Enhancement of spin mixing conductance in La$_{0.7}$Sr$_{0.3}$MnO$_{3}$/LaNiO$_{3}$/SrRuO$_{3}$ heterostructures

We investigate spin pumping and the effective spin mixing conductance in heterostructures based on magnetic oxide trilayers composed of La$_{0.7}$Sr$_{0.3}$MnO$_3$ (LSMO), LaNiO$_3$ (LNO), and SrRuO$_3$ (SRO). The heterostructures serve as a model system for an estimation of the effective spin mixing conductance at the different interfaces. Our results show that by introducing a LNO interlayer between LSMO and SRO, the total effective spin mixing conductance increases due to the much more favourable interface of LSMO/LNO with respect to the LSMO/SRO interface. Neverheless, the spin current into the SRO does not decrease because of the spin diffusion length of $\lambda_\text{LNO}\approx$3.3 nm in the LNO. This value is two times higher than that of SRO. Our results show the potential of using oxide interfaces to tune the effective spin mixing conductance in heterostructures and to bring novel functionalities into spintronics by implementing complex oxides.


I. INTRODUCTION
The current research on charge-to-spin current conversion effects such as the spin-Hall effect (SHE) offers great potential for applications in the field of spintronics and spinorbitronics 1,2 . Among many studies on magnetic metallic and dielectric materials for the most efficient charge-to-current conversion, oxides have attracted less attention. However, incorporating oxides into the spin current research field can be advantageous due to their tremendous variety of properties (e.g. electronic transport, magnetism) that can be tuned by deposition parameters (e.g. stoichiometry, O 2 pressure, strain) and that depend on the operation conditions (e.g. temperature, magnetic and electric fields). Furthermore, many oxide materials have commensurate lattice constants with perovskite-like structure that allow for very smooth interfaces in oxide heterostructures and hence can lead to well-defined properties at these interfaces.
In this paper, we investigate spin pumping and we calculate the effective spin mixing conductance at low temperatures in LSMO/LNO/SRO heterostructures. LSMO is a prominent oxide material with a rich phase diagram 3 . We use La 1−x Sr x MnO 3 (LSMO) with x = 0.3 where a ferromagnetic metallic phase up to 370 K in bulk material 3 is observed. Also, the inherently bad-metallic 4 oxide SRO, shows a paramagnetic to ferromagnetic transition around 155 K 5 . LNO, contrary to all other rare earth (R) nickelates RNiO 3 with a metal-insulator transition 6 , is known to remain in a paramagnetic conducting phase even at low temperature. Previous studies on the spin pumping and the inverse spin-Hall effect in La 0.7 Sr 0.3 MnO 3 /SrRuO 3 (LSMO/SRO) bilayers 7 have shown that SRO layers were acting as a spin sink exhibiting an ISHE which is similar in magnitude to that of Pt but of opposite sign. Recently, Ghosh et al. 8 proved the Kondo effect and a quite strong magnetoresistance in LSMO/LNO/SRO trilayers using ferromagnetic resonance (FMR) at room temperature. Here, we demonstrate the influence of a LNO interlayer between LSMO and SRO on the effective spin mixing conductance of the different interfaces. The spin mixing conductance g ↑↓ is one of the key concepts in the spin current transport through interfaces 9 since it describes the transport of spins at the interface between a ferromagnet and a second layer made from a different material. It should be noted that according to Tserkovnyak et al. 9 g ↑↓ only includes the transmission of said interface which is only a valid approach if the second layer exhibits very strong spin scattering. For a full description additional layer properties need to be taken into account, which is typically done using an effective spin mixing conductance g ↑↓ eff instead of g ↑↓ . A large g ↑↓ eff means a large spin current and if the difference in chemical potential of spin-up and spin-down in the ferromagnet is caused by ferromagnetic resonance, as in spin pumping experiments, it also means a larger damping of the resonance. However, the estimation of the spin mixing conductance in spin pumping experiments for magnetic/non-magnetic layer systems is not trivial. Usually the calculation is done by measuring the increase in damping and comparing it to the characteristic value of a single uncapped magnetic layer without the spin sink. This uncapped layer acts as a reference sample with no losses due to spin pumping. However, in most of the metallic magnetic layers a capping layer is needed. The capping can largely modify the damping properties of the magnetic layer, a fact that cannot be correlated to the investigated spin pumping.
Furthermore, different factors can influence the estimation of the increase in damping like, for example the emergence of a finite magnetic polarization in the non-magnetic layer (NM) in contact with a ferromagnetic layer 10,11 , the spin memory loss effect 12 or the two-magnon scattering effect 13 . This is the reason why in experiments typically g ↑↓ eff is determined. In our study no capping layer is needed because the bare LSMO reference layer is stable in air. Our work focuses on the estimation of g ↑↓ eff in an oxide trilayer system. Previous experiments in which spin pumping through oxide interlayers was investigated showed different results. For some oxides 14 the spin pumping efficiency was reduced while for NiO 15 the spin pumping efficiency and the inverse spin-Hall effect were increased. In our experiments we observe that the presence of an LNO interlayer increases the damping and as a consequence also g ↑↓ eff . We derive the spin diffusion length for the interlayer LNO, as well as the effective spin mixing conductance for our trilayers. Magnetization and Curie-temperatures are measured by SQUID magnetometry and the samples are structurally characterized by X-ray diffraction and transmission electron microscopy to confirm the interface quality.

II. SAMPLE FABRICATION
The heterostructures are deposited on (001)-oriented strontium titanate SrTiO 3 (STO) substrates, which are TiO 2 -terminated by wet etching and annealing 16 . The deposition is done in a copper-sealed PLD chamber with a background pressure lower than 4·10 −8 mbar.
For deposition an excimer laser with a wavelength of 248 nm is used. The laser fluency is  The red curve is a fit to the data. b) and c) Reciprocal space maps for sample S3 of the symmetric (002) and the asymmetric (103) peak, respectively. The heterostructure is fully strained.
For X-ray characterization we use a Bruker D8 diffractometer with focussed CuK α1 radiation. For the detection a scintillation detector is used in an unlocked ω-2Θ scan of the (002) -reflection. Figure Table I. 18 GHz is applied at a power of 10 dBm. The RF transmission is measured using a diode.
The external magnetic field is modulated with 0.2 mT amplitude at a frequency of 20 Hz and lock-in technique is used to improve the signal-to-noise ratio.
The FMR field-swept measurements are fitted with a derivative of a Lorentzian function, which yields the half-width at half maximum FMR linewidth H FMR and resonance field H FMR 24 . With Kittel's equation 25 : where H 0 is the inhomogeneous linewidth broadening. The values of α, H 0 , and M eff for all our heterostructures are summarized in Table II  To simplify a further discussion we rename g ↑↓ to g ↑↓ FM/NM . The quantity g ↑↓ FM/NM does not take into account properties of the non-magnet like conductivity or spin diffusion length.
Only in the case where spins entering the NM layer are immediately flipped, this spin mixing conductance alone needs to be considered for the additional damping by spin pumping as done by Tserkovnyak et al. 9 . Starting from a bilayer system with immediate spin flip we consinder a model for the spin mixing conductance which is shown in Figure 6 a). As soon as a spin accumulation appears in the non-magnet the spin flow through the spin mixing conductance is reduced and the spin current is no longer defined by g ↑↓ FM/NM but by g ↑↓ eff . In an equivalent circuit (Figure 6 b)) this can be implemented by adding a resistance R sf,NM between the spin accumulation (µ ↑ and µ ↓ ) in the non-magnet which represents the spin flip, necessary to accomodate the steady state of one spin direction flowing into the non-magnet and the other flowing back. Only for immediate and complete spin flip this resistance is a short circuit leading back to g ↑↓ eff = g ↑↓ FM/NM . For a finite resistivity σ NM and finite spin diffusion length λ NM the effective spin mixing conductance can be calculated from the additional damping in a bilayer system 28,29 for λ NM d NM : with: 1 for the additional damping in a bilayer system needs to be used. Here δ SD is the energy level between two scattering states. Equation 3 is the limiting case of equation 4 for large d NM .
In our experiments the limit of λ NM d NM is not yet reached and any addition of another layer will further increase g ↑↓ eff . In case a third layer (NM2) is added, the interface between NM1 and NM2 needs to be considered again in a similar way as for the first interface now adding the spin transmission g ↑↓ NM1/NM2 to our picture (Figure 6 c)). And again we have to take into account the layer properties of NM2 by adding R sf,NM2 . The resulting additional damping α sp in a trilayer system can according to Tserkovnyak et al. 9 be written as: It should be noted that also in this equation Tserkovnyak et al. 9 assume immediate spin flip in the third layer so that for the third layer only the transmission through the interface to the second one needs to be considered. For the limiting case of λ NM1 d NM1 the third layer should have no influence any more and indeed we find that in this limit the result of equation 5 becomes identical to that of equation 4 only with λ NM1 d NM1 replaced by It should be noted that the introduced model ( Figure 6) does not include a spin flip at the interface by scattering which would be associated with the so called spin memory loss 12 .
The equivalent circuit might be extended to include this effect but this will be described elsewhere.
For our measurements of the effective spin mixing conductance, shown in Figure 5 b), we can fit the data to equation 5. SRO has a low spin diffusion length so the assumption of immediate spin flip after entering the SRO is valid and only g ↑↓ NM1/NM2 for the LNO/SRO interface, g ↑↓ FM/NM1 for the LSMO/LNO interface and the spin flip and resistance of the LNO need to be taken into account. Here we consider g ↑↓ eff ∝ α sp . In most of the published experiments the interlayer exhibits little spin flip while the spin sink (e.g. Pt) has a very high spin mixing conductance. In this case we have g ↑↓ NM1/NM2 > h τ SF δ SD and an increase in thickness of the interlayer results in a decrease of the effective spin mixing conductance, as for example in FM/NM1/Pt trilayer systems 9,29,30 . For LNO apparently the spin diffusion length is small, which combined with a large conductivity leads to g ↑↓ NM1/NM2 < h τ SF δ SD and we get an increase of the spin mixing conductance with increasing interlayer thickness. We can fit the data with a spin diffusion length of λ LNO = (3.3 ± 0.9) nm for LNO. Taking the error bars of the measured data into account we can set a lower limit for λ LNO at 1.7 nm.
We can now compare the different contributions to the effective SMC. When a 6 nm SRO layer is put on LSMO (sample R1 → sample S1) the effective spin mixing conductance in-creases from 0 to 2 · 10 19 m −2 . Adding 3 nm of LNO onto LSMO (sample R1 → sample R3) increases the effective spin mixing conductance from 0 to 9 · 10 19 m −2 . Thus we assume that g ↑↓ for LSMO/LNO is bigger than for LSMO/SRO. The ratio must even be more than 9:2 because we found that for 3 nm of LNO the spins are not yet flipped completely but some backflow occurs. When SRO is added to the LSMO/LNO bilayer (sample R3 → sample S3) the increase of g ↑↓ eff is even identical within the error bars to the transition from pure LSMO to LSMO/SRO (sample R1 → sample S1). This leads to the following picture for all parts of g ↑↓ eff : The interface contribution g ↑↓ LSMO/LNO is much larger than g ↑↓ LSMO/SRO for the LSMO/SRO bilayer. g ↑↓ LNO/SRO is similar to g ↑↓ LSMO/SRO . Because of the extremely short spin diffusion length in SRO we can consider the connection between spin-up and spin-down channel in SRO as a short circuit, consistent with equation 5. The spin diffusion length in LNO is comparable to the layer thickness so the spin-flip conductance 1/R sf,LNO has a finite value.
However, from figure 6 b) it becomes clear, that just because of Ohm's law, the values of 1/R sf,LNO and g ↑↓ LSMO/LNO both must be larger than g ↑↓ eff of the LSMO/LNO bilayer (because all three resistors are in series) and hence are also much larger than g ↑↓ LNO/SRO . In Figure 6 d) this is depicted by the size of the different resistors (large g → small R).
It is important to understand that the increase in g ↑↓ eff when a LNO interlayer between LSMO and SRO is introduced is mainly due to the spin-flip and the large conductivity of LNO.
Even if the transmission through the LSMO/SRO interface were perfect (g ↑↓ LSMO/LNO → ∞) the insertion of the LNO layer would not increase g ↑↓ eff but mainly leave it constant because we know that g ↑↓ LNO/SRO ≈ g ↑↓ LSMO/SRO . The increase only can occur if an additional spin flip channel is created inside the LNO layer. It should be noted that also spin memory loss at the LSMO/LNO interface might be a cause but the evident dependence of g ↑↓ eff on the LNO thickness tells us otherwise. Our maximum values for the effective spin mixing conductance are higher than the recently published values of Ghosh et al. 8 , who estimated the effective spin mixing conductance in LSMO/LNO/SRO trilayers at room temperature.
Most likely this is due to the increase in conductivity of the samples at lower temperature which increases g ↑↓ sf,LNO .
Because g ↑↓ is related to the Sharvin resistance 30 it is also understandable that its value increases with conductivity of the spin sink and the number of available conducting channels.
This assumption is well in line with our results for sample R2 (LSMO/Pt) which has the highest effective spin mixing conductance of all samples and the highest conductivity with a second interface is generated with an additional spin sink NM2, which can be described using the interface transmission g ↑↓ NM1/NM2 and a second spin flip resistance R sf,NM2 . d) In our LSMO/LNO/SRO trilayer g ↑↓ LSMO/LNO and 1/R sf,LNO are both much larger than g ↑↓ LNO/SRO . This is pointed out by the size of the corresponding resistors (large g → small R). a pure metal spin sink.
Finally, it should be noted that we also tried to measure the inverse spin-Hall effect (ISHE) 31

VI. CONCLUSION
We have shown that the insertion of a LNO layer between LSMO and SRO increases the effective SMC. This effect can be linked to a highly transparent interface between LSMO and LNO and a large spin flip in the highly conducting LNO. Thickness dependent measurements indicate a spin diffusion length of approx. 3.3 nm which is still twice as long as shown for SRO. 7 g ↑↓ for LSMO/SRO and for LNO/SRO seem to be of similar magnitude. The increase for the effective spin mixing conductance leads to increased damping, however, only the outflow of spin current from the LSMO but not the inflow of spin current into the SRO is increased.

VII. ACKNOWLEDGEMENT
This work was supported by the SFB 762. We thank the Max-Planck-Institut for microstructure physics for the access to transmission electron microscopy.