Spin-polarized quasiparticle transport in exchange-split superconducting aluminum on europium sulfide
aa r X i v : . [ c ond - m a t . s up r- c on ] A ug Spin-polarized quasiparticle transport in exchange-split superconducting aluminum oneuropium sulfide
M. J. Wolf, C. S¨urgers, G. Fischer, and D. Beckmann ∗ Institut f¨ur Nanotechnologie, Karlsruher Institut f¨ur Technologie (KIT), Karlsruhe, Germany Physikalisches Institut, Karlsruher Institut f¨ur Technologie (KIT), Karlsruhe, Germany (Dated: September 26, 2018)We report on nonlocal spin transport in mesoscopic superconducting aluminum wires in contactwith the ferromagnetic insulator europium sulfide. We find spin injection and long-range spin trans-port in the regime of the exchange splitting induced by europium sulfide. Our results demonstratethat spin transport in superconductors can be manipulated by ferromagnetic insulators, and opensa new path to control spin currents in superconductors.
I. INTRODUCTION
In conventional superconductors, electrons are boundin singlet Cooper pairs with zero spin. In hybridstructures with magnetic elements, triplet Cooper pairsand spin-polarized supercurrents can be created.
Inaddition, spin-polarized quasiparticles can be injectedinto superconductors, with very long spin relaxationtimes. Both effects open the possibility to achievespintronics functionality with superconductors. Re-cently, we have observed long-range spin-polarized quasi-particle transport in superconducting aluminum in thepresence of a large Zeeman splitting of the density ofstates, and demonstrated that the superconductor actsas a spin filter for quasiparticles injected from a param-agnetic metal. These observations open the possibilityto use superconducting aluminum as an active elementfor spintronics. The design of complex structures withswitchable elements requires, however, a local control ofthe spin splitting, which cannot be achieved by a ho-mogeneous applied magnetic field. In hybrid structuresof ferromagnetic insulators and superconductors, an ex-change splitting of the density of states of the super-conductor can be induced due to spin-active scatteringat the interface between the materials.
Such struc-tures are candidates for new spintronics functionality insuperconductors, and in particular to control andmanipulate the spin splitting. A very promising mate-rial for this purpose is europium sulfide (EuS), which hasbeen used in the past in superconducting hybrid struc-tures as a means to induce an exchange splitting, as a spin-filter material, and for superconductingspin valves and spin switches. EuS is a II-VI semi-conductor with a direct band gap of E g = 1 . T C = 16 . At low temperatures (few K) it can be considered asan insulator. In this paper, we extend our previousexperiments to spin transport in mesoscopic super-conducting aluminum wires with an exchange splittinginduced by the ferromagnetic insulator EuS.
FIG. 1. (color online) False-color scanning electron mi-croscopy image of a section of one of our samples togetherwith the measurement scheme with the injection (inj) anddetection (det) circuits.
II. SAMPLES AND EXPERIMENT
Our samples were fabricated in a two-step process.First, EuS films of thickness t EuS = 10 −
25 nm were evap-orated onto a Si (111) substrate heated to T S ≈ ◦ C.The films have a strong h i texture with a small frac-tion of h i -oriented grains. The Curie temperature T C ≈ . M s ≈ µ B per formula unit agree well with bulk properties. Thecoercive field is typically a few mT, consistent with neg-ligible magnetocrystalline anisotropy as expected for aHeisenberg ferromagnet. Details of the film preparationand characterization can be found in Ref. 24. In the sec-ond step, aluminum/iron structures were fabricated bye-beam lithography and shadow evaporation techniqueson top of the EuS films. The EuS films were coated withPMMA resist, and after exposure and development theywere mounted in the evaporation chamber. First, a shortAr ion etching step was used to clean the exposed surface TABLE I. Overview of sample properties. Range of normal-state tunnel conductances G , EuS film thickness t EuS . Aluminumfilm properties: film thickness t Al , critical temperature T c , critical magnetic field µ H c , diffusion constant D , maximum exchangefield B ∗ sat . G t
EuS t Al T c µ H c D B ∗ sat Sample ( µ S) (nm) (nm) (K) (T) (cm / s) (T)A 690 −
750 22 10.5 1.55 0.95 20.4 1.75B 380 −
450 10 9.5 1.6 1.45 13.6 1.2 of the EuS film to ensure good contact with the metalfilms. Next, a thin superconducting aluminum strip ofthickness t Al ≈
10 nm was evaporated and then oxidized in situ to form an insulating tunnel barrier. Then ferro-magnetic iron ( t Fe ≈ −
25 nm) was evaporated undera different angle to form six tunnel junctions to the alu-minum, with contact separations d spanning 0 . µ m.Additional copper layers were evaporated under differentangles to reduce the resistance of the iron leads. Figure 1shows a scanning electron microscopy image of a sectionof one of our samples, together with the experimentalscheme.The samples were mounted into a shielded box ther-mally anchored to the mixing chamber of a dilution re-frigerator. A magnetic field was applied in the planeof the substrate, along the direction of the iron wires.We will refer to the applied field by H throughout thispaper, whereas B will be used to describe the effec-tive spin splitting of the density of states (both field-induced and exchange-induced). Using a combination ofdc bias and low-frequency ac excitation, we measuredboth the local differential conductance g loc = dI inj /dV inj of individual junctions as well as the nonlocal differen-tial conductance g nl = dI det /dV inj for different injec-tor/detector pairs in the superconducting state. Forthe nonlocal conductance, we plot the normalized signalˆ g nl = g nl / ( G inj G det ) throughout the paper, where G inj and G det are the normal-state conductances of the injec-tor and detector junction, respectively. Also, we mainlyfocus on data at T = 50 mK. In addition to the con-ductances in the superconducting state, we measured thenonlocal linear resistance R nl = dV det /dI inj in the normalstate at T = 4 . III. RESULTS
Before we describe the results in the superconductingstate, we first characterize spin transport in the normalstate. Figure 2(a) shows the nonlocal resistance R nl asa function of applied magnetic field H for different pairsof contacts at T = 4 . FIG. 2. (color online) (a) Nonlocal resistance R nl as a functionof applied magnetic field H for different contact separation d in the normal state at T = 4 . R nl as a functionof contact distance d (symbols), and fit to an exponentialdecay (line). clarity. In both sweep directions, two switches can beobserved between parallel (P) and antiparallel (AP) con-figuration. From these, we extract the spin-valve signal∆ R nl = R (P)nl − R (AP)nl . The spin-valve signal is plottedas a function of contact distance d in Fig. 2(b), togetherwith a fit to the standard expression ∆ R nl = P ρλ N A exp( − d/λ N ) , (1)where P is the spin polarization of the tunnel conduc-tance, ρ is the normal-state resistivity of the aluminum, A is the cross-section area of the aluminum, and λ N is the normal-state spin-diffusion length. From the fit,we obtain P = 12 . ± .
8% and λ N = 289 ±
21 nm.With the electron diffusion coefficient D determined fromthe normal-state resistivity we obtain the spin relaxationtime τ sf = λ /D = 41 ps.We now focus on results in the superconducting state.Figure 3(a) shows the local differential conductance ofone contact as a function of the injection bias voltage V inj for different applied magnetic fields H at T = 50 mK.The data at zero field show negligible subgap conduc-tance and a gap singularity at V inj ≈ µ V, consis-tent with the expected gap ∆ = 1 . k B T c = 230 µ eV.Upon increasing the field, a spin splitting of the densityof states quickly develops, which is much larger than theZeeman splitting due to the applied field. We fit our datawith the standard model for high-field tunneling to FIG. 3. (color online) (a) Local differential conductance g loc = dI inj /dV inj of one junction as a function of injector bias V inj for different applied magnetic fields H (symbols) and fits(lines). (b) Magnetization of the EuS film (solid line, left or-dinate) and induced exchange field B ∗ for different contacts(symbols, right ordinate) as a function of the applied field.(c) Pair potential ∆ as a function of normalized field H/H c .(d) Normalized pair-breaking parameter Γ / ∆ as a functionof ( H/H c ) . extract the normal-state junction conductance G inj , thespin-polarization P of the tunnel conductance, the pairpotential ∆, the orbital pair-breaking parameter Γ, thespin-orbit scattering strength b so , and the spin splitting.The latter appears as an effective magnetic field in thefit, which we denote by B fit . The spin splitting consists oftwo parts, the Zeeman splitting due to the applied field µ H , and the exchange splitting induced by the EuS,which we will denote by B ∗ = B fit − µ H , following theliterature. In Fig. 3(b), we plot B ∗ obtained from fitting the spec-tra of all six junction as a function of the applied field. B ∗ increases almost linearly at small field, and then sat-urates for µ H > . B ∗ sat = 1 .
75 T. Consequently,most of the spin splitting of the density of states resultsfrom the exchange field. A similar behavior was found forall samples, with some variation of both the magnitudeof B ∗ sat and the applied field where saturation sets in.For comparison, we show the magnetization M EuS of theEuS film obtained by SQUID magnetometry in the sameplot. As can be seen, the magnetization is fully saturatedat a field of a few 10 mT, much below the saturation ofthe exchange splitting. The reason for the discrepancyof the field dependence of M EuS and B ∗ is not known.In the past, averaging over multi-domain magnetizationstates of EuS has been assumed as a possible cause of the slow saturation of B ∗ . However, this explanation is atvariance with the fast saturation of M EuS , as well as thesmall junction size of the order of the dirty-limit coher-ence length of the aluminum film ( ξ S = 76 nm). Consid-ering the fact that the induced exchange field is the resultof spin-active scattering of quasiparticles at the interfacebetween Al and EuS, we assume that a difference betweenbulk magnetism (as seen by magnetometry) and interfacemagnetism (as seen by the aluminum) is the cause of thedifferent field scales. Magnetic moments at the inter-face may deviate from the magnetization direction dueto the broken symmetry and different anisotropy at theinterface. A further clue supporting this interpretationis the fact that B ∗ sat varies from sample to sample evenfor similar aluminum film thickness. In our two-step fab-rication process, we expect that the interface propertiesdepend sensitively on the Ar ion etching between fabri-cation steps.The pair potential ∆, plotted in Fig. 3(c), remainsalmost constant at ∆ ≈ µ eV (dashed line) as afunction of applied field up to the critical field. We find B ∗ sat + µ H c = 2 . µ H p = ∆ / √ µ B = 2 .
75 T.The normalized orbital pair breaking parameter Γ / ∆ is plotted in Fig. 3(d) as a function of ( H/H c ) . Fora thin film in parallel magnetic field, the expectationis Γ / ∆ = ( H/H c ) / This assumption is plotted as a dashed line.Indeed, Γ follows an H dependence at high fields, butwith a smaller slope and an additional offset (solid line).From these observations we conclude that the criticalfield is determined by spin splitting rather than by or-bital pair breaking. Below 0 . H dependence at high fields extrapo-lates to an offset Γ( H = 0) / ∆ ≈ .
03. This may indicateadditional pair breaking due to magnetic inhomogeneityof the EuS film, or the fringing fields of the iron wires.For the spin-orbit parameter we obtain b so ≈ .
14 at highfields, much larger than expected for aluminum. In Fig. 4, we focus on the nonlocal differential conduc-tance. Figs. 4(a) and (b) show the normalized nonlocalconductance ˆ g nl as a function of injector bias V inj for dif-ferent magnetic fields H . As in our previous work, asymmetric peaks due to spin injection into the spin-split density of states are observed upon increasing themagnetic field, as seen in Fig. 4(a). Due to the increasedspin splitting by the exchange field of the EuS, the peaksare clearly visible even at a field as small as 10 mT. Atlarger fields, the peaks broaden due to the increased spinsplitting. In contrast to the previous work, however, thepeaks actually split into two sub-peaks at small and largebias, as seen in Fig. 4(b). The dashed lines indicate thepair potential. The two sub-peaks essentially follow thespin splitting of the density of states. In Figs. 4(c) and(d), we show the evolution of the spin signal as a functionof contact distance for low and high fields, respectively.In the low-field regime, Fig. 4(c), where a single peak isobserved for each bias polarity, the peak uniformly de- FIG. 4. (color online) Normalized nonlocal differential con-ductance ˆ g nl = g nl / ( G inj G det ) as a function of injector bias V inj . (a) and (b): Data for different applied magnetic fields H for one pair of contacts. (c) and (d): Data for differentcontact distances at two different applied fields.FIG. 5. (color online) (a) Normalized nonlocal differentialconductance ˆ g nl as a function of bias voltage V inj for one con-tact pair and applied field (symbols) and theoretical predic-tion ˆ g nl ∝ g ↓ − g ↑ (line). (b) Relaxation length λ S of the spinsignal as a function of bias voltage V inj for different magneticfields H . creases with increasing contact distance. At high fields,Fig. 4(d), the two sub-peaks (indicated by arrows for thepositive bias side) decay on different length scales. Thiscan be clearly seen by comparing the data at d = 0 . µ mand 5 µ m. At small contact distance, the low-bias peak(at about V inj = 140 µ V) is larger, whereas at large dis-tance, the high-bias peak (at about V inj = 310 µ V) islarger.Spin injection into the spin-split density of states isproportional to the difference of the conductances for spinup and down, g nl ∝ g ↓ − g ↑ . We can therefore predict the bias dependence of g nl from the fits of the local con-ductance. Fits to this prediction have been successful indescribing the data of our previous experiments. InFig. 5(a), we compare the bias dependence of the mea-sured spin signal to the predicted signal for one set of pa-rameters. The model predicts a single peak for each biaspolarity, restricted to the bias window of the spin split-ting. As soon as the bias reaches the upper spin band, thesignal should be cancelled by injection of quasiparticleswith opposite spin. The observed data are in qualitativecontrast to this expectation. Instead of a cancellation,the spin signal actually further increases once the upperspin band is reached and shows a second sub-peak. Thisobservation is systematic for the high-field data.To analyze the relaxation length of the spin signal, wemade exponential fits of ˆ g nl at a given bias as a functionof contact distance. In Fig. 5(b), the relaxation length λ S obtained from these fits is plotted as a function ofbias voltage V inj for different magnetic fields H . λ S is afew µ m, similar to samples without EuS film. In general, λ S increases with bias. At small bias, in the range ofthe spin splitting, λ S also increases with magnetic field,again similar to the previous experiments without EuS.At higher bias, where both spin bands contribute to con-ductance, λ S becomes nearly independent of the field. IV. DISCUSSION
The microscopic explanation of the induced exchangesplitting is spin-active scattering at the interface betweenEuS and Al, which can be expressed in terms of spin-mixing angles.
For diffusive systems, a broad distri-bution of spin-mixing angles is expected. Recently, ap-propriate boundary conditions for the Usadel equationhave been derived. For a thin superconducting layeron top of a ferromagnetic insulator, the spin-active scat-tering can be expressed in this model by dimensionlessparameters γ φ,i . The γ φ,i depend on moments of increas-ing order of the distribution of spin-mixing angles. Thefirst-order parameter, γ φ, , acts like an effective Zeemanfield, whereas the second-order parameter, γ φ, , acts inthe same way as pair breaking. The higher-order termshave no apparent analogy. With this analogy, we can ex-press B ∗ sat as γ φ, ≈ .
062 (0 . H = 0) to spin-active scattering, this yields γ φ, ≈ .
004 (0 . b so ≈ .
14 from the fits. However, if we inter-pret the normal-state spin-diffusion time as the spin-orbitscattering time (Elliott-Yafet mechanism ), we can es-timate b so = ¯ h/ τ so ∆ = 0 . and is also similar to literaturedata for aluminum on EuS. An interesting question totheory is whether fits including higher-order γ φ termsmight remove the discrepancy, and provide additional in-sight into the scattering mechanism at the interface.For the nonlocal signal, we find that applied fields of10 mT are sufficient to enable spin injection and trans-port. The relaxation length of a few microns is similarto what has been found in structures without EuS. Athigh fields, the spin signal is qualitatively different fromthe expectation, with increased spin injection instead ofcancellation as the upper spin band starts to contribute.In our previous experiments, we have found a high-biastail of the spin signal in some samples. A possible ex-planation for this behavior are spin flips in combinationwith fast energy relaxation, as explained in Ref. 11. Thesame mechanism could be at play here, and might bemore pronounced because the density-of-states featuresare sharper due to the relative weakness of orbital pair-breaking effects. On the other hand, spin-active scatter-ing may lead to the generation of triplet Cooper pairs inthe superconductor. This might lead to a qualitativelydifferent spin injection and relaxation behavior. Lackinga quantitative model for either effect, we can only referthis question to theory.
V. CONCLUSION
In conclusion, we have shown spin injection and trans-port in mesoscopic superconducting aluminum wires withan exchange splitting induced by the ferromagnetic in-sulator europium sulfide. The salient features observedin the experiment are consistent with the previous lit-erature on spectroscopy and spin transport in high-fieldsuperconductivity. Our results show that ferromagneticinsulators are promising materials to control spin trans-port in superconductors at mesoscopic length scales andto implement spintronics functionality.
ACKNOWLEDGMENTS
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