Separating Inverse spin Hall voltage and spin rectification voltage by inverting spin injection direction

We develop a method for universally resolving the important issue of separating the inverse spin Hall effect (ISHE) from 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, inversion of the spin injection direction changes the ISHE voltage signal, while 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 GMR effects by Grünberg and Fert in the late 1980's, 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 adjacent nonmagnetic(NM) metal materials were proposed 4,5 . This is a breakthrough in this field, because the spins are effectively injected from FM to NM metals. DC voltages were generated in the NM metal due to the inverse spin Hall effect, which follows the line shape of the ferromagnetic resonance(FMR) spectra. Soon after, it was realized that in FM/NM bilayers, voltage at FMR has contributions not only from spin pumping, but also from spin rectification effect (SRE) 8 . The voltages from SRE can not 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 TE 011 mode 6 . However, it is difficult to explore the frequency characteristics of the FM/NM bilayers with microwave cavity because the cavity only works near its resonance frequency.
It is convenient to study the ISHE at different frequencies with transmission line such as CPW 8 or shorted microstrip 9 . 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 Hu 8 and Ong 10 . It was shown that the two effects have endowed different dependences of the static magnetic field direction. Thus, rotation of the field in the film plane can be used to separate the two effects. However, due to the limitation of linear response, the method is not applicable to high power cases. Another generalized methods were proposed by Hoffmann et al. 7 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 high power cases to study the nonlinear effects.
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 are inverted. It reveals that the SRE has both Lorentian 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 8 , the anisotropic magnetoresistance contributes to the DC voltage because of the phase differences of the microwave current ( j) and magnetization ( m) 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 ω r is the FMR frequency involved in both V SRE and V ISHE .
The total photon voltage is expressed as the summation of both: As clearly shown in Equ. (1) and (2), The V ISHE is an odd function of e z while V SRE is independent on it. This is quite understandable because e z is related to the spin diffusion direction, which is irrelevant to produce V SRE . Thus, when only the spin diffusion direction is reversed as in Fig. 1 In this case, the two contributions can be separated by summation and subtraction of the two measurement: . This symmetry property was demonstrated by measuring the voltage in samples with reversed stacking order of NM/CoFeB on thermally oxidized Si substrate 12 . However, because film quality may be quite sensitive to the underlayers, cautions should be taken when extracting the informations. We thus propose the following measurement schemes.  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 shows clearly 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. 8 . 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 of 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") magnetic films are deposited directly on the CPW substrate.
In order to have a comparison of our measurement to those of rotation samples as used by Ong 10 and repeated by us 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 φ H . At each of these fixed φ H , a sweeping of the magnetic field was done. Then, their voltages under different fields were fitted to the Lorentzian and dispersive line shape. The amplitudes V AL and V AD were shown in Fig.3(a) by filled squares and circles. The voltage contributions from the ISHE and the SRE were obtained by fitting the curves according to Equ.(3) and (4) 10,13 . V We obtain the "Up" and "Down" curves at a specified φ H (=90 • ), where the ISHE and SRE take their maxima. The curves are shown in Fig.3 (b). The red solid line is reproduced from the V ISHE data obtained by the rotation sample method above. It follows well the curve (hollow blue circles) obtained by our new method. The V ISHE peak values obtained is 0.180 µV , which is comparable with 0.182 µV obtained above. The differences is within 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.
As pointed by Hu et al. 8 , when there are contributions of Lorentzian and dispersive types to the SRE, cares must be taken to get reasonable results. The phase difference of the microwave electric field and dynamic magnetic moment may change with microwave frequency. As argued in the work of Hoffman et al 7 , since equation (1) and (2) predicts, V ISHE ∝V SRE ∝ P/ω r , we may thus use this relation to check for consistency in our obtained results over the measured frequency range. As can be seen in Fig.4, the ratio of V AL to V AD , which is dependent on the phase, changes in a wide range of the frequencies and shoots up in the low frequency range. If we just took one of them, say V AD , the ratio of V ISHE to V AD shoots up at low frequency. In our measurements, the main contribution is from the V AL , because it is an "h ′ x " dominated FMR as classified in the work 8 . Thus, we may take the ratio of V ISHE to V AL separated from V SRE , or that of V ISHE to V SRE at the resonance field, since the term with V AD diminishes at resonance although V AD itself is finite. The results are shown in Fig. 4. As expected, the ratios of V ISHE to V AL and to V SRE@Hr are almost constant in the whole frequencies. However, in this wide frequency range there is a strong phase mixing between the e and h fields, especially when the frequency is lower than 4 GHz, as reflected by the variation of V AL /V 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 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 is not limited by the microwave frequency and power.