Observation of the dominant spin-triplet supercurrent in Josephson spin valves with strong Ni ferromagnets

We study experimentally nanoscale Josephson junctions and Josephson spin-valves containing strong Ni ferromagnets. We observe that in contrast to junctions, spin valves with the same geometry exhibit anomalous Ic(H) patterns with two peaks separated by a dip. We develop several techniques for in-situ characterization of micromagnetic states in our nano-devices, including magnetoresistance, absolute Josephson fluxometry and First-Order-Reversal-Curves analysis. They reveal a clear correlation of the dip in supercurrent with the antiparallel state of a spin-valve and the peaks with two noncollinear magnetic states, thus providing evidence for generation of spin-triplet superconductivity. A quantitative analysis brings us to a conclusion that the triplet current in out Ni-based spin-valves is approximately three times larger than the conventional singlet supercurrent.

We study experimentally nanoscale Josephson junctions and Josephson spin-valves containing strong Ni ferromagnets. We observe that in contrast to junctions, spin valves with the same geometry exhibit anomalous Ic(H) patterns with two peaks separated by a dip. We develop several techniques for in-situ characterization of micromagnetic states in our nano-devices, including magnetoresistance, absolute Josephson fluxometry and First-Order-Reversal-Curves analysis. They reveal a clear correlation of the dip in supercurrent with the antiparallel state of a spin-valve and the peaks with two noncollinear magnetic states, thus providing evidence for generation of spin-triplet superconductivity. A quantitative analysis brings us to a conclusion that the triplet current in out Ni-based spin-valves is approximately three times larger than the conventional singlet supercurrent.
The noncollinear magnetic state can be controllably created in mono-domain spin valves. The simplest is the pseudo spin valve F 1 NF 2 with two F 1,2 layers separated by a normal metal (N) spacer. Triplet current in this case is second-harmonic with respect to the phase difference and is proportional to the difference between F 1 and F 2 [8-10, 13, 14, 16] (see the Appendix for more details). Therefore, an asymmetric spin-valve F 1 =F 2 is needed for generation of the triplet current. The asymmetry (different coercive fields) is also needed for controllable tuning of the relative magnetization angle α between F 1,2 -layers.
Here we study experimentally nano-scale SFS Josephson junctions (JJ's) and SF 1 NF 2 S Josephson spin-valves (JSV's). We use strong F (Ni) to suppress singlet currents and to make triplet currents dominant. We focus on development of various methods for in-situ characterization of micromagnetic states in our nano-devices, including magnetoresistance (MR), absolute Josephson fluxometry (AJF) and First-Order-Reversal-Curves (FORC) analysis. We observe that JSV's behave qualitatively differently compared to JJ's with similar geometry: they exhibit non-Fraunhofer I c (H) modulation with two distinct peaks separated by a dip. In-situ characterization reveals a clear correlation of the supercurrent dip with the antiparallel (AP) state of the JSV and the peaks with two noncollinear states arround it. This provides an in-situ evidence for generation of spin-triplet superconductivity.
Thin film multilayers are deposited by dc-magnetron sputtering and patterned into µm size bridges by photolithography and reactive ion etching. Subsequently they are transferred into a dual-beam Scanning Electron Microscope (SEM) / Focused Ion Beam (FIB) and nanoscale devices are made by 3D FIB nanosculpturing [20,34] and JSV's have similar rectangular shapes with short sides 100 − 300 nm and long sides 250 − 1400 nm. Several devices with different sizes are made at the same chip. Figure 1 shows a SEM image of one of the studied JSV's with a clarifying sketch.
Measurements are performed in closed-cycle cryostats. For analysis of I c (H) modulation the in-plane magnetic field is applied either parallel (H , along the easy magnetization axis) or perpendicular (H ⊥ , along the hard axis) to the long side. More details can be found in the Supplementary [35].  Fig. 2 (c) shows I c (H ⊥ ) along the hard axis for the same Ni (5 nm) JJ. Up and down field sweeps are shown. They exhibit hysteresis due to finite coercivity. From Figs. 2 (a,b) it can be seen that the hysteresis starts/ends at about ∼ ±1.5 kOe, which represents the saturation field. In all cases SFS JJ's exhibit regular Fraunhofer-type I c (H), indicating good uniformity of Niinterlayers [36].

III. PROPERTIES OF SFS JUNCTIONS
A. First-Order-Reversal-Curves analysis FORC is a powerful tool for in-situ characterization of magnetic states in complex ferromagnetic structures [37][38][39]. The analysis starts at the same saturated state. Then field is swept to a reversal field H max and measurements are carried out on the way back to the saturated state. Figs

C. Combined AJF+FORC
For nano-devices with large ∆H the discretness of AJF is a limitation. To obviate this problem we combine AJF with FORC, which allows continuous determination of M (H max ) for arbitrary small devices. For example, the central maxima of FORC's in Figs. 2 (d,e) correspond to Φ = 0. Therefore, fields at which they occur, H(I c0 ), represent absolute values of remnant magnetization M rem = −H(I c0 )/4π. Since we can vary H max with arbitrary small step, we can get a continuous M rem (H max ) curve from such AJF+FORC analysis even for very small devices. This is demonstrated in Fig.  2 (f) where red circles represent −H(I c0 ) = M rem /4π as a function of H ⊥max for FORC's from Fig. 2 (d,e). It is seen that M rem switches rapidly at H ⊥max 1.1 kOe, which represents the coercive field. Blue squares represent I c0 , which apparently stays constant. Thus, hysteresis in SFS JJ's is trivial: remagnetization of the F-layer changes the internal flux, which just shifts I c (H) patterns without changing their shapes.  [36]. Therefore, the double-peak distortion in the easy axis orientation for the same devices can not be ascribed to non-uniformity or defects. This is our central observation that we will analyze below.

A. Hard-axis orientation
We start with the hard-axis orientation because in this case I c (H ⊥ ) patterns have Fraunhofer-type shapes facilitating similar analysis as for SFS junctions.  . It is seen that I c0 is reduced by up to a factor two within the hysteresis region, marked by vertical lines, demonstrating the nontrivial type of hysteresis, compared to SFS junctions, see Fig. 2 (f).

B. Easy-axis orientation
In Figure 5 we analyze behavior of the 160 × 860 nm 2 JSV's in the easy axis orientation. Fig. 5 (a) represents FORC analysis. FORC's are reversible untill H max passes the first I c (H ) peak in the uppward sweep (thin white lines). At higher fields hysteresis appears, accom- panied by the reduction of I c . The I c reaches a minimum when H max passes the second maximum at 816 Oe. At H max = 916 − 1473 Oe a state with one dominant peak is observed. With further increase of H max ≥ 1475 Oe, the second peak reemerges. Finally, for H max larger than the saturation field, 2 kOe, the reversal curve becomes mirror symmetric with respect to the uppward curve. Thus, hysteresis in JSV's is non-trivial for both field orientations: the appearance of hysteresis is always accompanied by the reduction of supercurrent, as indicated in Figs. 4 (d) and 5 (c).

C. Difference between SFS junctions and JSV's
To understand the difference in behavior of JJ's and JSV's, we first note that the conventional Fraunhofer I c (H) modulation in JJ's occurs due to flux quantization with field independent critical current density, J c (H) = const. The observed trivial hysteresis in SFS junctions suggests that upon remagnetization of a single F-layer only the total flux changes, but J c remains unchanged. Conversely, the non-trivial hysteresis in JSV's indicates that J c is not constant, but depends on the relative orientation α of the two F-layers. It is anticipated [8][9][10]32] that the triplet component should vanish in the collinear α = 0, 180, 360 • states and should have maxima in the noncollinear α = 90, 270 • states, see numerical analysis in the Appendix.
The origins of magnetic hysteresis in JJ's and JSV's are also different. For JJ's with a single F-layer it is caused predominantly by the shape anisotropy. Presence of the second F-layer in JSV's leads to another mechanism caused by magnetostatic interaction between F 1,2layers, which favors the AP state. In a mono-domain case remagnetization of a JSV starts by a scissor-like rotation of M 1,2 [32]. Such rotation is reversible and nonhysteretic. It continues until the softer F 1 -layer flips and JSV switches into the AP state. Magnetostatic stability of the AP state leads to the appearance of hysteresis: if the field is reversed, the spin valve will remain in the AP state. With increasing field the harder F 2 -layer also flips and JSV enters into the second scissor-like noncollinear state, which gradually turns into the parallel ↑↑ state [32]. Micromagnetic simulations for our JSV's, presented in the Appendix, confirm such a behavior but also demonstrate that remagnetization may involve formation of two domains. Few domains do not change the overall picture, but lead to additional hysteresis associated with the disappearance of each domain wall.
To summarize the above discussion, the principle difference between JJ's and JSV's is in J c (H) dependence, which is constant for JJs and depends on magnetization orientation, in I c should unambiguously reveal the dominant type of supercurrent. If I c increases than it is singlet and if decreases -triplet. The later is qualitatively consistent with our observations, see Figs. 4 (d) and 5 (c).

D. In-situ characterization of JSV state
Unambiguous confirmation of the triplet nature of supercurrent requires detailed knowledge of the micromagnetic state. Figs. 5 (b-e) represent the in-situ analysis of the magnetic state evolution for the easy axis orientation of the JSV. Fig. 5 (b) represents hysteresis, i.e., area between uppward I c (H ) and FORC's from Fig. 5 (a)  in FORC's. Fig. 5 (e) shows high-bias spin-valve magnetoresistance measured at the same device [35]. Parallel and AP states of JSV correspond to minima and maxima of MR, respectively [20]. Such the analysis provides a self-consistent understanding of the magnetic state evolution in the JSV. The saturation field, at which FORC's stop changing, see Fig. 5 (b), and MR reaches minimum, see Fig. 5 (e), is ∼ ±2 kOe. At H < −2 kOe the JSV is in the ↓↓ parallel state α 0. In a broad range -2 kOe < H max < 26 Oe, there is no hysteresis. Consequently, the JSV is in a mono-domain noncollinear scissor state with reversible rotation 0 < α < 180 • . Hysteresis appears at H max 26 Oe, indicating switching into the magnetostatically stabile AP state α 180 • , as confirmed by the large value of MR. At H max > 816 Oe a sudden change occurs both in hysteresis, Fig. 5 (b), and I c1 , Fig. 5 (c). It indicates a switching out of the AP state into a second noncollinear state 180 • < α < 360 • . At H max 1473 Oe there is yet another jump in both hysteresis, and I c1 , before reaching the saturated ↑↑ parallel state, α = 360 • , at ∼ 2 kOe. Such a two-step switching from AP to ↑↑ parallel state is fully consistent with micromagnetic simulations presented in the Appendix and is due to formation of two domains in both layers. At H max 1473 Oe the thinner F-layer switches into the monodomain state, followed by the thicker F-layer close to the positive saturation field. Arrows in the top part of Fig. 5 (b) sketch the evolution of magnetic states during the remagnetization.  Figs. 5 (b,c), indicates that the field range of the primary hysteresis, 26 Oe < H max 816 Oe, associated with magnetostatic stability of the AP state, coincides with the field range between the two peaks and that the appearance of this hysteresis is accompanied by the reduction of the I c1 peak. Consequently, entrance into the AP state leads to a significant reduction of I c through the JSV. However, the supercurrent recovers upon leaving the collinear AP state in both direction, resulting in the observed double-peak I c (H) pattern. We emphasize that such the behavior is opposite to expectations for the singlet current, which should be at maximum in the AP state and is consistent with the predictions for the oddfrequency spin-triplet supercurrent, see the Appendix.
We note that such an unsusual behavior has not been reported in an earlier similar work [20] on JSV's containing dilluted CuNi ferromagnets because in that case the dominant supercurrent (∼ 80%) had a singlet nature. An estimation based on numerical fitting of our data, presented in the Appendix, indicates that in our Ni-based JSV's the triplet current amplitude is approximately three times larger than the singlet. This helps to uncover the characteristic double-peak modulation, which provides an unambiguous evidence for generation of the spin-triplet order parameter. Yet, even in Ni-based JSV's the dip in the AP state does not go to zero, indicating that there is still a significant subdominant (∼ 30%) singlet supercurrent even through a relatively thick Ni.

V. CONCLUSION
To conclude, both singlet and triplet supercurrents can flow through S/F heterostructures [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. The unique feature of our work that adds to further understanding of the triplet state, along with earlier experimental works [17][18][19][20][21][22][23][24][25][26][27][28], was development of in-situ characterization techniques for an accurate assessment of micromagnetic states in actual nano-devices. In particular, we developed a new AJF+FORC technique, a powerful tool allowing absolute magnetometry of nano-devices and accurate identification of micromagnetic states. We fabricated and studied nano-scale Josephson junctions and (pseudo) spin valves with Ni-interlayers. Small sizes enabled mono-(or few) domain configurations, which could be unambiguous identificatied. A strong F (Ni) was employed for reduction of the singlet current, enabling the dominant triplet component. This was instrumental for observation of an extraordinary behavior of JSV's, qualitatively different from similar-size SFS JJ's. Namely, I c (H) modulation of studied JSV's had two main peaks separated by a dip and exhibited a non-trivial hysteresis, accompanied by reduction of I c . The in-situ characterization showed a clear correlation of the I c dip with the antiparallel state of the spin valve and the two peaks to the two noncollinear states aside of it, thus providing unambiguous evidence for generation of the spin-triplet order parameter.

Appendix: Numerical modeling of Josephson spin-valve
To clarify the behavior of JSV we perform numerical analysis. Josephson current in JSV's has three main components [10]: the short-range spin-singlet I ss , the longrange spin singlet I sl and the long-range spin-triplet I tr .
Their local values depend on relative angles, α(x, y), between magnetizations, M 1,2 , of the two F-layers and the Josephson phase difference between S-electrodes ϕ(x, y): To calculate I c (H) we follow the procedure from Ref. [32]. First we perform a micromagnetic simulation in OOMMF, which provides the two-dimensional distribution of components M x1,2 (x, y) and M y1,2 (x, y). Next, we calculate ϕ by direct integration of: ∂ϕ(x, y) Here H x is the applied magnetic field in the x-direction and d 1,2 are the thicknesses of F 1,2 layers. The total su- . Panel (f) demonstrates that in this hysteresis the singlet current is enhanced, while the triplet is reduced. Therefore, enhancement/reduction of Ic upon appearance of the hysteresis is an unambiguous fingerprint of dominant singlet/triplet supercurrent.
percurrent I s = I ss + I sl + I tr , Eq. (1-3), is integrated over the JSV area using the obtained values α(x, y) and ϕ(x, y). To find the critical current we maximized the supercurrent with respect to the integration constant. For more details of the simulation procedure see Ref. [32]. In Figures 6 and 7 we show results corresponding to one of the studied JSV's Ni(5nm)/Cu(10nm)/Ni(7.5nm) with sizes 160×860 nm 2 . Simulations are shown for the following set of supercurrent amplitudes: I ss0 = 0.1, I sl0 = 1.0, I tr0 = 3.0, which fits well the experimental data. From this we conclude that the triplet current amplitude in our JSV's is approximately three times larger than the singlet, I tr0 /(I sl0 + I ss0 ) 3 . Fig. 6 (a) shows the magnetization curve along the easy axis (see the inset). Black lines represent the major hysteresis loop and color lines -FORC's with H max indicated by circles. The spin valve appears to be at the border between the mono-and the two-domain states. Upon sweeping of the field upwards from the saturated ↓↓ state, magnetization in F-layers first curves into a Cshape (state-A), which is reversible without hysteresis (see the green line). Then the F 1 and F 2 layers switch sequentially into the state with two domains (states B and C) simultaneously flipping the x-component of magnetization. Hysteresis appears in the state B (red line), which corresponds to the AP state. Fig. 6 (b) shows amplitudes of the long-range singlet (blue) and triplet (red) supercurrents for an upward field sweep. In the AP state-B the singlet amplitude is large and the triplet is small. On both sides of it, there are two noncollinear states A, C with large triplet and small singlet amplitudes. At large positive/negative fields the JSV is in the parallel state with vanishing of both singlet and triplet long-range components. The shape of I c (H) pattern of the JSV depends on relative amplitudes of singlet and triplet components. Fig. 6 (c) shows the case with the dominant triplet current (I ss0 = 0.1, I sl0 = 1.0, I tr0 = 3.0) for the total (black), singlet (blue) and triplet (red) currents. Since in this case the total current is dominated by the triplet current, I c (H) has two peaks corresponding to the noncollinear states A and C, separated by a dip, corresponding to the AP state B, similar to the experimental data in Fig. 5 (d).
In Figs. 6 (d-i) we analyze I c (H ) FORC's, corresponding to M (H) curves with the same color in Fig. 6 (a). Panel (d) represents the case when H max is within the first I c (H) peak. Here the spin valve is in the reversible noncollinear state-A. In (e) H max is within the dip in the AP state-B. As emphasized in the main text, the fingerprint of the AP state is the appearance of hysteresis, see red line in Fig. 6 (a). Panel (f) demonstrates that within this hysteresis the singlet current is increased (top panel) and the triplet is decreased (bottom panel). Thus, the change of the current upon appearance of hysteresis tells us about the nature of the dominant supercurrent. Since in our simulations the triplet current is dominant, there is an overall drop of I c at the hysteretic branch, as seen in Fig. 6 (e). Panels (g) and (h) show FORC's after switching out of the AP state B into the noncollinear state C with domains. Note that along with some metastability associated with domains, in Fig. 6 (h) we observe a net enhancement of the central noncollinear peak at the expense of the second peak. Finally, panel (i) shows I c (H) starting from fully saturated states. Overall, presented simulations are in a good agreement with experimental data for JSVs' from Fig. 5 (a). Simulations reproduce both the double-peak I c (H ) patterns and the nontrivial hysteresis with reduction of I c in the AP state.
We note that we assumed that the JSV is narrow enough so that flux quantization field is larger than the saturation field. Therefore, critical current modulation is not upset by flux quantization. However, in larger JSV's flux quantization does strongly affect the I c (H) modulation [32]. This is the main reason for size-dependence of I c (H) patterns, see Fig. 3. For long JSV's with a small ∆H the double-peak structure of I tr0 (H) is completely masked by rapid flux-quantum oscillations, leading an overall Fraunhofer-type modulation of I c (H).
To demonstrate this, in Figure 7 we present simulations for the same device in the hard axis orientation with larger L = 860 nm, see the sketch in Fig. 7 (a). Fig. 7 (a) shows the large hysteresis of magnetization curve M y (H y ). Here the intermediate AP step is also present, but with a limited range of existence, compared to the easy axis, Fig. 6 (a). This occurs because at H = 0 moments tend to align with the easy x-axis, destroying the AP state. To the contrary, the range of fields for coherent rotation of magnetization is broader and both layers remain in the monodomain state. Corresponding distributions of magnetizations are shown in Fig. 7 (b) for points A) the first non-collinear state upon coherent rotation from the negative parallel state, B) antiparallel state and C) the second non-collinear state upon switching from the AP state. Fig. 7 (c) shows sample-averaged values of normalized triplet, ∝ sin 2 (α) (red) and singlet, ∝ sin 2 (α/2), (blue) current amplitudes, see Eqs. (3) and (2). The behavior of both components is similar to the easy axis case, Fig.  6 (b). I.e., in this respect the field orientation does not make a principle difference. However, the I c (H) pattern is strongly affected in this orientation. Figs. 7 (d-f) show magnetic field modulation of (d) triplet, (e) singlet, and (f) total currents. It can be seen that although triplet current amplitude in panel (c) has two clear peaks (A, C), however, the large length L of the JSV at this field orientation makes ∆H much smaller than the coercive field. Therefore at points A and C with the largest triplet amplitudes there are already many flux quanta inside the JSV, suppressing the triplet critical current by more than an orders of magnitude. As a result, the characteristic double-maxima feature becomes unrecognizable in the total I c (H) modulation. Thus, the difference between easy and hard axis orientations is entirely due to the flux quantization effect. Nevertheless, both numerical simulations, see Figs. 6 (b) and 7 (c) and experimental analysis in Figs. 4 and 5 demonstrate that the essential physics remains independent of the field orientation. , red) and singlet (∝ sin 2 (α/2), blue) current amplitudes for the upward field sweep. Panels (d-f) show magnetic field modulation patters for (d) triplet, (e) singlet, and (f) total critical currents. It can be seen that although triplet current amplitude in (c) has two clear peaks in noncollinear states A, C, however, small flux quantization field at this field orientation leads to rapid damped oscillations, which suppresses the triplet supercurrent (see the vertical scale). Therefore, the characteristic double-maxima become unrecognizable in the total Ic(H) modulation (f). This explains how flux quantization effect changes Ic(H) patterns for JSV's from a double-to a single-peak for easy-and hard-axis orientations, respectively.