt capping layer is not shown). (c) Out-of-plane hysteresis loop of the sample measured by the polar MOKE.

Close modal

Figure 1(b) shows a schematic of the sample used for this study. The complete layer stack is GaAs/Ta (4.0)/Pt (3.0)/Co (0.7)/Cu (3.0)/Py (3.0)/Pt (3.0) (unit in parentheses: nm, Py = Ni80Fe20). All layers were fabricated by magnetron sputtering in a 3.0 mTorr Ar environment. The base pressure was lower than 2 × 10−7 Torr before sputtering. Here, Py has an easy axis in-plane, and Co is a perpendicularly magnetized layer (PML). As shown in Fig. 1(c), out-of-plane magnetization hysteresis was characterized by polar-MOKE magnetometry, indicating nearly 100% remanence of the PML.

We expect the spin current Qz generated from the Co layer to have a QSH component with spin in the y-direction and a QSR component with spin in the x-direction. Both QSH and QSR can generate dampinglike (DL-) and fieldlike (FL-) SOTs on Py magnetization. Their corresponding effective fields are: (1) hSHDL=ξSHDL2eμ0MPydPymPy×QSH; (2) hSHFL=ξSHFL2eμ0MPydPyQSH; (3) hSRDL=ξSRDL2eμ0MPydPymPy×QSR; and (4) hSRFL=ξSRFL2eμ0MPydPyQSR. Here, is the reduced Planck constant, e is the electron charge, mPy, μ0MPy, and dPy are the unit magnetization vector, saturation magnetization, and thickness of the Py layer, respectively, and ξSHDL (ξSHFL), and ξSRDL (ξSRFL) are unitless charge to spin efficiencies of the spin Hall effect and spin rotation effect, respectively, which are sometimes referred to as effective spin Hall angles.7,30,31 It should be pointed out that an in-plane Oersted field (hOe) is also generated, which is collinear with hSHFL.

We first measure the spin current induced FL-SOTs on the Py magnetization mPy with the second-order PHE technique, which is more sensitive to in-plane effective fields than out-of-plane ones due to the negligible anomalous Hall effect voltage applied on Py.24,25 By applying an AC of 20 mA in a 50 μm × 250 μm Hall bar device at a frequency of 346 Hz, we detect the PHE voltage ΔVPHE at twice the frequency:

ΔVPHE=I2·ΔR·χ[Hex]·hI,
(2)

where ΔR is due to the total anisotropic magnetoresistance (AMR),32,χHex=1Hex+Hani is an external field dependent susceptibility, where Hani is the in-plane magnetic anisotropy field,25 and h is the current-induced in-plane effective field including hSHFL, hSRFL, and hOe.

The FL-SOT due to QSH is measured using the configuration shown in the inset of Fig. 2(a), where the external magnetic field Hex is applied parallel to the electric current I (φ = 0°, φ is the angle between I and Hex). In this case, hSRFL=0, and h=hSHFL+hOe, both terms are independent of the Co layer (mCo). Therefore, as shown in Fig. 2(a), ΔVPHE is the same when the Co layer is reversed from mCo=+z to mCo=z. In the configuration φ = 90°, shown in the inset of Fig. 2(b), QSH has spin direction parallel with mPy at saturation; thus, both hSHFL and hOe do not contribute to magnetization reorientation. h can only arise from QSR induced effective field hSRFL. According to Eq. (1), hSRFL, which arises from QSR, should switch sign as mCo switches. This is confirmed by the measurement results shown in Fig. 2(b).

FIG. 2.

Measurements of SOTs induced by spin-Hall-spin current and spin-rotation-spin current. The configurations of conventional spin Hall effect (φ = 0°) and spin rotation effect (φ = 90°) SOTs measurements, and their corresponding second-order PHE results (a) and (b) and polar-MOKE results (c) and (d), which indicate that the conventional spin-Hall spin current is independent of the orientation of PML magnetization mCo, but the spin-rotation spin current shows mCo dependency.

FIG. 2.

Measurements of SOTs induced by spin-Hall-spin current and spin-rotation-spin current. The configurations of conventional spin Hall effect (φ = 0°) and spin rotation effect (φ = 90°) SOTs measurements, and their corresponding second-order PHE results (a) and (b) and polar-MOKE results (c) and (d), which indicate that the conventional spin-Hall spin current is independent of the orientation of PML magnetization mCo, but the spin-rotation spin current shows mCo dependency.

Close modal

By calibrating the susceptibility χ[Hex] with an external calibration field,25 we extrapolate hφ=0°=hSHFL+hOe=149±8 A/m in the spin-Hall-spin current configuration of Fig. 2(a) and hφ=90°=hSRFL=47±7 A/m in the spin-rotation-spin current configuration of Fig. 2(b). In this paper, we do not attempt to distinguish hSHFL from hOe, as they have the same symmetry and are always entangled in all detection techniques discussed in this paper.

The second-order PHE measurement is sensitive to FL-SOT, while the polar-MOKE is sensitive to DL-SOT.18,28 An AC of 40 mA is applied through the MOKE sample (50 μm × 50 μm) at a frequency of 1777 Hz. The out-of-plane magnetization tilting, which is induced by AC generated DL-SOTs, modulates the light polarization as the light is reflected off the sample via the polar-MOKE, which is readout by a balanced detector locked into the AC frequency. Our previous work has demonstrated that the polar Kerr rotation Δθk is a direct indication of the effective field from DL-SOT:28,33

Δθk=η·I·χ[Hex]·hI,
(3)

where η is the polar-MOKE coefficient, the susceptibility χHex=1/Hex+Meff.28,33Meff=Ms2Kμ0Ms arises from the demagnetization effect, and h represents the current induced out-of-plane effective field.

The DL-SOT due to QSH is measured by using the polar-MOKE, which is shown in Fig. 2(c) (φ = 0°). The polar Kerr rotation Δθk resembles Py magnetization hysteresis, which is a typical signature of the MOKE-based DL-SOT measurement. Δθk is proportional to the effective field hSHDL that is independent of mCo. In the configuration φ = 90°, shown in Fig. 2(d), the MOKE signal reverses as mCo switches, which is consistent with the effective field hSRDL due to QSR=σSRmCo×ẑ×E, as described in Eq. (1).

To extrapolate the magnitudes of hSHDL and hSRDL, we calibrate the polar-MOKE coefficient by applying an out-of-plane Oersted field. The calibration field with a known value of hCal=680 A/m is generated by a calibration wire patterned around the sample with Ical = 400 mA current, as is shown in the inset of Figs. 2(c) and 2(d).34 We are able to extract the effective fields induced by DL-SOTs hφ=0°=hSHDL=872±12 A/m and hφ=90°=hSRDL=50±4 A/m, respectively.

Finally, we perform the ST-FMR measurement on this spin valve sample. As shown in Figs. 3(a) and 3(b). A radio frequency (RF) current IRF=IRF0sinωt is applied across the sample strip (20 μm× 50 μm) along the x direction, with a nominal input power of 0 dBm. A lock-in amplifier and a bias tee are used to measure the rectified voltage.26 Besides IRF induced time-dependent change of AMR, ΔRAMR, there is also a contribution from giant magnetoresistance (GMR) oscillation, ΔRGMR, in this experiment. The rectified voltage contains symmetric and antisymmetric Lorentzian components, which are due to out-of-phase and in-phase RF magnetization, respectively. The in-plane effective fields h|| on Py induce in-plane magnetization resonance Δm, which is in-phase with IRF and contributes to the AMR change ΔRAMR. h|| also induces out-of-plane magnetization oscillation Δm, which is out-of-phase with IRF and contributes to the GMR oscillation ΔRGMR. Therefore, h|| leads to an antisymmetric Lorentzian line shape in the AMR voltage VAMRAsym, but a symmetric Lorentzian GMR term VGMRSym. In contrast, the out-of-plane effective field h leads to a symmetric Lorentzian line shape in the AMR rectified voltage VAMRSym, but an antisymmetric Lorentzian GMR term VGMRAsym. The voltage signals with different symmetries can be expressed as

VGMRAsym=14IRFΔRGMR11+H0/Han2μ0MPydPyH0/H0+Meffαγ2H0+Meffh,
(4)
VGMRSym=14IRFΔRGMR11+H0/Han2μ0MPydPyαγ2H0+Meffh,
(5)
VAMRAsym=14IRFΔRAMRsin2φμ0MPydPy1+Meff/H0αγ2H0+Meffh,
(6)
VAMRSym=14IRFΔRAMRsin2φμ0MPydPyαγ2H0+Meffh,
(7)

where H0 is the ferromagnetic resonance (FMR) field. α is the Gilbert damping coefficient and γ is the gyromagnetic ratio. Han = 280 kA/m is the effective perpendicular anisotropy field of the PML layer, which is determined by the vibrating sample magnetometer. μ0Meff=0.820±0.005 T and α=0.017±0.001 are extracted from the additional FMR fitting procedure. According to Eq. (4)–(7), in configurations of both φ = 0° and φ = 90°, only the GMR components contribute to the rectified voltage Vmix, and the AMR induced rectified voltage is zero.

FIG. 3.

ST-FMR measurement results. (a) The conventional spin-Hall as well as (b) the spin-rotation spin current induced rectified voltage when the PML magnetization mCo switches from +z to –z. (c)-(f) The effective field ratio comparison based on the second-order PHE, polar-MOKE, and ST-FMR results. The red shaded area is calculated with FL-SOT results from the second-order PHE measurement and DL-SOT results from the polar-MOKE measurement. The black data points indicate the ST-FMR results.

FIG. 3.

ST-FMR measurement results. (a) The conventional spin-Hall as well as (b) the spin-rotation spin current induced rectified voltage when the PML magnetization mCo switches from +z to –z. (c)-(f) The effective field ratio comparison based on the second-order PHE, polar-MOKE, and ST-FMR results. The red shaded area is calculated with FL-SOT results from the second-order PHE measurement and DL-SOT results from the polar-MOKE measurement. The black data points indicate the ST-FMR results.

Close modal

In configuration of φ = 0°, the ratio of the in-plane and out-of-plane effective fields h(φ=0°)h(φ=0°)=hSHFL+hOehSHDL=H0/H0+MeffVmixSymVmixAsym at given frequency 3–4GHz, which is as shown in Fig. 3(c). For comparison, we calculate the same effective field ratio of h(φ=0°)h(φ=0°)=hSHFL+hOehSHDL=0.17±0.01 based on the second-order PHE and polar-MOKE measurements, which is marked with a red shadow area in Fig. 3(c). The good agreement indicates that these SOT measurement methods are consistent with each other.

In configuration of φ = 90°, the ratio between in-plane and out-of-plane effective fields induced by the spin rotation symmetry h(φ=90°)h(φ=90°)=hSRFLhSRDL=H0/H0+MeffVmixSymVmixAsym is shown in Fig. 3(d). Similarly, h(φ=90°)h(φ=90°)=0.94±0.15 is calculated based on previous results at φ = 90°. The other effective field ratios can also be extracted as h(φ=90°)h(φ=0°)=hSRFLhSHFL+hOe=0.33±0.05 and h(φ=90°)h(φ=0°)=hSRDLhSHDL=0.06±0.01. As shown in Figs. 3(e) and 3(f), the ST-FMR measurement result is highly consistent with that of the other SOTs measurements.

As mentioned previously, based on one parameter fitting to the resonance frequencies, the effective demagnetization field and the Gilbert damping show a good match with the magnetic properties of Py. In addition, the ultrathin Co layer on top of Pt tends to have much higher damping than Py.35 The FMR response of Pt/Co under an in-plane external field follows f=γ/2πH0H0Meff1/2, which therefore indicates no Co resonance within the range of Hex < 32 kA/m in our experiment. Meanwhile, we estimate the RF current density is lower than 1.0 × 1010 A/m2. Thus, we expect that it can avoid the overheating issue in our ST-FMR study.

In summary, we demonstrate a series of experimental procedures, which can be used to quantitatively study the SOTs induced by spin-rotation-spin current. We expect that these techniques will be useful for understanding the spin rotation process as well as for developing materials that exhibit a strong spin rotation effect for advanced spin-orbitronics devices. In our experiment, the spin current generated by the Pt/Co PML layer with spin Hall and spin rotation symmetries can be detected and separated. The second-order PHE method is sensitive to in-plane effective fields induced by FL-SOTs applied on FMs, especially the FMs that have larger PHE resistance than anomalous Hall effect resistance. The polar-MOKE magnetometry directly probes the out-of-plane magnetization component, which can simplify the SOT extraction process without complications from PHE, AHE, and thermal effects. The ST-FMR based on AMR or even larger GMR could be a highly sensitive SOT detection technique, and more importantly, ST-FMR is a ferromagnetic resonance-based technique, which provides layer-resolved capability to separate contributions from different FM layers in FM1/NM/FM2 structures. However, in ST-FMR measurements, although the RF current calibration procedure has been demonstrated by different approaches,16,36,37 it is more challenging to determine the exact amount of RF current flowing through the sample than the AC currents in the second-order PHE and polar MOKE techniques, which are at much lower frequency. Moreover, the numerical fitting process in the ST-FMR method could potentially induce large error especially when the Lorentzian line shape contains a much stronger symmetric or antisymmetric component than its counterpart.

J.Q.X. acknowledges support from the NSF under Award No. DMR-1904076. M.B.J. acknowledges support from the NSF under Award No. 1833000.

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