Study of the itinerant electron magnetism of Fe-based superconductors by the proximity effect
Yu. N. Chiang, M. O. Dzuba, O. G. Shevchenko, A. N. Vasiliev
aa r X i v : . [ c ond - m a t . s up r- c on ] A p r Study of the itinerant electron magnetism of Fe-basedsuperconductors by the proximity effect
Yu. N. Chiang , M. O. Dzuba , , O. G. Shevchenko and A. N. Vasiliev B. I. Verkin Institute for Low Temperature Physics and Engineering,National Academy of Sciences of Ukraine, 47 Lenin ave., Kharkov 61103, Ukraine. Lomonosov Moscow State University,GSP-1, Leninskie Gorky, Moscow, 119991, Russian Federation. International Laboratory of High Magnetic Fields and Low Temperatures,53-421 Wroclaw, Poland.E-mail:[email protected]
Abstract
We used the proximity effect as a tool to achieve an ideal ("barrier-free") NS boundary forquantitative evaluation of transport phenomena that accompany converting dissipative current intosupercurrent in NS systems with unconventional superconductors – single-crystal chalcogenide FeSeand granulated pnictide LaO(F)FeAs. Using features (limitations) of Andreev reflection in the NSsystems with dispersion of the electron spin subbands, we revealed direct evidence for spin-polarizednature of transport and the absence of residual magnetization in iron-based superconductors in thenormal state: In heterocontacts with single-crystal FeSe and granular LaO(F)FeAs, we detecteda spin-dependent contribution to the efficiency of the Andreev reflection associated with the spinaccumulation at the NS boundary, and a hysteresis of conductivity of FeSe in the ground state in lowexternal magnetic fields. Based on our findings, we conclude that in iron-based superconductors,the itinerant electron magnetism is predominant, magnetism of iron atoms being localized.
Along with the discovery of superconductivity in multi-component compounds with elements havingsignificant local magnetic moment (Fe, Ni) [1], the detection of the same phenomenon in two-componentcompounds with the same elements proved to be an important discovery [2, 3]. Thus, a number ofmulti-component superconducting compounds of different composition, including iron-based, is closedby a compound directly adjacent to the family of single-element conventional superconductors. In thisregard, there is no doubt that the appearance of superconductivity in multi-element compounds withdelocalized electrons is closely related to the reduced symmetry of the crystal, in particular, such asthe symmetry of "layered" type. This symmetry is characteristic of structures in a large family of com-pounds, containing a wide range of rare earths, pniktogens, chalcogens, and transition elements Mn, Fe,Co, Ni, Cu, and Ru. It leads to the anisotropy of the electronic and magnetic properties accompaniedby an increased electron density of states in the layers with quasi-two-dimensional (anisotropic) Fermisurface and by an increased role of electron-electron interaction. Anisotropy of the properties seemsto be that feature under which condition in the same material, the magnetic interactions coexist withthe interactions that generate superconducting pairing of the excitations in the electron subsystem oflayered superconductors of complex composition, including iron-based ones.By now, the notion of crystal structures of layered superconductors and the nature of couplingin them is sufficiently developed and experimentally established, while their magnetic and electronicstructures in the ground state are still a subject of debate and active research. In this regard, it is ofconsiderable interest to compare electronic properties of layered iron superconductors which share thecrystal structure of PbO type ( P nmm ) that predetermines related quasi-two-dimensional structuresof the electronic bands with nesting [4 - 6]; relevant examples are the binary phase α - FeSe andoxypnictide LaO(F)FeAs. 1heoretical collective efforts using local density of states approximation (see, eg, [4, 7, 8]) leadto the conclusion that the mechanism of superconductivity in iron-based pnictides and chalcogenidesis likely to have nothing to do with the electron-phonon mechanism, even when the value of thecritical temperature, T c , does not extend beyond the McMillan criterion [9], based on the values of thecoupling constants and phonon dispersion characteristic of the electron-phonon pairing concept. Thisconclusion is sufficiently proved, despite the fact that the calculations "from the first principles" bythe density functional method can give certain ambiguity in the definition of density of states and, asa consequence, of the band structure at the Fermi level [10 - 12]. In any case, the main argument infavor of this conclusion is as follows: The superconductivity in the presence of magnetic elements isobserved in a wide range of compounds with layered crystalline structure of the same type and in awide range of critical temperatures both satisfying and not satisfying (exceeding) the electron-phononcriterion.One of the common methods of studying the electronic properties of superconductors is, as known,the investigation of the Andreev conductance, G if , of NS interfaces, either artificially created (het-erosystems) or naturally produced in a homogeneous material, in the form of wide or narrow channels[13]. As the number of open Andreev levels ( N ⊥ ) is directly proportional to the cross section of theinterface, A ( N ⊥ ∼ A /λ , where λ F is the Fermi wavelength of an electron), it is clear that to studyAndreev conductance is generally preferable to use wide channels. In this case, the only inconveniencefor an experimenter, in the absence of artificial barriers on the interface ( z = 0 where z is a parametercharacterizing the energy barrier strength), is essentially low resistance of the channels. Intrinsic barrierheight and a corresponding resistance which we will call an own resistance of the interface R NN if (knownas the "Sharvin resistance" of restrictions [14]), are inversely proportional to the cross section of theinterface: R NN if = ( G if ) − = ( p F /e n ) / A ≡ N (0) e v F ] − / A (here, e, p F , v F , n, and N (0) are thecharge, the Fermi momentum and velocity, the concentration and density of states per spin for free elec-trons, respectively). For substances with the conductivity of conventional metals, R NN if ≈ · − / A [Ω] if A is expressed in cm . It follows that the restrictions (interfaces) with a diameter of the order of µ m cannot have an own resistance exceeding ∼ − Ω . Greater values often demonstrated by realpoint contacts indicate that, along with the resistive contribution from the interfaces R NN if , dissipativecontributions exist from extraneous inclusions, such as parts of a probe (eg, the tip of the scanningprobe) or defective or oxide barriers. In most cases, this is due to the fact that a "four-probe" methodof measuring the current-voltage characteristics (IVC) when applying to point contacts, appears to beessentially two-contact one (see Fig. 1 a, b ). That is why an area of incomparably greater length thanballistic one is forced to be measured; therefore, not only own contribution from the interface in theballistic approximation is gauged [15]. In other words, the real contacts of point geometry, in general,cannot be considered ballistic in case of electrical measurements [16].Physics of such contacts includes several mechanisms controlling the value of the system conduc-tance G NS pc in the NS state of the interface. After the system switches from the NN to NS state, totalresistance of a real point contact, R NS pc , contains at least the following additive contributions: ( i ) adissipative contribution from the N - side of the interface of the total length of L N (by this we meanan overall contribution from a part of the tip, from an oxide layer, and from the layer which thicknessmeasures alike the coherence length where the scattering cross section by impurities doubles underAndreev retroreflection [17]); ( ii ) an own contribution from the interface R NN if with the weight deter-mined by the efficiency of the Andreev reflection which is a function of the energy parameters of thesystem (electron energy and the energy gap of a superconductor [15]); ( iii ) a dissipative contributionfrom the part of a superconductor related to the dispersion of the order parameter at the NS interface[18] due to the proximity effect. At the NN → NS transition, the contribution ( i ) generally decreasesthe conductance of the contact and the contribution ( ii ) increases it. Previously, we have shown [16]that in a barrier-free non-ballistic contact, the contribution ( i ), in general, should prevail over thecontribution ( ii ) within the energy range k B T ; eU ≪ ( L N /l N el ) k B T c ; here, T, U, l N el , and T c are thetemperature, bias voltage, electron mean free path in the N – side, and the critical temperature of thesuperconductor, respectively.Among these contributions, the contribution ( iii ) is the least known, especially that aspect of theproximity effect which is associated with the ability to generate a perfect NS boundary. Indeed, dueto the dispersion, the order parameter at the NS boundary changes from 1 to 0 over the spatial range2igure 1: ( a ) and ( b ) illustrate the ways to measure IVC of the point-contact samples; ( c ) displaysdispersion of the order parameter induced by the proximity effect near the NS boundary (dashed line)in the absence of transport current I ; ( d ) depicts a change in the position of NS boundary (dashedline) after the current is turned on. The region of the superconductor passed to the normal state ishighlighted. See text for details.of the order of the Ginsburg-Landau characteristic length scale ξ ( T ) (Fig. 1 c ). This means that theNS boundary can be moved by a macroscopic magnetic field of the transport current, no matter howsmall it is, deep into the superconductor, as shown in the Figure, provided that that field can suppressthe superconductivity in the S-side of the contact. Thus, at finite values of the transport current, theNS boundary can be an ideal interface between the two parts of the same superconducting materialwhich are in different states - normal and superconducting.In this paper, we used this feature of the proximity effect for studying the nature of the mag-netism of the ground state in new iron-based superconductors, chalcogenide FeSe and oxypnictideLa[O − x F x ]FeAs. One might hope that the absence of extraneous inclusions at the NS boundary, oftenwith uncontrolled characteristics that reduce the informativeness of Andreev reflection phenomenon,allows to judge with certainty about the presence or absence of the dispersion of the spin subbands inthe normal ground state of a superconductor. Thus, we will be able to understand whether magnetism(and, indirectly, superconductivity) of iron-based superconductors is mainly itinerant and long-rangephenomenon or localized and short-range one. Since the contributions ( i ) and ( iii ) are directly pro-portional to the thickness of the respective layers, their weight should be more noticeable as a totallength of the NS sample approaches these thicknesses. Hence, we are led to maximum possible "short-ening" of this length, ie, to a point-contact geometry of the samples and to the schemes for measuringCVC shown in Fig. 1 and corresponding, as explained above, with a two-contact measurement design.Here, we present the results of the research of Andreev conductance of non-ballistic point-contact NSheterostructures with relatively wide interfaces (of the area A ∼ − cm ). We study the systemsCu/FeSe and Cu/La[O − x F x ]FeAs. 3
50 100 150 200 250 300 R , O h m T, K FeSe bulk point contact R / R K T , K Figure 2: Resistance of FeSe samples as a function of carriers energy set by the temperature T : 1 -bulk samples measured in the geometry of non-concurrent probes (Inset shows the scaled-up region ofthe superconducting transition); 2 – point-contact samples measured in the geometry of the concurrentprobes depicted in Fig. 1 a, b . Starting materials of the superconductors used for preparing hybrid samples with point-contactgeometry have a different structure in line with the technology of their preparation. PnictideLa[O . F . ]FeAs was obtained by solid-phase synthesis, such as described in Ref. [19], and had apolycrystalline structure. X-ray diffraction and spectroscopic studies have shown the presence of thisphase in an amount of not less than 97 %. Iron chalcogenide was made as a single crystal. To obtain itwe used the technology of crystallization from solution in the melt KCl/AlCl at constant temperaturegradient 5 K over the range 47 K. Typical sizes of the single crystals are . × . × . mm . X-raystudies carried out on an automatic single-crystal diffractometer "Xcalibur-3" (Oxf. Diffr. Ltd) showthat the crystals of both materials belong to the tetragonal space group P nmm of PbO type andhave lattice parameters a, b = 3 . ˚A; c = 5 . ˚A (these almost repeat the data from Ref. [20])for the basic binary α - phase FeSe and a, b = 4 . ˚A; c = 8 . ˚A for fluorine-doped oxypnictideLaO(F)FeAs.Point-contact samples were produced by mechanically clamping method. As a result they provedto be very high-resistive (up to several Ohms) due to preferential contribution to their resistancefrom oxide layers, the temperature behavior of the resistance being generally of a semiconductor type.CVC measurements were conducted using stabilized dc power supply. Its output resistance was lowerthan that of the samples, which required maintaining the same selected measurement mode, namelythe constant-current regime within all current, temperature, and field ranges during the experiment.Represented here are the results obtained in this mode of electrical measurements. Generally speaking,the constant-voltage regime is more informative, though rarely used. The latter, however, is nottechnically accessible in all the intervals of control parameters in a single measurement cycle. In Fig. 2, over a wide temperature range, we demonstrate the difference between the dependencies ofthe resistance of the bulk FeSe sample on the carriers energy set by the temperature T , derived from theconventional four-probe measurement geometry, and the same dependencies for point-contact samples4 R ( T ) / R N T, K N
0, 5 )
FeSe (pc) N
3, 43 )
Figure 3: Normalized temperature dependences of the resistance of point contacts Cu/FeSe measuredat different transport currents.Cu/FeSe with oxide barriers at the interface obtained in the measurement geometry of combined probesshown in Fig. 1 a, b . We see that the difference is qualitative: The character of the formers correspondsto the metallic behavior while that of the latters is semiconducting. In all the samples with FeSe, bothbulk and hybrid, the superconducting transition was observed in the range of (4 ÷ K (see Inset). Ingeneral, the above features of the temperature behavior are also characteristic of both bulk and hybridNS samples with LaO(F)FeAs which experiences a superconducting transition at ∼ K.Figs. 3 and 4 show typical temperature dependencies of the normalized resistance of point con-tacts Cu/FeSe and Cu/LaO(F)FeAs measured at different transport currents. It is seen that, whileincreasing measuring current in the studied range I = 1 ÷ mA, the share of a normal part of thepoint-contact system is increasing while that of a superconducting part corresponding to the changein the contact resistance at the superconducting transition is decreasing. The absolute value of thesuperconducting jump in resistance is the same for contacts with different total resistances but mea-sured at the same current [compare curves 1 ( R N = 0 . ) and 2 ( R N = 3 . ) in Fig. 3]. Thisindicates that the interface resistance in the samples with pressed point contacts, in addition to thetemperature-dependent semiconductor-type part, contains a temperature-independent part of the typeof residual resistance which does not vanish at T → .In Fig. 5, presented are the dependencies of the resistance for the system Cu/FeSe on the biasvoltage U at the contact as an addition to the energy k B T . Applying that voltage is an alternativemethod of controlling energy of the carriers. Curves 1, 2, and 5 correspond to the temperature rangecovering the area of the superconducting transition ( T ≤ T c , NS mode) while curves 3 and 4 weretaken in the same interval of bias voltages at temperatures T > T c (NN mode). It is seen that incomparable energy ranges, the resistance behavior depending on the parameters T (Figs. 2, 3) and U (Fig. 5) is qualitatively similar in both NN and NS interface modes, the values of contact resistancein the NN mode differing by an order of magnitude. From this and from a comparison between curve2 in Fig. 2 and curves 3 and 4 in Fig. 5, an important conclusion follows that in the energy rangesupporting heterocontacts in NN mode, the semiconductor type of behavior of the generalized contactconductance most likely is due to the energy-dependent dissipative contribution from the oxide layer,as the conductivity of FeSe over the entire temperature range above T c has a metallic behavior (Fig.2, curve 1) while the resistance of the part of the copper probe included in the measurement, as smallas ∼ µ m in length, cannot exceed a few µ Ω at liquid helium temperatures. The theory predicts [18]that the proximity effect in "dirty" conductors extends to a depth proportional to the electron meanfree path. Hence, at typical thickness of the "dirty" oxide layers ≃ ˚A, the electron mean free pathin them is apparently of the same order. In other words, the residual resistance of contacts in NS statebelow the superconducting transition is formed by the intrinsic contribution from the interface ( R z )5 ,0 0,5 1,0 1,5 2,0 2,5 3,0 3,50,500,550,600,650,700,750,800,850,900,951,001,05 R ( T ) / R ( K ) T/T c
1 1 mA2 10 mA3 50 mA4 100 mA
23 4
La[O F x ]FeAs (pc) Figure 4: Normalized temperature dependencies of the resistance of point contacts Cu/LaO(F)FeAsmeasured at different transport currents.which is not associated either with oxide layers or with the N-side of the interface. As can be seenfrom Figs. 3, 4, and 5, R z for different contacts amounts to ( ÷ ) % of the normalizing resistance R N measured in NN mode just before the superconducting transition. Most likely, R z reflects thepresence in the heterojunction of a potential barrier of the Schottky type, or the contribution fromsurface localized states, or both.We believe that all these features of the experimental data are directly related to the proximityeffect associated with the dispersion of the order parameter | ψ | which is especially significant in therange of T not too far from T c , where its spatial scale defined by the Ginsburg-Landau coherencelength ξ T ∼ (1 − T /T c ) − / ξ , is quite large. This can be seen by comparing the magnetic energy W of tangential self-magnetic field of the current H I ( x = 0) = 2 I /r ≃ (10 − ÷ Oe at the penetrationdepth λ T with the potential of electron pairing | ψ | = ∆ = ~ v F /ξ ∼ k B T c . The notations are asfollows: r is the radius of the channel, x is the coordinate measured from the interface on the side ofa superconductor occupying a half-space x > , v F and ξ are the Fermi velocity and the correlationlength. The estimation by the formulae of phenomenological theory [18] leads to the following result: W = wV = H I π A λ T ≫ ∆ , (1)[in the interval λ T , we replaced the distribution H I ( x ) by H I = const; A is the interface area ( ≥ − cm )]. Thus, for a current of 1 mA, with a typical for London superconductors λ T ∼ . µ m, theenergy of the self-magnetic field of the current amounts to W ∼ meV, while the value of ∆ is just ∼ . meV. (Note, incidentally, that indicated strength of this inequality for currents greater than 1 mA isalso preserved for Pippard superconductors with λ ∼ . µ m.) Thus, the examined current interval issuitable for the manifestation of the effect discussed. Moreover, the fact that the current self-field at I =100 mA can eliminate the manifestation of the superconducting transition, either almost completelyfor FeSe (Fig. 3, curve 4) or significantly for LaO(F)FeAs (Fig. 4, curve 4), means the following.First, the Ginsburg-Landau parameter κ = λ T /ξ T ≥ and hence discussed superconductors, must becharacteristic of the London type-II superconductors and, second, the thickness of the superconductingpart of the contacts is of order of the London penetration depth λ L ≃ . µ m [18]. It follows that thelength of the measured contact area is of the order of a micron or slightly more - the typical mesoscopicsize which turns out to be non-ballistic due to the presence of the areas with even shorter elastic meanfree paths of electrons and because of the contact geometry characterized by combined current andpotential probes [16]. 6 point contact R ( U ) / R N U, mV Cu/FeSe R N =0,4 N =3,5 Figure 5: Normalized resistance of the heterojunction Cu/FeSe measured at different temperatures asa function of bias voltage U at the contact as an addition to the energy k B T .Inequality (1), of course, overstates the requirements for the value of H I needed to suppress super-conductivity in the range of x = λ T , since it implies H I to be constant over the whole length of theinterval. However, as noted above, the suppression should be also implemented at lower values of thefield at a spatial scale of ξ T , due to the dispersion of the order parameter | ψ | in the proximity effectarea. Indeed, the distribution of the magnetic energy in the superconductor side ( x > ) dependson the law of magnetic field distribution along the length of the penetration depth; according to thephenomenological theory [18], it can be written as H ∗ = H (0) exp( − x/λ ) . (2)Let H ∗ is the lowest field, energy density of which w is comparable in value to the reduced, due to theproximity effect, value of | ψ | normalized to a volume unit. Then, the suppression of superconductivityat arbitrary H (0) will extend to a depth of x depending on H (0) ≡ H I ( x = 0) , ie, on the transportcurrent value I , up to that value of x at which one reaches w = ( H ∗ ) / π . For larger x , ie, for H < H ∗ , the superconducting state persists. Thus, the value of x ( H ∗ ) sets the position of a defect-freeNS boundary between normal and superconducting parts of the superconductor. From this point, letus analyze, for example, the data depicted in Fig. 3. From a comparison of Eq. (2) for two values of H I (0) it follows x i − x k = λ T ln I i I k , (3)where i, k = 1 mA, 10 mA, or 100 mA; i = k . From the system of pairwise equations we find x (1mA) = 0 x (10mA) = λ T ln 10 (4) x (100mA) = λ T ln 100 . Here, the displacement of the boundary is measured relative to its position at x (1 mA) which position,as shown by measurements at I < mA (see below), is very close to the starting point x = 0 inthe absence of current. Based on Eqs. (4), Fig. 6 explains the physics of this effect that would beimpossible in the absence of the proximity effect in the fields the maximum value of which, as we have,does not exceed H ( I = 100 mA) ≈ Oe. For FeSe, for example, that value is more than an order ofmagnitude lower than that of the first critical field [21].The possibility to get a defect-free NS boundary inside a superconductor allows us to interpret withreasonable certainty the effects associated with converting the dissipative current into supercurrent7
N SSN w ( a r b . un i t s ) x/ T w(1mA) w(100 mA) N S * * * H* /8 * = || / || (r ep r . sc a l e ) w(10 mA) Figure 6: Displacement of the NS boundary by transport current at the dispersion of the order pa-rameter caused by the proximity effect.through the mechanism of Andreev reflection. On R ( T ) /R N temperature dependencies measured at I = 1 mA for Cu/FeSe (Fig. 3, curve 2) and at I = 100 mA for Cu/LaO(F)FeAs (Fig. 4, curve 4) aswell as on R ( U ) /R N bias-voltage dependencies for Cu/FeSe (Fig. 5, curve 5), gap features are clearlyvisible. These are positive jumps in the contact resistance at the transition from the NN to NS regimewhich value amounts to around 2-3 % (with resolution better than 0.1 %) relative to the resistance R N before the superconducting transition. Similar feature is barely visible on curve 1, Fig. 5, whilecontrolling the energy by bias voltage U . It can be easily understood by noting that under conditionswhere most of the energy of the electrons is set by the temperature, an addition eU required for therealization of a gap peculiarity is too small at T = 3 K and for low-resistance sample ( R N ∼ . );besides, in a constant-current mode (see above), the current itself is small. Indeed, the area of thefeature controlled by bias voltage at 3 K (curve 1, Fig. 5) corresponds to the current of order of 0.04mA, while that current at 2 K (curve 5, Fig. 5) amounts to around 0.5 mA. Thus, it is of the sameorder as the current 1 mA which value corresponds to the discussed jump in resistance controlled bytemperature in the contacts Cu/FeSe with the resistance R N greater by almost an order of magnitude( ≈ . . This should mean that the self-field of the current 0.04 mA is too small to invade into adispersion region of the order parameter on the FeSe side in NS-interface mode, while at I = 1 mA,the NS boundary is already shifted deep into the superconductor and thus presents an ideal boundarybetween normal and superconducting parts of FeSe at which the conversion of the dissipative currentinto non-dissipative one takes place. In contacts Cu/LaO(F)FeAs, this specific feature manifests itselfonly at the current I = 100 mA, probably due to too low value of T /T c at 4.2 K where ξ T ≈ ξ .In NS systems with non-magnetic superconductors, gap features in the conductance upon Andreevreflection can occur because of the coherent scattering by impurities on the normal side of the interface[17, 13] [we recall that we have included the relevant contribution to the resistance from this effect intothe total resistance of the contact N-side and denoted it by ( i ), see Sec. 1]. In systems with magneticsuperconductors, a decrease in the conductance of a contact [contribution ( iii )] at the transition to asub-gap energy region should also occur as a consequence of the spin polarization of the current due tothe limitation of the Andreev reflection process in the presence of the dispersion of the spin subbandsrelated by magnetic exchange interaction [22]. As a result of these limitations, the accumulation ofspin should occur at the interface [23, 24] accompanied by the appearance of a positive addition to the8 ,0 0,2 0,4 0,6 0,8 1,0 1,2 1,40,980,991,001,01 0,2 0,4 0,6 0,8 1,00,720,760,800,840,940,950,960,970,98 R ( T ) / R N T/T c R ( U ) / R N U, mV FeSe LaOFFeAs
Figure 7: The effect of spin accumulation - increased resistance of spin-polarized FeSe and LaO(F)FeAsat the NS interface in the transition from the NN to NS regime.applied bias voltage which, given constant-current mode, manifests itself as an additive to the totalresistance of the contact in the NS regime. We associate the features observed on the R ( U ) and R ( T ) dependencies shown in Figs. 3, 4, and 5 with this additive. From these figures it also follows thatthe residual resistance of the contacts in the NS regime, particularly at the current of 1 mA, is byseveral orders of magnitude greater than the possible coherent effect of increasing in the resistancein the normal region of the probe as already noted for the systems in the same situation [16]. Thisallows us to attribute the observed features to the manifestation of only the spin accumulation effect.As a direct consequence of the spin polarization, the effect thus gives an indication of the magneticcharacteristics of a superconductor in the normal ground state which is implemented in a finite regionof NS heterojunction due to the proximity effect.Fig. 7 shows an enlarged view of these features depending on both control parameters, temperatureand bias voltage, for the contacts with FeSe and on temperature for the contact with LaO(F)FeAs.Previously, we observed the effect of spin accumulation in the systems "ferromagnet-superconductor"Fe/In and Ni/In where its value reached 20 % and 40 %, with degree of spin polarization of 45 %and 50 %, respectively [25]. Recall that the nature of the effect in the NS systems with conventionalferromagnets is associated with the destruction of the symmetry with respect to spin rotation whichimposes limitations on the probability of Andreev reflection and results from high internal magneticfield that manifests itself in the spontaneous magnetization. Manifestation of spin accumulation inunconventional superconductors in normal ground state also points to the absence of such symmetry,but it cannot be associated with the bulk magnetization, for the latter, in our opinion, is not compatiblewith superconductivity at the microscopic level. Thus, once again we get the arguments in favor of thatthe magnetism of iron-based superconductors is limited by band magnetism of conduction electrons,for example, of the type of antiferromagnetic exchange interaction [26].Knowing the magnitude of the effect of spin accumulation indicating the presence of spin po-larization of the conduction electrons in the normal ground state of FeSe (strictly speaking, of thesuperconducting phase of FeSe in the normal state which can amount to as low as 15 % [26]), we esti-mate the polarization factor of the current P in studied contacts with single-crystal FeSe. Accordingto the theory [23, 24], corresponding normalized additive to the resistance R N of the spin-polarized9rea due to spin accumulation is of the scale δR N / S R N = P − P , (5) P = ( σ ↑ − σ ↓ ) /σ ; σ = σ ↑ + σ ↓ ; R N = λ s / ( σ A ) . Here, σ, σ ↑ , σ ↓ are the total and spin-dependent conductivities; λ s is the spin relaxation length; A is the cross section of NS boundary (of the contact). As R N , we take the total resistance of thesuperconducting phase of the sample in the normal state equal to the value of the resistive jump atthe superconducting transition, assuming that the length of the spin relaxation λ s is of order of thedimension of this phase, L , and the whole area in the normal state is completely spin-polarized. Then P = (cid:20) δR N / S R N / (1 + δR N / S R N ) (cid:21) . (6) -1500 -1000 -500 0 500 1000 1500-101234567 FeSe
T 4 K [ R ( H )- R ( ) ]/ R ( ) , % H , Oe Figure 8: Hysteresis of magnetoresistance of point-contact FeSe samples under proximity effect.Substituting the experimental values of δR N / S = 7 · − Ω (from curve 2, Fig. 3), σ − ≈ . · − Ω · cm (from independent measurement by a standard four-probe method), λ s ∼ L = 5 · − cm, and A ≈ · − cm , we get P ≃ %. We shall verify that this value corresponds to thatratio of spin-dependent conductivities at which a negative correction can exist to the conductance ofspin-polarized ferromagnetic area (F) at the transition from the F/F to F/S regime. To do this, weuse the estimates from Ref. [22] which establish the sign criterion for the resistive addition at a similartransition. The estimates are based on the arguments that the electrons retroreflected as Andreev holesmust double their contribution to the conductance since at each reflection, a charge 2 e is transferred.Here, however, the possibility of limiting the effect is not included due to doubling the cross sectionof subsequent coherent scattering by impurities in non-ballistic samples with short mean free path, asnoted above. Expressing the ratio of spin-dependent conductivities in polarization we get this criterionin the form: σ ↑ σ ↓ = 1 + P − P ( > , G F / S < G FF(N) < , G F / S > G FF(N) . (7)10
200 400 600 800 1000 1200-8-6-4-2024681012
FeSe ++ +++ R - R , - O h m H, Oe + Figure 9: Difference between the values of the magnetoresistance on the branches of the hysteresiscurves for the same values of the magnetic field and the following directions of magnetization: ++ thesame directions of the field, +— the opposite directions of the field.Our experimental situation is entirely equivalent to the first case: σ ↑ σ ↓ ≈ .The estimate of the polarization for granular material LaO(F)FeAs by the same method (fromcurves 1 and 4, Fig. 4) gives a value of P ≈ % which is in contradiction with the criterion (7). Thisagain suggests that the physics of conductivity of granular compounds is much more complicated thanthat of single-crystal ones, in particular, because of the network of intergranular connections.In addition to probable itinerant magnetism, we have tested the concept of spin-polarized conduc-tivity of FeSe for the possibility that an alternative type of magnetism exists which is characterized byresidual magnetization at reverse magnetizing. To do this, we measured the conductance of the normalpart of FeSe within boundaries defined, as a reasonable belief, by the proximity effect, in an externalmagnetic field, a lot of smaller values in comparison with those converting the order parameter to unity.The measurements show that the hysteresis of magnetoresistance does not contain an irreversible ef-fect at H = 0 for any sequence of magnetizing, as can be seen from the form of the magnetoresistancehysteresis curves shown in Fig. 8. Besides, other characteristic features of hysteresis strike the eye (seeFig. 9): ( a ) The branches belonging to different magnetic field directions are asymmetric and ( b ) thevertical displacement of the hysteresis branches in the fields exceeding the first critical field ≃ Oe[21] is of the same order of magnitude as the gap features in Fig. 7. These features of the hysteresisare, of course, directly related to the spin polarization of the current, and the absence of residual mag-netoresistance at H = 0 for all sequences of magnetizing shows that the nature of superconductivityin layered superconductors is associated with the magnetism of conduction electrons (itinerant mag-netism) which does not interfere with the local magnetism of magnetic ions (such as iron ion). Notethat the hysteresis of magnetoresistance was usually observed in granular systems, but in contrast toour results obtained in a single-crystal FeSe, it contained non-reversible values of the resistance duringreversible magnetizing. This gave rise to interpret its nature in terms of percolation mechanism ofcurrent flow along the network of Josephson junctions [27]. The data from our single-crystal samplesof FeSe rejecting such a possibility are closest to a vortex scenario of hysteresis which is based on thedissipative mechanism of synchronizing the vortices in the presence of defects [28].11 Conclusion
We have investigated the electron transport through a barrier-free NS boundary set by the proxim-ity effect and the transport current inside unconventional iron-based superconductors, single-crystalchalcogenide FeSe and granular oxypnictide LaO(F)FeAs, as parts of heterocontact samples of meso-scopic scale.The evidence for the spin polarization of electron transport is obtained based on the sensitivity ofAndreev conductance to symmetry with respect to the spin rotation.The nature of the hysteresis of magnetoresistance observed in the fields much less in value than thatof the second critical field, under dispersion of the order parameter, also points to the spin polarizationof the charge carriers.The results suggest that the nature of superconductivity in layered superconductors is connectedwith the magnetism of conduction electrons (itinerant magnetism) which has nothing in common withthe local magnetism of iron ions.
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