Crossover between short and long range proximity effects in SFS junctions with Ni-based ferromagnets
O. M. Kapran, T. Golod, A. Iovan, A. S. Sidorenko, A. A. Golubov, V. M. Krasnov
CCrossover between short and long range proximity effects in SFS junctions withNi-based ferromagnets.
O. M. Kapran , T. Golod , A. Iovan , , A. S. Sidorenko , , A. A. Golubov , and V. M. Krasnov , ∗ Department of Physics, Stockholm University, AlbaNova University Center, SE-10691 Stockholm, Sweden; Department of Applied Physics, Royal Institute of Technology, SE-10691 Stockholm, Sweden; Institute of Electronic Engineering and Nanotechnologies ASM, MD2028 Kishinev, Moldova; I.S. Turgenev Orel State University, 302026 Orel, Russia; Faculty of Science and Technology and MESA+ Institute of Nanotechnology,University of Twente 7500 AE, Enschede, The Netherlands; and Moscow Institute of Physics and Technology, State University, 141700 Dolgoprudny, Russia.
We study Superconductor/Ferromagnet/Superconductor junctions with CuNi, PtNi, or Ni in-terlayers. Remarkably, we observe that supercurrents through Ni can be significantly larger thanthrough diluted alloys. The phenomenon is attributed to the dirtiness of disordered alloys leadingto a short coherence length despite a small exchange energy. To the contrary, pure Ni is cleanresulting in a coherence length as long as in a normal metal. Analysis of temperature dependenciesof critical currents reveals a crossover from short (dirty) to long (clean) range proximity effects inPt − x Ni x with increasing Ni concentration. Our results point out that structural properties of a fer-romagnet play a crucial role for the proximity effect and indicate that conventional strong-but-cleanferromagnets can be advantageously used in superconducting spintronic devices. I. INTRODUCTION
A competition between superconductivity and ferro-magnetism leads to an unconventional proximity effect,studied both theoretically [1–18] and experimentally [19–41]. In strong ferromagnets (F) Fe, Co, Ni, exchangeenergies, E ex ∼ ∼ −
10 K, in low- T c superconductors (S).Therefore, spin-singlet Cooper pairs are usually brokenat a very short range ∼ l e , and, thus, on theinternal structure. In particular, it has been predicted,that in clean F even a singlet supercurrent should ex-hibit LRPE [2, 8, 12, 14, 15, 24]. Experimental analysisof SFFS spin-valves has shown that the singlet current isdominant for diluted F [36] and remain considerable evenfor pure Ni [41]. Clarification of LRPE mechanisms andthe ways of controlling supercurrents in S/F heterostruc-tures is important both for fundamental understanding of unconventional superconductivity [42], and for appli-cation in superconducting spintronics [18, 32, 34, 39, 41].Here we study nanoscale SFS Josephson junctions(JJ’s) containing either diluted Ni-alloys Cu − x Ni x andPt − x Ni x , Cu/Ni bilayer or pure Ni. Counterintuitively,we observe that the supercurrent density, J c , throughNi can be much larger than through diluted alloys withthe same thickness. Using in-situ absolute Josephsonfluxometry (AJF), we demonstrate that Ni interlayers inour junctions exhibit full saturation magnetization as inbulk Ni, which precludes presence of extended dead mag-netic layers. The clue to understanding of our results isobtained from the analysis of evolution of temperaturedependencies, J c ( T ), in Nb/Pt − x Ni x /Nb JJ’s with in-creasing Ni concentration. It shows that in diluted Ni-alloys, x (cid:39) .
5, the proximity effect is short range, de-spite a small E ex , due to an extremely short m.f.p. issuch atomically disordered alloys. To the contrary, pureNi remains clean, facilitating ballistic Cooper pair trans-port and LRPE similar in scale to that in the normalmetal Pt. Our results demonstrate that the proximityeffect in ferromagnets depends not only on compositionand E ex , but also essentially on the internal structure.This may help to resolve some of the controversies aroundLRPE. We conclude that strong-but-clean ferromagnetsmay have advantages compared to weak-but-dirty for de-vice applications.The paper is organized as follows. In sec. II we de-scribe sample fabrication and experimental procedures.In sec. III we discuss main experimental results, includ-ing III A. in-situ magnetic characterization of Ni inter-layers via AJF and III B. analysis of temperature depen-dencies of critical currents, which reveals a crossover be-tween clean (ballistic) and dirty (diffusive) transport. Inthe Appendix we provide additional information about a r X i v : . [ c ond - m a t . s up r- c on ] F e b I Adrian SP Cu Junction 6 µ m SiO S (Nb) F (a) FIB cuts NbFNb
Junction (c)(d) (e)(f)(b)
FIG. 1. (color online). (a) SEM image of an SFS junction and (b) a sketch with indication of current flow paths. (c) The I - V curve of Nb/Cu . Ni . /Nb junction with d F = 10 nm. (d) A set of I - V ’s of a Nb/Ni(7 nm) /Nb junction at different T . (e,f ) Temperature dependencies of the critical current density for (e) the same Nb/Cu . Ni . /Nb junction and (f) Nb/Ni/Nbjunctions with different Ni thicknesses 5, 7, 10 and 20 nm. Note that the J c ( T = 3 K ) for the Ni-junction, d F = 10 nm, isalmost an order of magnitude larger than that for the junction with diluted Cu . Ni . interlayer with the same d F . A. film structure, B. junction characteristics, C. prop-erties of Nb/Pt − x Ni x /Nb junctions, D. interface resis-tances in Nb/Pt − x Ni x /Nb junctions, and E. extractionof magnetization curves from AJF analysis. II. SAMPLES AND EXPERIMENTAL
We present data for nano-scale SFS junctions with F-interlayers made of Cu . Ni . and Pt − x Ni x alloys with x = 0 −
1, pure Ni and a Cu/Ni (N/F, N-normal metal)bilayer. SFS multilayers were deposited by dc-magnetronsputtering in a single cycle without breaking vacuum.Cu − x Ni x films were deposited by cosputtering from Cuand Ni targets and the concentration was controlled bythe corresponding sputtering rates. Pt − x Ni x films weredeposited from composite targets with different areas ofNi and Pt segments and Ni concentration was estimatedusing energy-dispersive X-ray spectroscopy. More detailsabout fabrication and magnetic properties of Pt − x Ni x films can be found in Refs. [43, 44] and in Appendices Cand D. Nb/Ni/Nb JJ’s with different d F were fabricatedfrom the same wafer with a calibrated Ni-thickness gra-dient [24]. Nb(S) electrodes were ∼
200 nm thick. Multi-layers were first patterned by photolithography and reac-tive ion etching and then processed by focused ion beam(FIB). Nano-scale JJ’s with sizes down to ∼
60 nm weremade by FIB-nanosculpturing [26, 36, 45]. Small sizesare necessary both for achieving the monodomain state[41, 46] and for enhancing normal resistances to comfort- ably measurable values, R n (cid:38) . d F ,and compositions. Junction parameters are listed in Ta-bles I-III of the Appendix. Properties of Josephson spinvalves with similar CuNi and Ni interlayers can be foundin Refs. [36] and [41]. Figure 1 shows (a) a scanningelectron microscope (SEM) image of one of the studiedNb/Ni/Nb JJ’s and (b) a sketch with a current path.Measurements are performed in He and He closed-cycle cryostats. Magnetic field, parallel to the junctionplane, is supplied by a superconducting solenoid. We willshow measurements with field oriented either parallel H (cid:107) (easy axis), or perpendicular H ⊥ (hard axis) to the longside of the JJ. III. RESULTS AND DISCUSSION
Figs. 1 (c,d) show Current-Voltage characteristics ( I - V ) at zero field for (c) Nb/Cu . Ni . /Nb junction with d F = 10 nm at T (cid:39) . d F = 7 nm at different temperatures, T = 1 . − . I - V ’s are typical for proximity-coupledJJ’s, described by the resistively shunted junction model.Figs. 1 (e,f) show temperature dependencies of criticalcurrent densities for (e) the same Nb/Cu . Ni . /Nb JJ,and (f) Nb/Ni/Nb JJ’s with d F = 5, 7, 10 and 20 nm.It is seen that the JJ with a diluted Cu . Ni . interlayerhas a significantly smaller J c than the JJ with pure Niwith the same d F = 10 nm, compare red lines in Figs. 1 I c ( µ A ) (a) Ni 5 nm237x942 nm T = 6 K π M N i ( k G ) H ll (Oe) Φ / Φ (c) (b) Ni 7 nm220x1000 nm T = 2 K H ll (Oe) Ni 10 nm 250x925 nm T = 4.5 K H ⊥ (Oe) (d) Ni 20 nm250x1000 nm T = 0.4 K H ⊥ (Oe) FIG. 2. (color online). Top panels: magnetic field modulation of the critical current, I c ( H ), for Nb/Ni/Nb JJ’s with d Ni (a)5 nm and (b) 7 nm in the easy axis orientation and (c) 10 nm and (d) 20 nm in the hard axis orientation. Blue/red linesrepresent up/down field sweeps. Middle panels show the absolute Josephson fluxometry analysis of the data above. Symbolsrepresent positions of maxima and minima of the I c ( H ) patterns, which correspond to half-integer and integer values of Φ / Φ .Bottom panels represent magnetization curves of Ni interlayers obtained from the AJF analysis. Large values of the saturationmagnetization 4 πM Ni (cid:39) (e) and (f). It is also seen that the Cu . Ni . JJ exhibitsstronger superlinear temperature dependence with a pos-itive curvature d J c /dT > T , which is welldescribed by the power-law dependence J c ∝ (1 − T /T c ) a with a (cid:39) .
5. On the other hand, Ni JJ’s show almostlinear J c ( T ), irrespective of Ni thickness, albeit with avarying onset temperature T ∗ c . III A.
In-situ magnetic characterization of Niinterlayers via absolute Josephson fluxometry.
Top panels in Figure 2 represent measured I c ( H ) mod-ulation patterns for Nb/Ni/Nb JJ’s with different d Ni (a) 5 nm, (b) 7 nm, (c) 10 nm and (d) 20 nm. Junc-tion sizes and measurement temperatures are indicatedin the Figure. Modulation patterns are shown both foreasy (a,b) and hard (c,d) axis orientations. Blue and redlines represent up and down field sweeps. A hysteresisis due to finite coercivity of F-interlayers. It disappearsat H ∼ ± (1 − .
5) kOe, corresponding to transition intothe saturated magnetic state. All JJ’s, included in theanalysis, exhibit Fraunhofer-type I c ( H ) modulation, in-dicating good uniformity of interlayers [47]. Examplesof I c ( H ) patterns for Nb/PtNi/Nb and Nb/Ni/Nb junc-tions can be found in Refs. [45] and [41], respectively.The I c ( H ) modulation occurs due to flux quantization. This can be used for in-situ AJF analysis [32, 36, 41], pre-sented in middle panels of Fig. 2. Here symbols representthe flux, Φ( H ), at maxima and minima of I c ( H ), whichcorrespond to half-integer and integer number of the fluxquantum, Φ , respectively. The total flux is:Φ = BL Λ + 4 πM F Ld F , (1)where B is magnetic induction, L is the junction length,Λ is the effective magnetic thickness of the JJ and M F is magnetization of the F-layer along the field. The firstterm in the right-hand-side represents the flux inducedby magnetic field, the second - by magnetization of theF-layer (for more details see Appendix E).From Figs. 2 (a,b) it is seen that at large fields Φ( H )is linear. Since in this case F-layers are in the satu-rated state, M F = M sat , the linear field dependence iscaused solely by the first term in Eq. (1) with B ∝ H .Subtraction of this linear dependence, shown by dashedlines in middle panels of Fig. 2, reveals the contribu-tion, ∆Φ, from the second term in Eq. (1). This yieldsthe absolute value of magnetization in the F-interlayer4 πM F = ∆Φ /Ld F . Thus obtained magnetization curves,4 πM Ni ( H ), are shown in bottom panels of Fig. 2. Sat-uration magnetizations are 4 πM sat = 8 . ± . d Ni = 5 nm, 7 . ± . d Ni = 7 nm and 6 . ± . d Ni = 10 nm. For d Ni = 20 nm the satura-tion magnetization is not reached within the shown fieldrange (see Appendix E for clarifications). The main un-certainty in M sat is caused by the accuracy of estimationof d Ni , limited by the film roughness R q (cid:39) πM sat (cid:39) M sat ,were reported in earlier works [23, 26] and would makeinterpretation of proximity effect more complicated. Onthe other hand, a variation of the superconducting onsettemperature, which can be seen in Figs. 1 (f) and 3 (b),provides an evidence for existence of dead superconduct-ing (rather than magnetic) layers with suppressed T ∗ c atjunction interfaces.The large value of M sat confirms that supercurrents inour Nb/Ni/Nb JJ’s flow through a pure Ni with strongferromagnetic properties. Remarkably, we observe a large J c (cid:39) × A/cm , even through 20 nm of Ni, see Fig.1 (f). This is a much longer scale compared to earlierreports [21, 26, 27, 31, 34] in which supercurrent wasobserved only through few nm of Ni. Observation andclarification of such a profound LRPE through a strongF is the main objective of this work. III B. Temperature dependencies of criticalcurrents: crossover between dirty and clean regimes.
To clarify our observations, we start with a short sum-mary of proximity effects in SNS and SFS JJ’s (moredetailed analysis can be found in Ref. [50], where var-ious regimes have been considered). In SNS JJ’s J c isdetermined by the superconducting order parameter atthe junction interface, Ψ S/N , and the ratio of the thick-ness, d N , to the coherence length, ξ N , of the interlayer.Close to T c it can be written in the following simple form[51], J c ∝ Ψ S/N exp (cid:18) − d N ξ N (cid:19) . (2)For JJ’s with thick d N , or short ξ N , d N (cid:29) ξ N ( T c ), the J c ( T ) is determined predominantly by the T -dependenceof ξ N ( T ), leading to a strong superlinear T -dependence.In the opposite case, d N (cid:28) ξ N ( T c ), J c ( T ) is determinedby Ψ S/N ( T ), leading to a conventional linear J c ( T ) closeto T c and a saturation at T → ξ F is complex [6, 20], ξ − F = ξ − F + iξ − F . (3)The real part, ξ F , represents the decay length, the imag- Pt Ni PtNi (a)
Nb / Pt Ni x / Nb J c / J c ( . T c ) T / T c x = 0 x = 0.13 x = 0.2 x = 0.27 x = 0.4 x = 0.54 x = 0.6 x = 1.0 normal ferro-magnetic (b) T c * ( K ) x (Ni concentration) FIG. 3. (color online). (a) Temperature dependencies J c ( T )of Nb/Pt − x Ni x /Nb junctions with d F = 20 nm, normalizedto the value at T = 0 . J c ( T ) dependencies from linear for pure Pt, x =0, to superlinear at x (cid:39) . − . x = 1, indicates a transitions between SNS to dirty SFS andto clean SFS cases. (b) Corresponding onset temperatures ofthe junctions versus Ni concentration. inary, πξ F , the period of oscillations. In the clean case, ξ F ( c ) = (cid:126) v f πk B T + iE ex ) , (4)where v f is the Fermi velocity in F. In the dirty case, ξ F ( d ) = (cid:114) l e ξ F ( c ) . (5)Since here l e (cid:28) | ξ F ( c ) | , the coherence length in the dirtycase is shorter than in the clean case. For strong Fwith E ex /k B (cid:29) T c , in the dirty case ξ F ( d ) (cid:39) ξ F ( d ) (cid:39) ( (cid:126) l e v f / E ex ) / are equaly short. However, in the cleancase the two scales are different: ξ F ( c ) (cid:39) ( (cid:126) v f / πk B T ),is as long as ξ N , and ξ F ( c ) (cid:39) ( (cid:126) v f / E ex ) is short[8, 14, 15, 24]. From the discussion above, it follows thatthe shape of J c ( T ) provides an important clue about theproximity effect [20, 22, 23, 26].Figure 3 (a) shows evolution of J c ( T ), normalized tothe value at 0 . T ∗ c for Nb/Pt − x Ni x /Nb JJ’s with dif-ferent Ni concentrations and d F (cid:39)
20 nm. The onsettemperature T ∗ c is shown in Fig. 3 (b). Ferromagnetismin Pt − x Ni x appears at a critical concentration x c = 0 . T ∗ c for the pure Ni, x = 1, wecan also see a clear minimum at x c = 0 .
4. Both minimacan be interpreted as being due to suppression of Ψ
S/N atthe interface (dead superconducting layer) due to eithera reverse magnetic proximity effect for pure Ni, x = 1,or quantum fluctuations at the quantum critical point, x c = 0 . x = 0(black line), J c ( T ) is almost linear. As explained above,this is expected for SNS JJ’s with ξ N ( T c ) (cid:29) d N . Uponincreasing Ni concentration, J c ( T ) remains linear for non-magnetic interlayers x = 0 .
13, 0.2, 0.27. At the criticalconcentration, x c = 0 . J c ( T ). It becomes most pronounced for x = 0 . − . ξ F bothdue to enhancement of E ex and reduction of l e . While E ex increases linearly at x > x c , the m.f.p. reaches mini-mum at x (cid:39) .
5, corresponding to atomically disordered, l e ∼ x = 1 (orangeline), the linear J c ( T ) dependence is restored, similar to apure Pt, x = 0. Such a recovery implies that ξ F in pureNi is similarly long as ξ N for pure Pt, despite the large E ex ∼ K. As discussed above, this indicates occur-rence of clean, ballistic transport in Ni. Thus, variationof the shape of J c ( T ) reveals two crossovers in electrontransport regimes with changing Ni-concentration. Firsta crossover takes place from a clean SNS type proximityeffect in pure Pt to dirty SFS case in diluted, atomicallydisordered alloy x (cid:39) .
5. With further increase of x asecond crossover from dirty to clean ballistic transporttakes place for JJ’s with pure Ni.As mentioned in the Introduction, interpretation ofLRPE in strong ferromagnets is still controversial. Inseveral cases it was attributed to appearance of the un-conventional odd-frequency spin-triplet order parameter.Recently the dominant ( ∼ F S Josephson spin-valve structureswith similar Ni-interlayers [41]. However, the triplet su-percurrent appears only in the noncollinear state of thespin valve and is tuned by the relative orientation ofmagnetization in the two F-layers. Appearance and dis-appearance of the long-range triplet supercurrent uponremagnetization of the spin-valve leads to a profound dis-tortion of the I c ( H ) pattern [41]. Such a distortion is themain fingerprint of the triplet component [46] and, thus,provides the key evidence for it’s existence. SFS junc-tions, containing just a single F-layer, behave completelydifferently (see e.g. the discussion in sec. IV C of Ref.[41]). In particular, I c ( H ) patterns of all our junctionsare Fraunhofer-like, with the only distortion caused bythe hysteresis in M F ( H ). As discussed in the Introduc- tion, the triplet state is not anticipated in SFS junctionsbecause there is no obvious mechanism for appearanceof the noncollinear magnetic state in the perpendiculardirection across the single F-layer. Therefore, we wantto emphasize, that LRPE in Nb/Ni/Nb JJ’s with cleanNi is achieved by the spin-singlet current without involve-ment of the unconventional odd-frequency spin-triplet or-der parameter. Such LRPE is simply a consequence ofthe lack of scattering mechanism that can destroy singletCooper pair correlations in a clean metal (no matter For N) at T = 0 [12]. Thus, it is the cleanliness of pure Nithat facilitates LRPE in Nb/Ni/Nb JJ’s. Concurrently,the extreme dirtiness suppresses proximity effect throughdiluted F-alloys, despite a small E ex .We also studied Nb/Cu(10nm)/Ni(10nm)/Nb JJ’s,with Cu/Ni bilayer. Interestingly, they show an orderof magnitude smaller J c than Nb/Ni(10nm)/Nb JJ’s, seeTable I in the Appendix, consistent with earlier resultsfor Ni-based JJ’s with Cu buffer layers [27, 31, 34]. Thisis surprising because, due to a large ξ N ∼ µ m of Cu,10 nm should have little influence. On the other hand,neighbors in the periodic table Cu and Ni tend to easilyalloy with each other. Therefore, Cu/Ni bilayers likelycontain a dirty CuNi interlayer, which leads to suppres-sion of J c . CONCLUSIONS
To conclude, we have studied SFS junctions with dif-ferent Ni-based interlayers. We observed that supercur-rents through pure Ni may be much larger than throughdiluted alloys with much smaller E ex . Analysis of J c ( T )dependencies revealed that this counterintuitive result iscaused by the dirtiness of disordered Ni-alloys, leadingto a short coherence lengths ξ F ∼ ξ N ( T → → ∞ irrespective of cleanliness, forSFS JJ’s LRPE occurs only in the clean case, for which ξ F ( c ) → ∞ at T →
0, while for the dirty case ξ F ( d )remains short irrespective of T . This leads to a principledifference in the range of proximity effects for clean anddirty ferromagnets with otherwise similar compositionsand exchange energies.The work was supported by the EU H2020-WIDESPREAD-05-2017-Twinning project “SPIN-TECH”, grant agreement Nr. 810144 (sample prepa-ration and measurements) and the Russian ScienceFoundation grant No. 19-19-00594 (data analysis andmanuscript preparation). The manuscript was writtenduring a sabbatical semester of V.M.K. at MIPT,supported by the Faculty of Natural Sciences at SU. Appendix A. Nb/Ni film structure
Figure 4 shows topography maps obtained by atomicforce microscopy for (a) a Nb film with thickness d = 100nm and (b-d) Nb/Ni bilayers with increasing Ni thick-ness. It can be seen that the Nb film has a rise-seed-likestructure with elongated crystallites (a). In Nb/Ni bilay-ers, with increasing Ni thickness, d Ni , the structure of Nifirst inherits that of Nb (b) but at d Ni (cid:39) ∼
20 nm)with further increase of d Ni (in the studied range). Themean-square-root roughness of all films is R q (cid:39) ∼ ± d Ni < R q (cid:39) Appendix B. Summary of junction characteristics
Tables I-III represent characteristics of all types ofstudied junctions. Figure 5 summarizes measured criticalcurrent densities at T = 3 K for JJ’s with different in-terlayer composition and thickness, studied in this work. J c decreases both with increasing Ni concentration andinterlayer thickness. For Nb/Ni/Nb JJ’s (blue) we havesufficient samples to observe the non-monotonous depen-dence J c vs. d F due to 0 − π transitions [20, 22, 23, 26].The blue line, connecting points for Ni-JJ’s, however, isdrawn solely for the easiness of identification of the datapoints and does not reflect the anticipated J c ( d F ) de-pendence, which should oscillate at a much shorter scale ξ F ( N i ) ∼ J c value for Ni(20nm)JJ in Fig. 5 is the consequence of the much lower onsettemperature T ∗ < T = 3 K. Thistemperature was chosen because we have data for this T for all junctions. The low T ∗ of Ni-JJ results in themisleadingly low J c (3K), as can be seen from Fig. 1 (f). More appropriate comparison should be done for T (cid:28) T ∗ . Such data is listed in Tables I and III and isconsistent with our conclusion. One should also keep inmind the oscillatory dependence of J c on d F with a nm-scale period of oscillations. Since the periods are differentfor different ferromagnets, it becomes impossible to makea conclusion by comparing just two JJ’s with a fixed d F .For the same reason we do not claim that J c in Ni isalways larger than in an alloy (which can not be true dueto different oscillatory dependencies of the two). Also,because of that we can not make an estimation of decaylengths for our SFS junction. Somewhat reliable decaylength estimation from the data in Fig. 5 could be madeonly for non-magnetic alloys with x < . Appendix C. Properties of Nb/Pt − x Ni x /Nbjunctions Group-10 elements Pt and Ni are well intermixed witheach other and can form solid solutions at arbitrary pro-portions [52–54]. PtNi alloys should be fairly uniform,contrary to CuNi alloys which are prone to phase segre-gation and formation of Ni clusters. Therefore, we havechosen this alloy for detailed analysis of variation of prop-erties of SFS junction with the strength of F-interlayer.For that we made a series of Nb/Pt − x Ni x /Nb JJ’s withdifferent Ni concentrations x = 0 −
1. Composition ofPt − x Ni x films was estimated using energy-dispersive X-ray spectroscopy [43].Figures 6 (a) and (b) summarize magnetic properties ofthin Pt − x Ni x films (35-45 nm thick) obtained in earlierworks [43, 44]. Fig. 6 (a) shows the anomalous Halleffect (AHE) conductivity σ xy at the T - x phase diagram.The AHE indicates appearance of the ferromagnetic state[55]. Fig. 6 (b) shows the Curie temperature extractedfrom Hall measurements. It is seen that ferromagnetismin Pt − x Ni x thin films appears at x > .
4, similar to bulkalloys [53].Pt − x Ni x alloys may form a disordered fcc state ( A Ni ( L ),PtNi ( L ) and Ni Pt ( L ) with centra of stability at x = 0 .
25, 0.5 and 0.75, respectively [52, 54]. The mostremarkable feature of the AHE in PtNi films, Fig. 6 (a),is the sign-change of σ xy from electron-like to hole-like at x (cid:39) . − .
6, which coincides with the expected range ofstability of the layered L PtNi compound [52, 54, 56].Fig. 6 (c) represents residual longitudinal resistivitiesof the films at T = 2 K. The ρ xx increases upon mixingof Ni and Pt with maximum around x (cid:39) .
5. This indi-cates a progressive shortening of the electronic m.f.p. dueto the growing disorder. The 50-50 mixture has almostan order of magnitude larger ρ xx than the pure Ni film Nb Rq=0.796 nm
Nb/Ni(2nm)
Rq=1.18 nm
Nb/Ni(6nm)
Rq=1.22 nm
Nb/Ni(15nm)
Rq=1.07 nm (a) (b)(c) (d)
FIG. 4. (color online). Atomic force microscope topography maps of a 100 nm thick Nb film (a) without Ni on top, and (b)with 2 nm Ni, (c) 6 nm Ni and (d) 15 nm Ni films on top. It can be seen that the Ni film reconstruction occurs at about 5 nmthickness.
Cu(10nm)/NiPt Ni Pt Ni Ni Cu Ni Pt T = 3 K Pt Ni Pt Ni Pt Ni J c ( A / c m ) d F (nm) FIG. 5. (color online). A summary of measured critical cur-rent densities for different junctions at T = 3 K versus theinterlayer thickness. x = 1. Simultaneously we also see sharp peaks at x (cid:39) . L and L states. Since ferromagnetism in Pt − x Ni x alloy appears at x c (cid:39) .
4, diluted ferromagnets with small T Curie ∼ T c of Nb, correspond to an extremelydirty metallic state. The short electronic m.f.p. leadsto a short ξ F , which leads to a rapid suppression ofthe proximity induced superconducting order parameterwith increasing d F [6, 15]. Therefore, as discussed in themanuscript, SFS junctions with weak disordered ferro-magnets may have small critical current densities despitesmall exchange fields.Nb/Pt − x Ni x /Nb junctions with different x and d F were fabricated and studied, see Table II. An exampleof I c ( H ) modulation for Nb/PtNi/Nb JJ can be foundin Fig. 4 of Ref. [45]. Figure 7 (a) shows measured J c ( T = 3K) for Nb/Pt − x Ni x /Nb junctions versus Niconcentration and interlayer thickness. Fig. 7 (b) showsprojection of this data to the J c - x plane. Generally, J c decreases both with increasing x and d F . However, itdecreases non-monotonously. Oscillatory decay of J c vs. d F in SFS junctions is well documented and is caused bysequential 0- π transitions [20, 22, 23, 26].From Fig. 7 it can be seen that for a given d F the J c isdecaying non-monotonously with increasing Ni concen-tration x , as indicated by dashed red lines in Fig. 7 (a)for d F = 20 and 30 nm. We attribute such oscillatorybehavior to 0- π transitions at a given d F upon increasing TABLE I. Parameters of junctions with Ni, Cu/Ni and CuNi interlayers: d F is the thickness of F-interlayer; the size definesjunction area A = L x × L y ; R n is the normal resistance of the junction; ρ n = R n A/d is junction resistivity, for junctions withCu/Ni bilayer d = d Cu + d Ni = 20 nm, for the rest d = d F ; T is the temperature; I c is the maximum critical current, J c = I c /A is the critical current density; I c R n is the characteristic voltage. For some junctions values of I c , J c and I c R n at different T are provided.Interlayer d F Size R n R n A ρ n T I c J c I c R n (nm) (nm ) (mΩ) (10 − Ωcm ) (10 − Ωcm) (K) ( µ A) (10 (A/cm ) ( µ V)Ni 5 855 ×
160 46.8 0.64 1.28 6.2 378 27.7 17.7Ni 5 942 ×
237 28.3 0.632 1.26 5.2 1110 49.7 31.4Ni 5 896 ×
164 31 0.456 0.911 3 2800 124 86.85.5 760 51.7 23.6Ni 7 1100 ×
220 39.9 0.966 1.38 2 30 1.24 1.2Ni 7 1380 ×
220 21.7 0.66 0.943 2 67 2.21 1.45Ni 7 950 ×
300 32 0.912 1.3 3.5 100 3.51 3.2Ni 7 750 ×
220 68 1.12 1.6 2 262 15.88 17.8Ni 7 1000 ×
220 46 1.01 1.44 3 240 10.9 11.04Ni 10 865 ×
165 52 0.742 0.742 5.8 324 22.7 16.8Ni 10 926 ×
250 30.5 0.706 0.706 6.5 311 13.4 9.5Ni 10 925 ×
250 29 0.671 0.671 4.5 600 26 17.42 1800 77.8 52.2Cu(10 nm)/Ni 10 800 ×
275 31.5 0.693 0.347 0.49 100 4.55 3.15Cu(10 nm)/Ni 10 250 ×
200 158 0.79 0.395 0.5 8.5 1.7 1.34Cu(10 nm)/Ni 10 700 ×
160 53 0.594 0.297 1.8 13.4 1.2 0.71Cu(10 nm)/Ni 10 700 ×
300 29.15 0.612 0.306 1.8 215 10.2 6.29Cu(10 nm)/Ni 10 814 ×
250 33 0.6716 0.3358 2.86 95 4.67 3.14Cu(10 nm)/Ni 10 650 ×
250 47.5 0.772 0.386 0.37 57.5 3.54 2.73Cu(10 nm)/Ni 10 800 ×
175 53 0.742 0.371 0.37 180 12.86 9.54Cu . Ni .
10 730 ×
230 83.5 1.41 1.41 0.56 195 11.6 16.19Ni 20 1000 ×
250 14 0.35 0.175 0.4 500 20 7.0 (a) x (Ni concentration) <-50 T ( K ) σ A H E ( Ω c m - ) (c) ρ xx ( - Ω c m ) x (Ni concentration)(b) x (Ni concentration) Pt Ni x T C u r i e ( K ) FIG. 6. (color online). Characteristics of Pt − x Ni x thin films. (a) Anomalous Hall effect conductivity versus temperature andNi concentration. (b) Curie temperature obtained from the AHE data. Note that the magnetic quantum phase transition with T Curie (cid:39) x c (cid:39) .
4. (c) Residual in-plane resistivity of films. Maxima of ρ xx are observed at x (cid:39) . the ferromagnetic exchange energy E ex . The increase ofNi concentration leads to the enhancement of E ex , whichleads to the shrinking of ξ F and cause the 0- π transi-tion. As described above, ferromagnetism in Pt − x Ni x films appears at the critical concentration x c (cid:39) .
4. Weobserve that the relative spread in J c values increases in JJ’s with the ferromagnetic interlayer x > .
4. Mostlikely this is also a consequence of a rapid shrinkage of ξ F down to about 1 nm, comparable to the roughness ofour films, see Fig. 4. TABLE II. Parameters of junctions with Pt and paramagnetic PtNi interlayers.Interlayer d F Size R n R n A ρ n T I c J c I c R n (nm) (nm ) (mΩ) (10 − Ωcm ) (10 − Ωcm) (K) ( µ A) (10 (A/cm ) ( µ V)Pt 23.75 207 ×
104 340 0.732 0.31 1.8 1400 651 4763.2 762 354 259Pt 23.75 274 ×
113 220 0.68 0.287 1.8 1700 548 374Pt 25 180 ×
90 680 1.1 0.44 2.5 160 98.7 108.8Pt 30 106 ×
106 710 0.8 0.27 3.2 200 178.6 142Pt 30 170 ×
88 500 0.75 0.25 3.2 260 173.3 130Pt 30 117 ×
88 780 0.8 0.27 3.2 156 151.5 121.7Pt . Ni .
20 351 ×
85 270 0.806 0.402 3.0 180 60.4 67.2Pt . Ni .
20 308 ×
128 160 0.631 0.315 3.1 430 109 68.8Pt . Ni .
20 330 ×
139 133 0.61 0.305 3.1 570 124 75.8Pt . Ni .
20 372 ×
130 125 0.605 0.303 3.2 610 126 76.3Pt . Ni .
20 340 ×
122 138 0.572 0.286 3.2 510 122.9 70.4Pt . Ni . ×
222 146 0.733 0.38 3.0 460 91.7 67.2Pt . Ni . ×
175 187 0.746 0.314 3.0 360 90.2 67.3Pt . Ni . ×
192 133 0.60 0.253 3.0 510 113 67.8Pt . Ni . ×
134 190 0.603 0.21 2.8 240 76 45.6Pt . Ni . ×
180 210 0.824 0.286 2.8 300 76.5 63Pt . Ni .
30 110 ×
100 1180 1.298 0.432 2.76 28 25.4 33.0Pt . Ni .
30 140 ×
120 660 1.109 0.37 2.7 65 38.7 42.9Pt . Ni .
20 197 ×
144 180 0.511 0.255 2.9 230 81.3 41.4Pt . Ni .
20 229 ×
144 210 0.693 0.345 2.9 300 91.2 63Pt . Ni .
25 287 ×
106 302 0.919 0.367 3.0 120 39.5 36.2Pt . Ni .
25 277 ×
128 248 0.879 0.352 3.0 155 43.7 38.4Pt . Ni .
25 170 ×
106 462 0.833 0.333 3.0 80 44.4 37Pt . Ni .
25 287 ×
106 307 0.934 0.373 3.0 125 41.1 38.4Pt . Ni .
25 319 ×
64 390 0.796 0.318 3.0 80 39.2 31.2Pt . Ni .
30 319 ×
106 237 0.801 0.267 3.1 120 35.5 28.4Pt . Ni .
30 266 ×
128 228 0.776 0.258 3.1 130 38.2 29.6Pt . Ni .
30 319 ×
117 181 0.676 0.225 3.1 180 48.3 32.6Pt . Ni .
20 210 ×
120 415 1.046 0.523 3.2 101.5 40.3 42.1Pt . Ni .
20 210 ×
170 293 1.046 0.523 3.2 157 44 46Pt . Ni .
20 212 ×
90 530 1.011 0.506 3.2 72 37.7 38.2Pt . Ni .
20 210 ×
190 245 0.978 0.489 3.2 179 44.9 43.9Pt . Ni .
20 202 ×
140 360 1.02 0.509 3.2 120 42.4 43.2Pt . Ni .
20 180 ×
175 335 1.05 0.528 3.2 137 43.5 45.9Pt . Ni .
20 175 ×
140 300 0.735 0.368 3.2 130 53.1 39Pt . Ni .
20 255 ×
96 320 0.783 0.392 3.2 136 55.5 43.5Pt . Ni .
25 158 ×
149 375 0.883 0.353 3.1 61.5 26.2 23.1Pt . Ni .
25 175 ×
123 330 0.71 0.284 3.1 74 34.4 24.4Pt . Ni .
30 266 ×
193 203 1.04 0.347 3.1 104 20.3 23.9Pt . Ni .
30 266 ×
167 218 0.968 0.323 3.1 95 21.4 20.7Pt . Ni .
30 256 ×
140 278 0.996 0.332 3.1 73 20.4 20.3
Appendix D. Interface resistances inNb/Pt − x Ni x /Nb junctions Figure 8 (a) shows a 3D plot of measured normal resis-tivities, ρ n , of studied Nb/Pt − x Ni x /Nb junctions versus Ni concentration and interlayer thickness. Parameters ofJJ’s are listed in Table III. Here ρ n = R n A/d F , where A is the junction area. Fig. 8 (b) shows the 2D projec-tion of same data. It is seen that ρ n greatly increases at0 TABLE III. Parameters of junctions with ferromagnetic PtNi interlayers.Interlayer d F Size R n R n A ρ n T I c J c I c R n (nm) (nm ) (mΩ) (10 − Ωcm ) (10 − Ωcm) (K) ( µ A) (10 (A/cm ) ( µ V)Pt . Ni .
25 630 ×
230 50 0.725 0.29 2.2 160 11 8Pt . Ni .
25 770 ×
320 50 1.23 0.493 2.2 63 2.6 3.2Pt . Ni .
25 770 ×
320 220 5.42 2.17 2.2 2070 84 455 ∗ Pt . Ni .
30 300 ×
165 2000 9.9 3.3 3.0 140 28.3 280 ∗ Pt . Ni .
30 380 ×
180 1030 5.19 1.73 3.0 7.5 1.5 7.7Pt . Ni .
30 260 ×
110 2200 6.29 2.09 3.0 18.3 6.4 40.3Pt . Ni .
30 640 ×
225 120 1.73 0.58 3.3 0 0 0Pt . Ni .
30 640 ×
225 300 4.32 1.44 2.8 110 7.6 33Pt . Ni .
20 800 ×
225 50 0.9 0.45 1.8 63 3.5 3.23.0 28 1.56 1.4Pt . Ni .
20 1140 ×
230 120 3.15 1.57 1.8 2100 80 252 ∗ . Ni .
20 1140 ×
380 22 0.95 0.477 1.8 92 2.1 2.0Pt . Ni .
20 1200 ×
300 90 3.24 1.62 1.8 3490 96.9 314.1 ∗ . Ni .
20 1050 ×
420 25 1.1 0.55 1.8 136 3.08 3.43.0 62 1.41 1.6Pt . Ni .
25 630 ×
340 51 1.09 0.44 0.4 81 3.8 4.1Pt . Ni .
25 640 ×
340 53 1.15 0.46 0.4 73 3.4 3.9Pt . Ni .
25 670 ×
310 53 1.10 0.44 0.4 58 2.8 3.1Pt . Ni .
25 510 ×
310 73 1.16 0.46 0.4 73 4.6 5.3Pt . Ni .
25 550 ×
330 71 1.29 0.52 0.4 91 5.0 6.5Pt . Ni .
25 460 ×
300 86 1.19 0.47 0.4 110 8.0 9.5Pt . Ni .
25 560 ×
310 69 1.2 0.48 0.4 49 2.8 3.4Pt . Ni .
20 350 ×
190 160 1.064 0.53 2.0 0 0 0Pt . Ni .
20 350 ×
120 260 1.092 0.55 2.0 0 0 0Pt . Ni .
20 290 ×
182 200 1.056 0.53 2.0 0 0 0Pt . Ni .
20 410 ×
180 160 1.18 0.59 2.0 0 0 0Pt . Ni .
20 490 ×
160 130 1.02 0.51 2.0 0 0 0Ni 20 1000 ×
250 14 0.35 0.175 0.4 500 20 7.02.0 188 7.5 2.63.0 57 2.3 0.8 ∗ The very large I c R n values are not confident because the corresponding large I c is comparable to the onset of the flux-flowphenomenon in Nb electrodes. This leads to the non-linear I - V ’s at large bias and makes it difficult to correctly estimate R n . x = 0 . − . ρ n exhibits a muchlarger peaks at the frustration points x (cid:39) . . ρ xx . Especially at the onset of ferromag-netism x c = 0 .
4, where ρ n increases by almost an order ofmagnitude. This indicates that properties of SFS junc-tions depend not only on the electronic disorder (m.f.p.)but also on the magnetic disorder and, particularly, areaffected by quantum fluctuations at the quantum phasetransition reflected by the sign-change of the AHE, Fig.6 (a). From the comparison of ρ xx and ρ n , Figs. 6 (c) and8 (b) it is also seen that junction resistivity is severaltimes larger than the film resistivity. This indicates thatjunction resistances are dominated by an additional re-sistance at S/F interfaces due to a finite interface trans-parency β <
1. For SNS junctions the interface trans-parency is reduced by a mismatch between Fermi veloci-ties and Fermi surfaces (electronic band structures) of Sand N metals [57, 58]. For example, the transparency ofNb/Cu interface was estimated to be β (cid:39) . (a)(b) FIG. 7. (color online). (a) Three-dimensional plot of criticalcurrent densities of Nb/Pt − x Ni x /Nb junctions at T = 3 Kas a function of Ni concentration and interlayer thickness. (b)Projection of the same data to the two-dimensional plot. Reddashed lines in (a) indicate possible 0 − π transition for a fixed d F upon increasing Ni concentration. net [1, 4, 58–64]. The values R n A ∼ × − Ωcm in ourjunctions, see Tables I-III, are comparable to the value0 . × − Ωcm reported for Nb/Co interfaces [64].From Table III it can be seen that for Nb/Pt − x Ni x /NbJJ’s with x (cid:39) . σ AHE ( T = 0) (cid:39) R n A value and, thus,the interface resistance greatly increases. Simultaneouslythe critical current density increases, leading to extraor-dinary large I c R n products of several hundreds of µ V,comparable to that for SINIS (I-insulator) junctions [65].The origin of this phenomenon remains to be understood.So far we can only speculate that anomalous junctioncharacteristics at these critical concentrations are relatedto quantum phase transitions occurring between ordered L and L phases with different magnetic properties[52, 54, 56, 66]. For all our junctions, R n is dominated byS/F interface resistances, consistent with earlier reports (a)(b) FIG. 8. (color online). (a) Three-dimensional plot of normalresistivities of Nb/Pt − x Ni x /Nb junctions versus Ni concen-tration and interlayer thickness. (b) Projection of the samedata on the two-dimensional plot. Note sharp singularities atthe critical concentration x c = 0 . x (cid:39) .
6, corresponding to points of sign-reversal AHE inFig. S3 (a). for other types of S/F interfaces [58, 62, 64]. Therefore,there are significant barriers at S/F interfaces, despitethe deposition of SFS trilayers occurred in one run with-out breaking vacuum.
Appendix E. Clarification about extraction ofmagnetization curves from AJF analysis
In derivation of Eq. (1) we assumed that M F has anin-plane orientation. Due to the small thickness of F-interlayers, they have negligibly small demagnetizationfactors. In this case the F-layer does not generate mag-netic fields at S/F interfaces and, therefore, does not in-duce any additional flux in S-electrodes. This leads to asimple separation of flux contributions from S-electrodesand F-interlayer, represented by first and second terms2in Eq. (1). Here B in the first term does not contain M F (i.e it is not H + 4 πM F ) and differs from H solelydue to screening by superconducting currents and a fi-nite demagnetization factor of S-electrodes, just like inthe non-magnetic junction. Since for our junctions thetotal thickness of S-layers 2 d Nb = 400 nm is comparableto junction sizes, the demagnetization factor of electrodesis non-negligible and the difference between B and H canbe sensible. Nevertheless, this does not affect the linear-ity of Φ( H ) curves above the saturation field because B ∝ H in the presence of the demagnetization effect.Therefore, subtraction of the linear asymptotics, shownby dashed lines in middle panels of Fig. 2 (a-c), remainsunambiguous.The distance between points in the AJF analysis is de-termined by the flux quantization field ∆ H = Φ /L Λ. Itis smaller for the hard axis orientation of the field, cor-responding to the longest size of the junction L . There-fore, AJF curves for the hard axis, Figs. 2 (c,d), aremuch more detailed than for the easy axis orientation,Figs. 2 (a,b). Nevertheless, extraction of M F ( H ) forthe hard axis orientation is complicated by two factors:First, magnetization reversal in the hard axis orienta-tion occurs initially via coherent rotation of magnetiza-tion (without hysteresis), followed by a small flip, andcontinuing coherent rotation towards the saturated state[41, 46, 67, 68]. Since the flip is smaller than M sat , itdoes not allow direct extraction of M sat from the sizeof the magnetization jump. Second, since the length ofthe electrode L ∼ µ m in the hard axis orientation ismuch larger than the London penetration depth of S-electrodes, λ S (cid:39)
100 nm, junctions are prone to penetra-tion of Abrikosov vortices, which greatly distort junctioncharacteristics [45, 69]. Therefore, the field range of ouranalysis is limited by the range of the Meissner state.For the JJ with d Ni = 10 nm, Fig. 2 (c), the Meiss-ner state persists up the the saturation state and thestraightforward subtraction of the high-field linear slopefrom the AJF curves, shown by the dashed line in themiddle panel of Fig. 2 (c), provides a magnetization loopwith the expected saturation at high fields, as shown inthe bottom panel of Fig. 2 (c). It can be seen that satu-ration occurs at H (cid:39) d Ni = 20 nm, Fig. 2 (d), the fieldrange is limited by entrance of Abrikosov vortices. It issmaller than 1 kOe and the saturation is presumably notreached, which does not allow unambiguous determina-tion of the linear asymptotics. In this case we have cho-sen to assume B = H in Eq. (1) and calculate the firstlinear term using the definition of the magnetic thick-ness, Λ = d F + λ S tanh( d S / λ S )+ λ S tanh( d S / λ S ),where d S , = 200 nm are is the thicknesses and λ S , =100 nm are the London penetration depths of the two Nb-electrodes. The corresponding linear dependence Φ ( H ) is shown by the dashed line in the middle panel of Fig.2 (d). Thus obtained magnetization curve, M Ni ( H ⊥ ),shown in the bottom panel of Fig. 2 (d), is in line withthe expected magnetization curve for the hard axis orien-tation, as discussed above, and provides a correct valueof M sat . ∗ E-mail: [email protected][1] M. J. M. de Jong and C. W. J. Beenakker, Andreev Re-flection in Ferromagnet-Superconductor Junctions,
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