4 1 0 2 Detectionof smallexchangefieldsinS/F structures v o N A. S. Vasenkoa, S. Kawabatab, A. Ozaetac, A. A. Golubovd,e, V. S. Stolyarovf,g,h,e, F. S. Bergeretc,i, F. W. J.Hekkinga,j 3 aLPMMC, Universite´ Joseph Fourier and CNRS, 25Avenue des Martyrs, BP166, 38042 Grenoble, France ] bElectronics andPhotonics Research Institute (ESPRIT), n National Institute ofAdvanced Industrial Science andTechnology (AIST), Tsukuba, Ibaraki, 305-8568, Japan o cCentro de F´ısica deMateriales (CFM-MPC), Centro Mixto CSIC-UPV/EHU, Manuel de Lardizabal 5, E-20018San Sebastiań, Spain c dFaculty of Science andTechnology and MESA+ Institute for Nanotechnology, University ofTwente, 7500 AEEnschede, The Netherlands r- eMoscow Institute ofPhysics andTechnology, 141700 Dolgoprudny, Russia p fSorbonne Universite´s, UPMCUniv Paris 06, UMR7588, Institut des Nanosciences de Paris,F-75005, Paris, France u gCNRS, UMR 7588, Institut des Nanosciences deParis, F-75005, Paris,France s hInstitute of Solid State Physics RAS,142432, Chernogolovka, Russia t. iDonostia International Physics Center (DIPC),Manuel de Lardizabal 4, E-20018San Sebastiań, Spain a jInstitut Universitaire de France, 103, bdSaint-Michel 75005 Paris,France m - d n Abstract o [c Ferromagnetic materials with exchange fields Eex smaller or of the order of the superconducting gap D are important for applications of corresponding (s-wave) superconductor/ ferromagnet/ superconductor (SFS) junctions. Presently such materials 2 arenotknownbutthereareseveralproposalshowtocreatethem.Smallexchangefieldsareinprincipledifficulttodetect.Based v onourresultsweproposereliabledetectionmethodsofsuchsmallEex.Forexchangefieldssmallerthanthesuperconductinggap 6 thesubgapdifferentialconductanceofthenormalmetal-ferromagnet-insulator-superconductor(NFIS)junctionshowsapeak 4 atthevoltagebiasequaltotheexchangefieldoftheferromagneticlayer,eV=Eex.Thusmeasuringthesubgapconductanceone 6 canreliablydetermine smallEexD onecandeterminetheexchange fieldinscanning tunneling 0 microscopy (STM) experiment. The density of states of the FS bilayer measured at the outer border of the ferromagnet shows . 1 a peak at the energy equal to the exchange field, E=Eex. This peak can be only visible for small enough exchange fields of 0 theorder of few D . 4 1 : Key words: exchange field, S/F hybrid structures, proximity effect v PACS:74.45.+c, 74.50.+r, 74.78.Fk, 75.30.Et i X r a 1. Introduction brid structures[1–4].Let us briefly reviewthe essence ofthe S/Fproximityeffect. Asweknowfromthequantumtheoryofmagnetism UponenteringoftheCooperpairintothe ferromag- the ferromagnetic metal can be described by the pres- neticmetalitbecomesanevanescentstateandthespin ence of the so called exchange field, Eex. This field upelectroninthepairlowersitspotentialenergybyEex, is responsibleto manyinterestingphenomenain artifi- whilethespindownelectronraisesitspotentialenergy ciallyfabricatedsuperconductor/ferromagnet(S/F)hy- bythesameamount.Inorderforeachelectrontocon- serveitstotalenergy,thespinupelectronmustincrease its kinetic energy, while the spin down electron must decrease its kinetic energy, to make up for these addi- Email address:andrey.vasenko@lpmmc.cnrs.fr tionalpotentialenergiesinF.Asaconsequence,thecen- (A. S.Vasenko). PreprintsubmittedtoElsevier 4November2014 ter of mass motion is modulated and superconducting for 5.5% of Ni fitting gives E =0.11 meV, which is ex correlationsin the Flayer havethe dampedoscillatory 0.1 D , for 6% of Ni it gives E =0.45 meV, which is ex behavior[5,6].Ifweneglecttheinfluenceofotherpos- 0.4D ,for7%ofNiitgivesE =2.8meV,whichis2.2 ex sibleparametersofferromagneticmetal(likemagnetic D , andfor11.5%ofNiE =3.9meV,whichis3 D . ex scatteringrate,etc.)thecharacteristiclengthsofthede- Another promising alloy with small exchange field, cay and the oscillations are equal to x = D /E , Pd Fe ,was studiedin [24–26]. f f ex 0.99 0.01 where D is the diffusion coefficient in the ferromag- Finally, a small exchange field can be induced by a f p neticmetal[1]. ferromagnetic material into the adjacent normal metal Thelengthx isalsothelengthofdecayandoscilla- layer.Inrecentproposal[27],athinnormalmetallayer f tionsofthecriticalcurrentinJosephsonS/F/Sjunctions wasplacedontopoftheferromagneticinsulator.Itwas [7,8]. Negative sign of the critical current corresponds shown that the ferromagneticinsulator may induce ef- to the so-calledp -state [9–13].S/F/S p -junctionshave fectiveexchangefieldin thenormalmetallayer[27], been proposed as potential elements in superconduct- Eeexff=h¯DGf r /d, (1) ing classical and quantum logic circuits [14–16]. For whereDisthediffusioncoefficientinthenormalmetal, instance,S/F/Sjunctionscanbeusedascomplementary elements (p -shifters) in RSFQ circuits (see Ref. [17] Gf isasurfaceconductancelikecoefficientforthenor- mal metal/ ferromagnetic insulator interface, r is the and referencestherein).S/F/S based deviceswere also resistivity of the normal metal, and d is the thickness proposed as elements for superconducting spintronics of the normal metal layer in the direction, perpendic- [18]. Finally, S/F/S structures have been proposed for the realization of so called j -junctions with a j drop ular to the ferromagnetic insulator surface. The field inthe groundstate, where0D . In this paper we review several proposals for ferro- ex Weshouldmentionthatweproposemethodsofsmall magneticmaterialswithexchangefieldsE smalleror ex ofthe orderofthe superconductinggapD . Thenbased exchangefield detectionin the ideal case of ferromagnetic layer with homogeneous magnetization and ab- on our results we propose reliable detection methods sence of magnetic and spin-orbit scattering in contact of such small exchangefields in experiments.Another withasuperconductor.However,incaseofrealisticfer- detectionmethodwasrecentlysuggestedin [21]. romagnetssituation can be more complicated. We dis- cuss some possible limitations of the detection in the 2. Waystogeneratesmallexchangefields endofthe twofollowingsections. The easiest way to create small exchange field is to 3. Detection of exchange fields smaller than the applyanexternalmagneticfieldB to thenormalmetal superconductinggap lead, in which case E =m B, where m is the Bohr ex B B magneton. InthissectionweconsiderthefollowingSIFNstruc- It may be also an intrinsic exchange field of weak ture: a ferromagnetic wire F of a length d (smaller f ferromagnetic alloys. For example, in Ref. [22] were than the inelastic relaxationlength[28,29])is attached reportedexchangefieldsforPd Ni withdifferentNi at x=0 to a superconducting (S) and at x=d to a 1 x x f concentration,obtainedbyafitti−ngprocedure(seealso normal(N)electrode.Theinterfaceatx=0isatunnel [23]).ConsideringNbasasuperconductorwithD =1.3 barrierwhileatx=d wehaveatransparentinterface. f meV, we can estimate the exchange field in Pd Ni : We will show that the subgap differentialconductance 1 x x − 2 ofsuchastructurehasa peakatthebiasvoltageequal 3 totheexchangefieldoftheferromagneticmetalincase when E D in experiments by measuring the ex DOS at the outer border of the ferromagneticmetal in Attheouterborderoftheferromagnet(x=d )wehave f correspondingSF bilayerstructure,whichcanbe done ¶ q =0. At x =0 we use Kupriyanov-Lukichev x f ( ) byscanningtunnelingmicroscopy(STM). boun↑d↓ary conditions which in case of the transparent TheDOSN (E)normalizedtotheDOSinthenormal f interfaceisconvenienttowrite as state, canbewrittenas g¶ q =¶ q , (9a) Nf(E)= Nf↑(E)+Nf↓(E) /2, (6) x ngB¶ xxq ff|xx==00=sixnhs(|xq=f0 q s)x=0. (9b) where Nf ( )(E) are(cid:2)the spin resolved(cid:3)DOS written in | − | termsofs↑p↓ectralangleq f, Here g =s f/s s, s f(s) are the conductivities of the F N (E)=Re coshq . (7) (S) layers correspondingly, x n = D/2p Tc, Tc is the f↑(↓) f↑(↓) critical temperature of the superconductor, and gB = ToobtainNf,weuseaself-co(cid:2)nsistenttw(cid:3)o-stepiterative d R /x R =x /x W.Theparampeterg determinesthe f T n F s n procedure[8,42].In the first step we calculate the pair strength of suppression of superconductivity in the S potential coordinate dependence D (x) using the self- layer near the interface (inverse proximity effect). No consistency equation in the S layer in the Matsubara suppressionoccursforg =0,whilestrongsuppression representation. Then, using the D (x) dependence, we takesplaceforg 1.Inournumericalcalculationswe solvetheUsadelequationsinthe Slayer, assumesmallg ≫1.Sinceweconsiderthetransparent D ≪ 2i¶ x2xq s=Esinhq s+iD (x)coshq s, (8) Winterfa1c,ethReFre≫forReTg and1c.oNntoratircyettohathteinptrheeviEoquss.s(e8c)t-i(o9n) B ≫ ≪ together with the Usadel equations in the F layer wehaveomittedthesubscripts ( )becauseequations ↑ ↓ [Eq. (2)] and corresponding boundary conditions, re- for both spin directions are identical in the supercon- peating the iterationsuntil convergencyis reached [8]. ductor. 4 InFig.3weplottheDOSN (E)attheouterborder Detecting this peak one can carefully measure the f of the F layer in the FS bilayer calculated numerically valueofsmallexchangefiledE >D intheferromag- ex for different values of the exchange field E and for netic metal. ex different F layer thicknesses d . At large enough d Wementionthatinthepresenceofmagneticscatter- f f (d /x =3) we see the peak at E =E [see Fig. 3, ingtheDOSpeakatE=E donotchangetheposition f n ex ex lower panel]. For small d (d /x =1) the peakis not butgetssmearedatlargeenoughscatteringrate[8].We f f n visibleandDOStendsmonotonouslytounityforE>D did not consider the effect of domain structure of the [see Fig. 3, upperpanel].Theamplitudeof the peakis F layer on this peak, but we can expectsimilar behav- decreasingwithincreasingE :peakisonlyvisiblefor iorasdiscussedinprevioussection,i.e.thepositionof ex E ofthe orderof few D (see [8] fordetails). We also the DOS peak will move to the value of the “effective ex needtomentionthatincaseofE D one can determine the b↑(↓) F2(E)+1+1 (cid:18)− ↑(↓)x f(cid:19) exchangefieldinscanninexgtunnelingmicroscopyexper- whereweuspe thefollowingnotations, iment.ThedensityofstatesoftheFSbilayermeasured at the outerborderof the ferromagnetshowsa peakat p↑(↓)= 2/Eex√D −iER±iEex, (12a) theNeenxetrgwyeeaqruealpltaontnhiengextcohsaenagrechfieflodr,sEm=allEeexx.change F(E)=p , E =E+i0. (12b) iE + D 2 E2 R fields Eex >D in the experiments, using the ultrahigh − R − R vacuum Scanning Tunneling Microscopy (STM) and From Eqs. (10)-(1q1)we obtain for the full DOS the Spectroscopy (STS) technique, recently developed by followingexpressioninthelimitd x andforE D , oneofthe authors(Stolyarovetal.)[44]. f f ≫ ≥ We alsohopethatourresultswilltriggerfurtherex- (cid:229) 16D 2cos(bj)exp( bj) perimental activity in finding ferromagnetic materials N (E)=1+ − , (13) f (E+e )(√E+e +√2e )2 with small exchange fields. Good candidates for such j= ± materialscanbedilutedferromagneticalloys(likePdNi, PdFe,CuNi,etc.)andnormalmetalsinproximitywith 2d E+jE bj= x ffs| Eex ex|, e = E2−D 2. tfhererofemrraogmneatgicneitniscuilnastourlamtoarys (iFndI)u.cIentthheeelxatcthearncgaesefitehlde p We can clearly see the exponential asymptotic of the in the thin normalmetal layer, placed on top of the FI peak at E = E from Eq. (13). We should keep in material. ex mind that Eq. (13) is valid for large d /x , but nev- This work was supported by European Union Sev- f f ertheless we may qualitatively understand why we do enth Framework Programme (FP7/2007- 2013) un- not see the peak at E =E for small ratio of d /x : der grant agreement “INFERNOS” No. 308850, by ex f f if this factor is small the variation of the exponent Ministry of Education and Science of the Russian exp 2(d /x ) E E /E near the point E = Federation, grants No. 14Y.26.31.0007, No. 2014-14- f f ex ex {− | − | } E is also small. 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Detection of small exchange fields in S/F structures

Similar Detection of small exchange fields in S/F structures