Suppression of spin rectification effects in spin pumping experiments

Spin pumping (SP) is a well-established method to generate pure spin currents allowing efficient spin injection into metals and semiconductors avoiding the problem of impedance mismatch. However, to disentangle pure spin currents from parasitic effects due to spin rectification effects (SRE) is a difficult task that is seriously hampering further developments. Here we propose a simple method that allows suppressing SRE contribution to inverse spin Hall effect (ISHE) voltage signal avoiding long and tedious angle-dependent measurements. We show an experimental study in the well-known Py/Pt system by using a coplanar waveguide (CPW). Results obtained demonstrate that the sign and size of the measured transverse voltage signal depends on the width of the sample along the CPW active line. A progressive reduction of this width evidences that SRE contribution to the measured transverse voltage signal becomes negligibly small for sample width below 200 μm. A numerical solution of the Maxwell equations in the CPW-sample setup, by using the Landau-Lifshitz equation with the Gilbert damping term (LLG) as the constitutive equation of the media, and with the proper set of boundary conditions, confirms the obtained experimental results.


Scientific Reports
| (2022) 12:224 | https://doi.org/10.1038/s41598-021-04319-z www.nature.com/scientificreports/ symmetries of ISHE and SRE was proposed by Bai et al. 18 but a very precise control of the field orientation and a high-power microwave source are required, thus limiting its practical application. Other separation methods rely on the different magnetic field orientation dependence of ISHE and SRE signals [19][20][21][22] however, they require a long and tedious measurement process. The different dependencies on the thicknesses of the FM and NM layers has been used to disentangle ISHE and SRE contribution to the measured voltage signal 23 . Obviously, this method requires a large number of samples and measurements, as well as a proper account of the thickness dependence of different parameters, such as the resistivity of the FM or the spin mixing conductance. Separation of both signals by using the different behavior of ISHE and SRE under the inversion of the direction of spin injection has also been reported 24,25 . The corresponding signals are obtained simply by adding and subtracting the voltage signals measured by inverting the spin injection direction. However, reversing the stacking order in the bilayer may severely affect the quality of the interfaces and therefore, modify the effective spin injection. Thus, the direct addition/subtraction procedure may be affected by this experimental error. An alternative procedure, consisting of flipping the whole sample covered by a pristine substrate on top, to ensure as much as possible similar experimental conditions in both measurements, has also been proposed 23 . Nevertheless, this requires to make substrates on both sides thinner to guarantee a good signal to noise ratio. In this work we propose a new method to suppress the SRE contribution leading to a straightforward measurement of the ISHE transverse voltage signal in SP experiments in FM/NM bilayers. This method can be easily implemented and allows a full suppression of the SRE signal in SP experiments in coplanar waveguide (CPW) and microstrip experimental setups.

Results
FMR and transverse voltage signals measurements have been determined simultaneously. At the resonance frequency an absorption Lorentzian-shaped peak appears in the transmission coefficient of the CPW, S, whose derivative is described by the expression 26 : being k S and k AS the symmetric and antisymmetric FMR constants and H res and ΔH are the resonance field and linewidth, respectively. These two parameters are related to the magnetic features of the samples through the Kittel equations 27 : where f is the resonant frequency, γ = gμ B /ħ is the gyromagnetic ratio (in units of GHz/T), μ 0 is the vacuum permeability, H res and H k are the resonant and anisotropy fields respectively (H k is nearly zero in magnetically isotropic Py films), M S is the saturation magnetization of the Py film, ΔH(0) is the so-called inhomogeneous line broadening and α is the Gilbert damping constant [28][29][30] .
The values obtained for both M S and α in Py alone films are in good agreement with values previously reported (see Supplementary Information, Table S1) 15,31,32 . On the other hand, values of ΔH(0) are low, as expected for a magnetically and structurally homogeneous system. A substantial increase of the effective damping, α eff , is detected in Py/Pt bilayer samples which would be indicative of the existence of spin injection (see Fig. 1). The SP process can, therefore, be viewed as an extrinsic contribution to the Gilbert damping α eff. = α + α sp , whose value can be estimated from the increase of the FMR linewidth, ΔH, in samples with and without Pt layer 6,15 . The enhancement of the magnetic damping allows also determining the effective spin-mixing conductance, g ↑↓ ef 6,15,33 .
Being t FM the thickness of the FM layer and α Py and α Py/Pt the damping of the Py layer and of the Py/Pt bilayer respectively. The value obtained in our samples (t Py ~ 16 nm) is g ↑↓ ef ~ (2.31 ± 0.27) × 10 19 m −2 , in good agreement with previous values reported for Py/Pt 15,34,35 .
The effective spin injection into the Pt layer is detected through the transverse voltage signal generated by ISHE. Other potential sources, i.e. thermoelectric effects, are discarded since the temperature increase at resonance is about few hundreds of mK, even at large RF power 36 , thus their contribution to the final voltage signal is irrelevant. The voltage signal is generated by the same magnetization dynamics that governs FMR, thus the line shape of the voltage curves should be a Lorentzian 9 : where V S and V AS correspond to the symmetric and antisymmetric voltage amplitudes, respectively. The signal due to ISHE should only depend on the cone angle of the magnetization precession being, therefore, fully symmetric. However, SRE also contribute to the symmetric part of the experimental signal complicating the separation of both signals.  Table S1), as a function of the frequency, is shown in Fig. 2a. All the curves show the same shape as a function of the applied magnetic field. However, they have different intensities due to small differences in the absorption of the h rf field, higher resistivity of Py compared to Pt and/or the contribution due to ISHE.
It is also worth noticing that the measured voltage signal is negative. However, considering the electrical connections in our setup (see Supplementary Information. Fig. S1b), ISHE voltage signal is expected to be  is the inductive coupling between the sample and the CPW signal line, which creates an eddy current travelling in the opposite direction of the CPW signal line current 25,37 . Therefore, it may be reduced by laminating the sample in the direction of the induced current. According to this, at sufficiently short sample width, W, along the CPW signal line the circulating eddy current should be almost zero and therefore, SRE should vanish while ISHE voltage signal should be almost constant. The dependence of the transverse voltage signal on W was measured in the three sets of samples. For that purpose, samples with different values of W, ranging from 2 mm to 20 μm, have been analyzed (see Table S2 in Supplementary information).
It is important to notice that all samples, irrespective to W, share the same magnetic properties with the 5 × 5 mm 2 original films (see Table S1). The difference in the Gilbert damping values of Py and Py/Pt bilayers is also maintained. This indicates that, from the magnetic point of view, Py films are not affected by the patterning process.
As shown in Fig. 3a the transverse voltage signal measured in Py samples is always of negative sign irrespective to W and its amplitude decreases with decreasing W. Moreover, the amplitude of both the symmetric and www.nature.com/scientificreports/ antisymmetric components also decreases with increasing frequency (see Fig. 4a). It is also worth mentioning that both the symmetric and antisymmetric voltage amplitudes become zero at sufficiently small width, i.e. W ≤ 100 μm (see detail in Fig. 4d).
In the case of Py/Pt bilayers the first remarkable feature is that the sign of the voltage signal changes and becomes positive for W below about 200 μm (see Fig. 3b). As in the case of Py alone samples, the amplitude of the voltage signal decreases with decreasing W above 200 μm. However, for W below 200 μm the amplitude of the voltage signal becomes almost constant and fully symmetric (see Fig. 4b,e).
Finally, the stacking order of Py and Pt was inverted to take advantage of the different behavior of ISHE and SRE under the inversion of the spin injection direction 22,23 .
In Pt/Py bilayers the transverse voltage signal at resonance is always negative (see Fig. 3c) irrespective of W. However, unlike the case of Py alone samples, a closer look at their symmetric and antisymmetric voltage components reveals that while the amplitude of the antisymmetric component goes to zero with decreasing W, the amplitude of the symmetric component remains at a negative value (see Fig. 4c,f). Thus, results for the smaller W values are a mirror image of those obtained in the Si// Py/Pt samples, as expected for ISHE considering the inversion of the spin injection direction.
In all the cases it is observed that the intensity of the voltage signal slightly decreases on increasing the frequency, which is contrary to the expected behavior since, in principle, the spin current generated by SP should be proportional to the precession frequency, f 3 . However, a slight decrease is observed due to the compensation between the magnetization-precession frequency and the spin current generated by a cycle of the precession, due to their different frequency dependencies 3,38 .

Discussion
Considering that SRE are generated by a microwave eddy current, at sufficiently short W the current should be very small ( − → j ≈ 0 ). Therefore, SRE should vanish while ISHE voltage signal should be almost constant since it is not affected by the absence of − → j and no dependence on W should be observed. As a consequence, below a certain threshold value of W (about 200 μm) the contribution of SRE to the transverse voltage signal should be almost zero, as effectively observed in the case of Py alone samples (see Fig. 4a). It is worth noting that contributions to the transverse voltage signal due to self-induced charge current in the Py layer may also exist [39][40][41][42] . However, studies of the temperature dependence of the self-induced transverse voltage in Py demonstrate that spin-charge conversion efficiency at room temperature is very low 39   This behavior is similar to that observed in the Py alone samples and indicates that the measured voltage signal is dominated by the SRE contribution. When the W threshold value is approached the SRE contribution almost disappears and the measured voltage signal becomes positive and with a W-independent amplitude, thus indicating that only ISHE signal is contributing to the measured voltage signal (see Fig. 4b). In fact, it is observed that the line-shape corresponding to negative voltage values has both symmetric and antisymmetric contributions, while the line-shape associated to positive voltage signals is fully symmetric (see Fig. 4b), thus making evident that they are originated by ISHE.
In samples with inverted stacking order, i.e. Si//Pt/Py no change of sign in the measured transverse voltage signal was observed (see Fig. 3c). This contradicts the expected change in sign due to the inverted spin injection direction, and is due to the fact that SRE do not depend on the spin injection direction while ISHE is an odd function of it 22,23 , and in this configuration SRE and ISHE signals have the same sign. Our picture predicts that, below a certain threshold value of W, the amplitude of the signal should be almost constant, since SRE contributions should be zero and ISHE contribution does not depend on W, as it is in fact observed (see Fig. 4c). The spectral line-shape analysis confirms that below the threshold value the measured voltage signal is fully symmetric, and does not depend on W, while above it both symmetric and antisymmetric contributions are present (see Fig. 4c). Figure 5 shows the dependence of the symmetric component of the voltage amplitude as a function of the sample width, W, at a given frequency. The figure clearly illustrates that in Py alone samples the measured transverse voltage signal progressively goes to zero as W decreases. However, in both Py/Pt and Pt/ Py bilayer systems the symmetric component of the signal saturates at a positive and negative value respectively (according to the expected sign of ISHE), and has almost the same absolute value. This indicates that once SRE effects are suppressed the remaining measured signal corresponds to ISHE. Therefore, since the inversion of the spin injection direction must change the sign of the ISHE signal, while that of the SRE contribution remains the same, half the subtraction of both signals should give the value of the ISHE signal.
In Fig. 5b the half-sum (V S + ) and half-difference (V S -), defined as: Pt/Py s , of the bilayer symmetric voltage amplitude with respect to W are depicted. As expected, a constant value in the halfdifference is observed indicating the value of the ISHE component. On the other hand, the half-sum should decrease and go to zero as W decreases, since SRE contribution should be progressively reduced, as effectively shown in the picture. The W threshold value does not depend on the width of the active line of the CPW neither on the separation of the electrical contacts, provide they are far apart from the CPW active line were excitation of the magnetization takes place. However, it may be slightly dependent on the resistivity of the FM material, so this threshold value may be smaller in a FM material with higher conductivity.
From the values of the ISHE voltage signal, and assuming a λ S ≈ 8 nm (according to the resistivities of the Pt layer, namely ρ ~ 10 μΩ cm), a value of the Hall angle, θ SH ~ 0.015 ± 0.005 is derived. This value is in the range of low values reported in the literature. However, it should be noted that there is a broad range of values of Pt conductivity and, therefore, of the spin diffusion length, λ S , and a clear correlation between θ SH and λ S has been observed 43 . Taking into account this relation the value of θ SH derived in this work is comparable to values reported in systems with similar resistivities of the Pt layer. (See Ref. 43 and references therein).
To gain a deeper insight into the behavior of the induced current circulating through the Py layer a numerical study of the SRE on Si// Py/Pt bilayers in a CPW experimental setup has been performed. The time dependence of the magnetic field inside the sample induces a time dependent current density − → j as described by Maxwell's equations. Riet and Roozeboom 44 use a quite crude approximation in which the magnetic field inside the ferromagnet is assumed to have only one component (contained in the film plane). In our case, in order to make a  24,25,45,46 . The main results derived from the numerical solution are that the dominant effect contributing to SRE is the AMR term. Moreover, the AMR term has both symmetric and antisymmetric components being dominant the symmetric component (see Fig. S8). Results obtained also show that the sign of the SRE voltage signal and that of ISHE voltage signal are opposed for the Si//Py/Pt stacking. Additionally, our estimation of the finite size effects along the CPW direction shows that the voltage contribution to the measured transverse voltage signal progressively decreases as W is reduced (see Fig. 6) in agreement with our experimental results.

Conclusions
We have designed a strategy to suppress SRE contribution to the transverse voltage signal measured in SP experiments in FM/NM bilayers. SRE are generated by a microwave eddy current circulating through the sample due to the inductive coupling between the sample and the signal line of the CPW.  The static magnetic properties of the different samples were studied by using a SQUID magnetometer (MPMS-X7 by Quantum Design). Py layers exhibit coercive fields (μ 0 H C ) on the order of 10 -4 T and a saturation magnetization around 0.88 T (See Supplementary material) in good agreement with results reported in the literature. The dynamic magnetic properties were studied by means of a ferromagnetic resonance spectrometer (FMR) made of a broadband coplanar waveguide (CPW) (NanOsc), inserted in a physical properties measurements system (PPMS by Quantum Design) using a lock-in differential detection method. The transverse voltage signal across the sample was measured using a Keithley 2182A nanovoltmeter. Sample is located upside-down and connections are made at both sides by pins already mounted on the sample holder (See Fig. S1b). Electrical contacts (Au) have been deposited Ex situ by dc-magnetron sputtering. Finally, UV photolithography was used for the patterning of the single-striped samples and multiple stripes samples (fringed patterned). A schematic representation of both systems is shown in Fig. S1a.