We develop a method for universally resolving the important issue of separating the inverse spin Hall effect (ISHE) from the spin rectification effect (SRE) signal. This method is based on the consideration that the two effects depend on the spin injection direction: The ISHE is an odd function of the spin injection direction while the SRE is independent on it. Thus, the inversion of the spin injection direction changes the ISHE voltage signal, while the SRE voltage remains. It applies generally to analyzing the different voltage contributions without fitting them to special line shapes. This fast and simple method can be used in a wide frequency range and has the flexibility of sample preparation.

With the rapid development of spintronics, since the discovery^{1,2} of giant magnetoresistance (GMR) effects by Grünberg and Fert in the late 1980s, manipulation of transportation and detection of spins are two of the central problems in this blooming science and technology. The inverse spin Hall effect (ISHE) is one of the effects experimentally demonstrated^{3} right after that, where electric voltages are generated by pure spin nonequilibrium.

In order to produce the spin current, pumping of spins by microwave irradiation from the ferromagnetic (FM) materials to the adjacent nonmagnetic (NM) metal materials were proposed.^{4,5} This is a breakthrough in this field, because the spins are effectively injected from the FM to NM metals. The DC voltages were generated in the NM metal due to the inverse spin Hall effect, which follows the line shape of the FM resonance (FMR) spectra. Soon after, it was realized that in the FM/NM bilayers, the voltage at FMR has contributions not only from spin pumping but also from the spin rectification effect (SRE).^{6} The voltages from SRE cannot be neglected and suppressed except in special cases where the microwave electric field is kept to zero such as at the center of a microwave cavity with the TE_{011} mode.^{7} However, it is difficult to explore the frequency characteristics of the FM/NM bilayers with the microwave cavity because the cavity only works around its resonance frequency. It is convenient to study the ISHE at different frequencies with the transmission line such as coplanar waveguide (CPW)^{6} or shorted microstrip.^{8} However, the ISHE signal is in most cases contaminated by SRE because the SRE cannot be neglected in the transmission line, and it may contribute voltages with the same line shape as the ISHE. Then, it is necessary to extract the ISHE signal from the mixed signal. The intricacies of separating the two effects have been solved by work of Harder^{6} and Soh.^{9} It was shown that the two effects have endowed different dependences of the static magnetic field direction. Thus, the rotation of the field in the film plane can be used to separate the two effects. However, due to the limitation of the linear response, the method is not applicable to high power cases. Another generalized method was proposed by Bai *et al.*,^{10} where the different angular and field symmetries of the two effects were used to separate the two contributions. It does not rely on the linear approximation and can be used in the high power cases to study the nonlinear effects. However, in their proposal, very accurate magnetic field direction control and measurement were required, which will limit the application of the method.

In this letter, we proposed another universal method to separate the SRE and ISHE voltage by simplifying the measurement to two steps. Considering that the mixed contributions consist of odd and even function with respect to the spin injection direction, we separate them by taking two measurements where the spin injection is inverted. It reveals that the SRE has both Lorentzian and dispersive contributions to the voltage while the ISHE has only a Lorentzian contribution. These voltages are also a function of the microwave frequency, but their ratio remains almost constant.

We begin by pointing out the symmetry properties of the photovoltages. As shown in the previous work,^{6} the anisotropic magnetoresistance contributes to the DC voltage because of the phase differences of the microwave current ($j\u2192$) and magnetization ($m\u2192$) precession, which roots on the broken rotational invariance of FM as in the two-band model^{11} for spin transport.

The voltage V_{SRE} can be expressed by

where $m\u2192=M\u2192(t)\u2212M\u2192$ is the magnetization pumped by the FMR, which propagates in the FM and from the FM to NM layer. $e\u2192x,H$ are the directions of the *x*-axis in our coordinate and the static magnetic field (H), as shown in Fig. 1. The diffusion of the spins from the Py to NM layer gives rise to a DC voltage due to the spin-orbit coupling. The voltage (V_{ISHE}) is expressed by

where *ω _{r}* is the FMR angular frequency involved in

*V*.

_{ISHE}There is another important contribution from the anomalous Hall effect (AHE), which can be written as

The total photon voltage is expressed as the summation of both: $VPh=VSRE+VAHE+VISHE$. As clearly shown in Eqs. (1)–(3), the *V _{ISHE}* is an odd function of $e\u2192z$ while $VSRE,AHE$ are independent on it. This is quite understandable because $e\u2192z$ is related to the spin diffusion direction, which is irrelevant to produce $VSRE,AHE$. Thus, when only the spin diffusion direction is reversed as in Fig. 1(b) in our coordinate, the new voltage is $VPhI=VSRE+VAHE\u2212VISHE$. In this case, the symmetry dependent contributions can be separated by summation and subtraction of the two measurements: $VSRE+VAHE=12(VPh+VPhI)$ and $VISHE=12(VPh\u2212VPhI)$. In the following, we use

*V*to denote the voltages from both SRE and AHE. We will specify AHE voltage when necessary. This symmetry property was demonstrated by measuring the voltage in samples with the reversed stacking order of NM/CoFeB on the thermally oxidized Si substrate.

_{SRE}^{12}However, because the film quality may be quite sensitive to the underlayers, one must be cautious when extracting the information. We thus propose the following measurement schemes.

The measurement was done by our shorted microstrip fixture,^{13} which can work up to 8 GHz, as schematically shown in Fig. 1(c). Our samples include a permalloy (Py, Ni_{80}Fe_{20})(20 nm)/SiO_{2}(0.2 mm substrate) monolayer and Pt(10 nm)/Py(20 nm)/SiO_{2}(0.2 mm substrate) bilayer. Both samples have lateral dimensions of 5 mm × 10 mm. The monolayer serves as a control where the measured voltage should be the same when the sample is flipped. In order to put the samples at the same positions in the fixture and minimize the differences of the microwave field before and after sample flipping, we covered the samples with the same material with the same dimensions as the substrate. We obtained the voltage by lock-in techniques (SR830, Standford research system) with the microwave source power provided by Rohde & Schwarz (SMB 100A). At the fixed microwave frequency, we sweep the static magnetic field so that FMR was observed.

In a ferromagnetic monolayer, only SRE was generated. The voltage measured in the film is shown by hollow circles in Fig. 2(a). The curves of the monolayer clearly show a combination of the Lorentzian and dispersive contributions. The relative strength of the two contributions is a function of the phase angle of the microwave electric and current fields as pointed out by Harder *et al.*^{6} When the samples are flipped, the signal is identical to the previous one, as shown by filled circles in Fig. 2(a), which is expected by the symmetry of the SRE voltage. The signal of the bilayer under the normal (“Up”) and flipped (“Down”) configuration are shown in Fig. 2(b). A clear difference between the two curves comes from the inversed spin diffusion direction in our coordinate. The contributions from the ISHE and SRE can be obtained by simple subtraction (“Up-Down”) and summation (“Up+Down”) of the two curves, respectively. Clearly, the ISHE voltage is Lorentzian type while the SRE is a combination of the two types. The SRE voltages from the monolayer and the bilayer are proportional to each other because of the differences between the resistances of the samples: the Pt layer on the Py thin film acts as an electrical shunt.

When we compare the voltages obtained by our fixture with those measured by CPW, the latter usually being of the order of tens of *μV*, the voltage measured by the former is about one order smaller. This is due to the microwave magnetic field being smaller in our setups. The samples are about 0.5 mm away from the conducting strip. However, the signal is clearly above the noise level of the lock-in amplifier. The advantage of our methods is that the samples and the microstrips are reusable, so that comparison of different samples and other material characterizations of the samples can be readily done, while in the CPW setups, the magnetic films are deposited directly on the CPW substrate.

In order to have a comparison of our measurement with those of rotation samples as used by Soh^{9} and Han *et al*.,^{13} we show the separated voltages of the same sample measured at different angles in Fig. 3(a) by the same fixture. The data were rendered from sets of measurement at different magnetic field angles $\varphi H$. At each of these fixed $\varphi H$, a sweeping of the magnetic field was done. Then, their voltages *V _{Ph}* under different magnetic fields

*H*were fitted to the Lorentzian and dispersive line shape: $VPh=VAL\xb7L+VAD\xb7D$, with

where *H _{r}* and $\Delta H$ are the ferromagnetic resonant field and linewidth at half maximum, respectively. The amplitudes

*V*and

_{AL}*V*are shown in Fig. 3(a) by filled squares and circles. The voltage contributions from the ISHE and the SRE are obtained by fitting the curves according to the following equations:

_{AD}^{9,13}

where $VMRx(z)$, *V _{AHE}*, and

*V*are the voltages due to the anisotropic magnetoresistance, anomalous Hall effect, and inverse spin Hall effect, respectively. $\Phi $ is the phase difference between the microwave electric field and dynamic magnetic field, and $\varphi H$ is the angle between the static magnetic field and the direct current flow direction.

_{ISHE}We obtain the “Up” and “Down” curves at a specified $\varphi H$(=90°), where the ISHE and SRE take their maxima. We compare these curves from those obtained via the rotation method. To calculate the field dependence of SRE and ISHE (dashed and solid lines, respectively, in Fig. 3(b)) from the rotation method, we first perform a rotation measurement to obtain V_{AL} and V_{AD} as a function of angle, which are then fitted to Eqs. (6) and (7) to obtain the SRE parameters: V_{MRz}, V_{MRx}, V_{AHE}, and $\Phi $, and the ISHE parameter: *V _{ISHE}*. The ISHE solid line is then simply $VISHE\xb7L$, while the SRE dashed line is obtained from

*V*using Eqs. (4) and (5), substituting in the obtained SRE parameters and omitting the

_{Ph}*V*contribution. The obtained

_{ISHE}*V*via the rotation method well follows the curve (hollow blue circles) obtained by this method. The

_{ISHE}*V*peak values obtained is 0.180

_{ISHE}*μ*V, which is well comparable with 0.182

*μV*obtained above. The differences are within a few percent of the voltage. The SRE curves obtained by the two methods are shown by the black dashed line and red filled circles. The small deviation below the resonant field may come from the uncertainty of the data fitting. Thus, our methods provide the same information as the rotation method but with much reduced number of measurements.

Finally, we compare our obtained results across the frequency range. The phase difference between the microwave electric field and the dynamic magnetic field (i.e., $\Phi $ in Eqs. (6) and (7)) may change with the microwave frequency as a result of the frequency-dependent microwave propagation and losses within the setup. As argued in the work of Bai *et al.,*^{10} since Equations (1) and (2) predict, $VISHE\u221dVSRE\u221dP/\omega r$, where *P* is the microwave power and *ω _{r}* is the angular resonance frequency, we may thus use this relation to check for consistency in our obtained results over the measured frequency range. In Fig. 4, we plot the ratio $VISHE/VSRE$ obtained by this method. Clearly, this ratio is quite constant over the entire frequency range from 1.5 GHz up to 7.6 GHz. Thus, both

*V*and

_{ISHE}*V*have the same frequency dependence, in agreement with the results of Bai

_{SRE}*et al*.

^{10}As can be also seen in Fig. 4, the ratio of

*V*to

_{AL}*V*from SRE, which is dependent on the phase, changes in a wide range of the frequencies and shoots up in the low frequency range.

_{AD}In summary, we have proposed a method to separate the ISHE and SRE voltages in the sample by flipping the samples inside a shorted microstrip fixture. The proposal is based on the fact that ISHE is an odd function of the spin injection direction while SRE is not relevant to it. This method can also be generalized to other cases, like when the spin Seebeck effect is involved, where the voltage has a different coordinate parity with respect to SRE. Since the separation is independent of assumption of linear response of the magnetization to the microwave field, our methods are not limited by the microwave frequency and power. In our measurement regime, the magnetic response is linear, where we have verified by measuring a linear relationship between voltages and applied power. We are also free of very precise magnetic field direction control in the out-of-plane field orientation used by Bai *et al.,*^{10} which gives us more flexibility in experimental setups.

The financial support from NSFC (61471095), “863”-Projects (2015AA03130102), and Research Grant of Chinese Central Universities (ZYGX2013Z001) are acknowledged.