Direct penetration of spin-triplet superconductivity into a ferromagnet in Au/SrRuO3/Sr2RuO4 junctions

Efforts have been ongoing to establish superconducting spintronics utilizing ferromagnet/superconductor heterostructures. Previously reported devices are based on spin-singlet superconductors (SSCs), where the spin degree of freedom is lost. Spin-polarized supercurrent induction in ferromagnetic metals (FMs) is achieved even with SSCs, but only with the aid of interfacial complex magnetic structures, which severely affect information imprinted to the electron spin. Use of spin-triplet superconductors (TSCs) with spin-polarizable Cooper pairs potentially overcomes this difficulty and further leads to novel functionalities. Here, we report spin-triplet superconductivity induction into a FM SrRuO3 from a leading TSC candidate Sr2RuO4, by fabricating microscopic devices using an epitaxial SrRuO3/Sr2RuO4 hybrid. The differential conductance, exhibiting Andreev-reflection features with multiple energy scales up to around half tesla, indicates the penetration of superconductivity over a considerable distance of 15 nm across the SrRuO3 layer without help of interfacial complex magnetism. This demonstrates potential utility of FM/TSC devices for superspintronics.


Supplementary
. a, Calculated spatial variation of the imaginary part of the normalized p x -wave pair correlation F for spin  (blue closed circles) and  (red closed triangles) configurations with the spin quantization axis along the x axis. The exchange field h ex is assumed to be 0.16t, where t is the hopping amplitude. The inset shows a schematic of the model junction. In this configuration of the FM/TSC junction, F px and F py are equal and spin singlet s-wave and d-wave correlations are zero (open circles). b, Spatial variations of the square of Im(F px ) for both Cooper-pair spin directions. The inset shows the polarization deduced from [Im(F px )] 2 .  Supplementary Figure 2d shows the temperature derivative of resistance. It exhibits three main peaks corresponding to the resistance variations. Interestingly, the peak-top temperatures for the first two peaks are similar for both junctions A and B. These observations suggest that first two transitions are corresponding to the bulk SRO214-neck and SRO113/SRO214 interface respectively. The third peak is interpreted to arise at the Au/SRO113 interface. Note that the shape of this peak varies depending on junctions.

Supplementary
Junction A exhibits a broader peak, whereas junction B has a rather sharp peak. Also, the third peak appears at a lower temperature for junction A compared with junction B. These facts indicate that the induction of superconducting correlations in SRO113 layer for junction A is weaker than to junction B owing to the different interface transparencies.

Supplementary Note 2.
We mainly measure the current-voltage (I-V) curves and take the derivative to analyze the data. Supplementary We also measured the characteristic voltage V 1 -V 3 as a function of applied field along the ab-plane ( Supplementary Fig. 5). To evaluate the V 2 (H) and V 3 (H) data, we apply the theoretical fit of superconducting gap suppression with applied field, ∆( ) = ∆(0)√1 − . It obviously shows that at higher field (close to the transition), V 2 and V 3 are following the square root behavior. But at lower fields the linear behavior is also contributing. Since, V 1 originates from critical current transition therefore we apply the fit only for V 2 and V 3 . However, V 1 may also follow the same behavior at higher fields.

Supplementary Note 3: Other possible origins of V 2 and V 3
In the main text, we discuss that the origins of V 2 and V 3 are the Andreev reflection at the SRO113/SRO214 and Au/SRO113 interfaces, respectively. Here, we discuss other possible origins of these multiple energy scales.

(a) Multi-band superconductivity of SRO214
The first possibility is the multi-band superconductivity of SRO214 6 . This oxide has three Fermi surfaces labeled as , , and . Theoretical calculations 7 and specific heat measurements 8 reveal that the superconducting gap on the  surface is about 3 times larger than those on the  and  surfaces. This multi-gap nature may induce multiple features in the dI/dV data. For example, dI/dV curves in in-plane tunnel junctions exhibit multiple gaplike features whose voltage ratio exactly matches the gap ratio (3.3) 9 . However, in our junctions, the two junctions exhibit the different ratio between V 2 and V 3 (V 2 /V 3 = 5.7 for junction A and 1.5 for junction B at 0.5 T) in both junctions, V 2 /V 3 differs from the gap ratio. In addition, the V 2 and V 3 features persist up to 500 mT, whereas the gaps on the  and  surfaces are believed to be closed at around 150 mT 10 even for  o H||ab-plane. These facts indicate that V 2 and V 3 are related to the interface transparency, but not to the multiple bulk superconducting gaps.

(b) Reduced and induced gaps
The second possibility is that the features of V 2 and V 3 both originates from the SRO113/SRO214 interface. Indeed, in simple SN junctions, multiple gap like features have been observed 11 and attributed to the reduced superconducting gap close to the interface  red in the S side and the induced mini-gap  ind in the N side. In this scenario, V 2 corresponds to  red and V 3 corresponds to  ind . It is theoretically expected that  red improves with the reduction of the transparency of the interface. However, in our junctions, V 2 is larger for junction B, which has higher transparency. Thus, this second scenario cannot explain the observed behavior either.

(c) Andreev bound state
The third possibility is that the conductance peak within V 3 originates from the enhancement of density of states near the interface due to the formation of the Andreev bound state (ABS) 9 , which originates from the p-wave superconducting order parameter of SRO214. In this scenario, it is assumed that a tunneling barrier is accidently formed at the SRO113/SRO214 interface. However, for the quasi-two-dimensional p-wave state, ABS is not expected for out-of-plane tunnel junctions 9 . If in-plane tunneling occurs through atomic steps at SRO214 substrate surface, a broad hump-like behavior within the bulk superconducting gap should be observed 9 . In addition, the observed flat-top peak shape is less common for tunneling junctions but agrees with Andreev reflection behavior.
Therefore, the peak within V 3 is not attributable to the tunneling spectrum with the ABS.

Supplementary Note 4.
We summarize important parameters of junction A and B in Supplementary Table 1 to compare. The junction areas are different but the junction length is the same (15-nm thick SRO113 layer). Normal-state interface resistance is defined as N = J − 214−neck and surface area A s is taken between Au and SRO113. The ratio between the junction impedance Z=R N A S of junctions A and B is about 3.5. This indicates that the interface transparency of junction B is larger than that of junction A. According to the BTK theory for the Andreev reflection 5 , it is expected that the conductance enhancement near V  0 should be stronger for junction B with smaller Z. Indeed, dI/dV of junction B is 29.2  -1 at V  0, which is 49% higher than the conductance at the normal state (dI/dV  19.6  -1 ).
This enhancement is certainly higher than that for junction A (20% enhancement). At 0.3 K and 500 mT, junction B has three times higher V 1 and V 2 than junction A.
But V 3 of junction B is about 12 times higher than that of junction A. As a result,  * 113 is enhanced to 35 nm in junction B. This enhancement also agrees with the higher transparency of junction B. Most importantly, our devices exhibit rather high reproducibility.
Supplementary Figure 4 presents the deferential conductance as a function of the bias voltage measured at various applied fields along the ab-plane. At zero field, both junctions exhibits flat-top enhancement of conductance around V = 0, characteristics for the Andreev reflection. Three characteristic features V 1 , V 2 , and V 3 are evident for both junctions. Supplementary Figure 5 shows a complete set of dI/dV data that is used to produce the color map given in the main text.

Supplementary Note 5: Theoretical model
As we explain in the main text, the observed anomaly in the conductance of the SRO113/SRO214 junctions indicates direct penetration of spin-triplet superconductivity into SRO113. To strengthen our interpretations, we performed a theoretical model calculation.
For the calculation, we followed the model described in Ref. 12. We calculated the spatial profile of the spin-polarized ( and ) Cooper pair amplitude F for a c-axis oriented FM/TSC junction using a self-consistent Bogoliubov-de Gennes approach on a three-dimensional lattice (solved layer-by-layer). To model the junction, we considered a uniform FM layer with the exchange field corresponding to that of SRO113 ℎ ex = 0.16 (t is the hopping amplitude) attached onto an ab-surface of a uniform quasi-two-dimensional TSC that exhibits chiral p-wave orbital symmetry + as Sr 2 RuO 4 (see the inset of Supplementary Fig. 8a). The orbital angular momentum L and d-vector describing the superconductivity in the TSC are both assumed to be perpendicular to the interface (i.e. along the c axis). We fixed the orientation of the magnetization of the FM layer parallel to the interface (i.e along the a axis). The interface is assumed to be uniform and free of magnetic inhomogeneity. Note that the lattice spacing of our model does not directly correspond to the actual crystal lattices of SRO113 and SRO214.
Supplementary Figure 8a presents the imaginary part of the pair amplitude F with the orbital symmetry of p x and/or p y . We calculate ↑↑ and ↓↓ with the quantization axis along the x axis (parallel to the interface: along the magnetization direction). These two components exhibit exponential decay with weak spatial oscillations in the FM layer. Because the inversion symmetry breaks at the interface, the odd-frequency s-wave spin-triplet correlation can be generated at the FM/TSC interface as well. In case of a clean system with a smooth interface, the amplitude of such correlation is very small compared to that of the directly penetrating p-wave correlation. The detailed model calculations considering such odd frequency pairs as well as variation of parameters will be discussed in a separate publication.