Inverse spin Hall effect in a complex ferromagnetic oxide heterostructure

We present spin pumping and inverse spin Hall effect (ISHE) in an epitaxial complex oxide heterostructure. Ferromagnetic La0.7Sr0.3MnO3 (LSMO) is used as a source of spin pumping while the spin sink exhibiting the ISHE consists of SrRuO3 (SRO). SRO is a ferromagnetic oxide with metallic conductivity, however, with a Curie temperature (TC) of 155 K, thus well below room temperature. This choice allows to perform the experiment above and below TC of the SRO and to demonstrate that SRO not only shows an ISHE of a magnitude comparable to Pt (though with opposite sign) in its non magnetic state but also exhibits a finite ISHE even 50 K below TC.

(8 ± 1) nm of Pt. These two samples are referred to as reference 1 and reference 2, respectively. In a first set of measurements on sample 2 and reference 1 and 2 we determine the DC voltage over the sample during microwave excitation at a frequency of 9.6 GHz and a temperature of 190 K which is above T C of SRO but below the T C of LSMO (Fig. 1c). The magnetic field μ 0 H ext is swept from below to above the resonance field for the LSMO and the measurement is repeated for different in-plane alignments of the magnetic field in steps of 5°. This set of measurements is performed on all three samples. For the analysis it is necessary to remove the contributions which stem from RF-rectification due to anisotropic magnetoresistance (AMR) which can occur in a conducting ferromagnet under RF excitation. For certain conditions the precessing magnetization can cause the resistance to oscillate in phase with the induced RF currents, leading to rectification and DC voltages 26 . Only when the external field is perpendicular to the RF field no rectification is expected. These AMR-caused voltages need to be carefully separated from the ISHE voltage in order to extract the right result as has been shown by Obstbaum et al. 27 . Furthermore, the microwave currents that are coupled inductively or capacitively to the conducting bilayer have to be considered 27 . These currents might cause an additional Oersted field. The effect can be particularly pronounced in lithographically defined structures where the waveguide has a thickness comparable to that of the bilayer. In our case, however, the waveguide is macroscopic and a conservative estimate shows that any contribution from this effect is several orders of magnitude below the ISHE that we observe.
As a first step we compare the voltage signal generated in the LSMO/SRO heterostructure (sample 2) with that of a single LSMO layer of the same thickness (reference 1). We fit the data by a lorentzian line shape with a symmetric and an antisymmetric part. According to Obstbaum et al. 27 the ISHE voltage only results in a symmetric contribution, while the signal from AMR can result in both, symmetric and antisymmetric contributions. Figure 1d shows that for the single LSMO layer symmetric and antisymmetric contributions of finite amplitudes are generated at different magnetization directions in the sample plane. Only when the external magnetic field is directed along the waveguide (ϕ = 0 or ϕ = 180°), no DC voltage can be measured as is expected from theory 26 . We can thus conclude in reverse that for this alignment of the magnetic field any DC voltage generated in other LSMO based heterostructures does not stem from AMR rectification. It should be noted that both symmetric and antisymmetric contribution vanish at this particular angle because in the bilayer samples the vanishing antisymmetric contribution still shows that the angle is correctly aligned. Nevertheless, a possible misalignment of the angle might still lead to unwanted contributions from AMR. A simple estimate, however, shows that a misalignment of at least 10° would be necessary to provide an artifact of the observed magnitude while we can guarantee an alignment accuracy better than 1°. Asymmetries from the silver-glue electrodes can also be excluded because measurements with waveguides where the contacts are far away from the excitation region still show the same effect. Sample inhomogeneities are also negligible because the epitaxial quality of the layers is very high as has been shown by X-ray diffraction (see also sample fabrication).
For reference 2 (LSMO/Pt) the Pt has a much lower resistance than the LSMO and represents a short circuit for the AMR-generated signal while creating a strong ISHE voltage by itself. The angle dependent measurements ( Fig. 1d) confirm that in this sample the maximum DC signal appears for the angle at which no AMR signal could be observed for reference sample 1, as expected from geometric considerations.
For LSMO/SRO heterostructures the result represents a mixture of the two because the SRO has much lower conductivity than Pt and thus a sizeable AMR contribution from the LSMO remains visible. For SRO the ISHE has the opposite sign when compared to Pt, which has also previously been observed for Mo 1 , Ta 10 and W 12 .
Please note that in all measurements, a constant background has been subtracted which was independent from the direction and magnitude of the magnetic field.
For further analysis we limit ourselves to the amplitude of the symmetric contribution which can be precisely determined at the angle where the AMR signal and thus the antisymmetric contribution vanishes completely as we have shown for the pure LSMO layer (broken line in Fig. 1d). In this case, the spin Hall voltage can be written as if out-of-plane excitation is neglected. The formula is derived as described in other publications 1,2,27 and contains the thicknesses t FM and t NM and conductivities σ FM and σ NM of LSMO and SRO, respectively, the saturation magnetization of the LSMO layer (M S ), the length l over which excitation takes place, the excitation field in y-direction (h y ), the excitation frequency (ω/2π) and the susceptibilities of the precessing magnetization at resonance (χ yy res and χ zy res ). To determine the spin Hall angle Θ SH of the SRO, the spin-diffusion length λ SD of the SRO and the spin-mixing conductance g ↑↓ of the LSMO/SRO interface must be determined. The latter is obtained by comparing the damping parameter α = 1.8 × 10 −3 of the SRO-covered LSMO layer with that of the bare LSMO layer α 0 = 4.1 × 10 −4 similar to Azevedo et al. 2 . For this purpose FMR measurements are performed in the frequency range from 2 GHz to 37 GHz for both samples (Fig. 2b) and the damping parameters are extracted from the line widths. This yields a spin mixing conductance of g ↑↓ = (1.1 ± 0.3) × 10 19 m −2 . To calculate the spin diffusion length λ SD we measure the ISHE voltage on a total of seven samples with varying thickness of the SRO. The results are shown in Fig. 2a. These values are fit to  In further experiments we measure the temperature dependence of the effect from 100 K to 300 K to investigate the influence of the ferromagnetism in SRO which has a Curie-temperature of 155 K. Figure 3a additionally shows the magnetization of the LSMO/SRO bilayer during cooldown in a field of 0.2 mT measured by SQUID magnetometry. The curve is typical for LSMO/SRO because the SRO tends to couple antiferromagnetically to the LSMO effectively reducing the total magnetization 28 . Figure 3c, however, shows hysteresis loops at different temperatures and for taken either in-plane or perpendicular to plane. Although these measurements show that the total in-plane magnetization of the LSMO barely changes when SRO is below T C , it cannot be concluded that the direction of magnetization remains constant in the applied magnetic field. A deviation in angle of 10° or less would barely show up in the measurement because it only determines the projection of the magnetization on the magnetic field. It can, however, be concluded that no additional out-of-plane magnetization appears as might be expected for single SRO layers 25 . In addition, a large increase in coercive field (both in-and out-of-plane) occurs when the SRO becomes ferromagnetic indicating a coupling between the two layers. It should be noted that the saturation magnetization of SRO is much smaller than that of LSMO (1.4 μ B /Ru 25   temperature saturation magnetization for bulk material) which in addition with the much smaller layer thickness leads to the fact that the SQUID measurement mainly shows the magnetization of LSMO. Together with the cooling curve of the magnetization also the ISHE voltage is plotted for different temperatures. Obviously the ISHE voltage exhibits a maximum at around T = 180 K. When the temperature is increased starting from T = 180 K we observe a decay of the ISHE voltage. This is easily understood from the reduction of the magnetization (and thus the spin polarization) of the LSMO layer which also reduces the spin pumping.
Upon cooling beyond T C (SRO) the ISHE signal slowly disappears, however, it is noteworthy that a sizeable effect persists until well below T C (SRO) confirming other experiments showing ISHE in a ferromagnetic layer 22 . Note that the vanishing ISHE signal does not even prove that the ISHE itself is truly absent at lower temperatures. In principle it is possible either that due to its strong crystalline anisotropy the SRO may couple to the LSMO and pull the magnetization away from the magnetic field, thus changing the geometry of the experiment or that the magnetization vector of the SRO is non-collinear to that of the LSMO and the spin polarization of the current induced by the spin pumping is changed by spin transfer torque. A decreasing FMR amplitude and an increase in linewidth below T C (SRO) (Fig. 3b) point towards the first effect, however, the second effect cannot be ruled out.
For sake of clarity also possible artifacts from thermoelectric effects due to heating of the sample on resonance should be discussed. In principle the spin heat conveyer effect 30 can create a temperature gradient which can result in a thermovoltage that reverses sign when the magnetic field is reversed. In LSMO, however, the magnons are short lived and do not extend far enough to create the signals that we observe. Theoretically also the Nernst-Ettingshausen effect 31 can create a similar signal. Compared to our measurements it would, however, neither show a similar dependence on temperature nor layer thickness of the SRO so it can effectively be ruled out while in the pure LSMO layer no signal is observed at all, excluding the anomalous Nernst effect 32 .
In summary we have shown that SRO can act as a spin sink in a fully epitaxial heterostructure consisting of two complex oxide ferromagnets. SRO exhibits ISHE with a sign opposite to that of Pt. The spin Hall angle is smaller than for Pt and the effect persists even below the Curie temperature of the SRO. The fact that the effect can be investigated directly at the phase transition opens up new possibilities for future investigation of the ISHE. with a thickness of 30 nm on orthorhombic NdGaO 3 (110) substrates (NGO). Subsequently without breaking the vacuum a layer of SrRuO 3 (SRO) with a thickness of t NM is grown. Both materials are deposited using an oxygen pressure of 0.2 mbar at a substrate temperature of 650 °C. The laser fluency is 2.5 J/cm 2 at a repetition rate of 5 Hz. Using this recipe a total number of 7 samples is fabricated with different respective thickness t NM . For each sample the layer thickness is verified by X-ray reflectometry. Furthermore for the samples with thickest SRO layer XRD measurements are carried out which are shown in Fig. 4. The presence of thickness-fringes in the ω2θ-scan indicates a low interface roughness. Complementary rocking-curves of the 220-reflex for all layers show a small contribution from mosaicity of the LSMO and SRO layers.

Methods
In addition two reference samples are fabricated, one single LSMO layer and one sample where the SRO is replaced by 8 nm of Pt which is also deposited without breaking the vacuum by magnetron sputtering. The samples are cleaved to approximately 2 mm times 5 mm rectangles where the substrate [001] direction is oriented along the short sides. On these sides copper leads are attached using silver glue to serve as voltage probes for the ISHE. Fig. 1a samples are placed on top of a coplanar waveguide with a 600 μm wide inner conductor and 100 μm gap made of a 35 μm thick Cu layer on hydrocarbon ceramic laminate. The waveguide is electrically isolated by an approximately 100 nm thick polyimide layer. The waveguide is placed in a cryostat which is in constant magnetic field μ 0 H ext of a rotatable electromagnet. A microwave current is transmitted through the waveguide whose RF magnetic field excites ferromagnetic resonance and thus spin precession in the LSMO layer. As depicted in Fig. 1b the precessing magnetization causes spin pumping to the adjacent SRO layer where the ISHE leads to spin scattering and consequently in the generation of a DC voltage. The cryostat is liquid nitrogen cooled allowing for temperature dependent measurement in the range from 300 K down to 80 K. It is possible to modulate the RF amplitude and to use a lock-in amplifier to measure the ISHE or to apply a small AC magnetic field allowing for lock-in detection of the absorption and thus the ferromagnetic resonance. Data analysis. In analogue manner to Obstbaum et al. 27 , the data from individual voltage measurements are fit to V DC = A s × L s (H) + B a × L a (H) + offset with L s (H) = Δ H 2 /((H − H r ) 2 + Δ H 2 ) and L a (H) = (H − H r )Δ H/ ((H − H r ) 2 + Δ H 2 ) to obtain the amplitudes for the symmetric and antisymmetric contribution of the voltage signal A s and B a respectively. For the case of ϕ = 0 or ϕ = 180°, A s is equal to V ISHE since any contribution from AMR becomes zero for this configuration. FMR measurements have been carried out subsequently to the voltage measurements from which the susceptibilities at resonance can be extracted.