Planar superconductor/ferromagnet hybrids: Anisotropy of resistivity induced by magnetic templates
aa r X i v : . [ c ond - m a t . s up r- c on ] M a y Planar superconductor/ferromagnet hybrids: Anisotropy of resistivity induced bymagnetic templates
A.Yu. Aladyshkin,
1, 2
J. Fritzsche, and V.V. Moshchalkov INPAC – Institute for Nanoscale Physics and Chemistry,K.U. Leuven, Celestijnenlaan 200D, B–3001 Leuven, Belgium Institute for Physics of Microstructures RAS, 603950, Nizhny Novgorod, GSP-105, Russia (Dated: October 6, 2018)We investigated experimentally the transport properties of a superconducting cross-shaped alu-minium microbridge fabricated on top of ferromagnetic BaFe O single crystal. It was demon-strated that a one-dimensional domain structure in the ferromagnetic substrate can induce theformation of superconducting channels above magnetic domains. This leads to a giant anisotropyof resistivity of the superconducting bridge, caused by the appearance of continuous paths of super-currents flowing along domain walls. PACS numbers: 74.78.-w 74.78.Fk 74.25.Dw
Hybrid superconductor-ferromagnet (S/F) structureshave attracted considerable attention in connection withthe possibility to control thermodynamic and transportproperties of the S/F hybrids by manipulating the mag-netic state of the ferromagnetic constituents ([1, 2, 3, 4]and references therein). Provided an insulating layer pre-vents the diffusion of Cooper-pairs from the superconduc-tor to the ferromagnet, the exchange interaction betweensuperconducting and ferromagnetic parts can be effec-tively suppressed and the interaction between both sub-systems occurs via slowly decaying stray magnetic fields.Nonuniform magnetic field, induced by the ferromagnet,can modify the conditions for the appearance of super-conductivity due to the effect of a local field compensa-tion, resulting in the field-induced superconductivity [5]and an exotic dependence of the superconducting criticaltemperature T c on an applied magnetic field H [6, 7, 8].An increase of the width of the equilibrium magnetiza-tion loop M ( H ) of the S/F hybrids, compared with plainsuperconducting films, can be interpreted as an enhanced“magnetic” pinning of vortices by various magnetic tex-tures: periodic arrays of magnetic dots [9, 10] or irregularmagnetic bubble domains [11]. The magnetostatic inter-action between the vortices and the “built-in” magneticfield is also known to lead to the unusual field dependenceof the electrical resistance R ( H ) of the S/F hybrids attemperatures close to the superconducting critical tem-perature T c [5, 12, 13, 14].Recently, electrical transport in S/F hybrids at lowtemperatures was studied for the following planar struc-tures: Nb/Co [15], Al/CoPd [16], NbSe /Py [17],MoGe/Py [18, 19], Pb/Py [20]. Superposition of the biascurrent and the supercurrent that is induced by hard fer-romagnets may lead to a remarkable change of the cur-rent ( I ) – voltage ( V ) characteristics of superconductingbridges [15, 16], what can be interpreted as a “current”compensation effect [21]. The tunable alignment of mag-netic domains in low-coercive ferromagnetic films, usingan in-plane oriented external field H , makes it possible to introduce a guided vortex motion in a desirable direction– along the domain walls [17, 18, 19, 20].In this Letter we are aiming at the investigation of theanisotropy of the electrical transport properties of theS/F hybrids, induced by a single straight domain wall.We measured both the magnetoresistance R ( H ) and the I − V dependencies of a superconducting bridge in twoperpendicular directions (i.e. along and across a domainwall in the ferromagnetic substrate).In order to study the anisotropy of the low-frequencytransport properties in a planar S/F hybrid, we prepareda bi-layered sample consisting of a bulk ferromagneticsubstrate and a thin-film Al microbridge on top. The fer-romagnetic and superconducting parts were electrically FIG. 1: (color online) The planar S/F hybrid system underinvestigation. The top layer shows an atomic force microscopyimage (AFM) of the cross-shaped Al bridge (lighter shades).The areas labelled I–IV were used as contact pads for trans-port measurements. The bottom layer shows a magnetic forcemicroscopy image (MFM) of the ferromagnetic BaFe O substrate. Light and dark regions correspond to the mag-netic domains with M z > M z <
0. Note that theMFM image is vertically extended to illustrate the magneticdomains. Black solid lines depict the edges of the Al bridge. isolated by a 5 nm SiO buffer layer, so that the inter-action between these parts can be expected to be exclu-sively electromagnetic. When cut along the proper crys-tallographic direction, a ferromagnetic BaFe O sin-gle crystal exhibits a one-dimensional (1D) stripe-typedomain structure with dominant in-plane magnetizationand relatively small out-of-plane component M z (the bot-tom image in Fig. 1). Measurements with a vibratingsample magnetometer (VSM) revealed that at low tem-peratures the magnetization of the used crystal dependsalmost linearly on the applied perpendicular magneticfield with the slope dM/dH ≃ . · (A/m)T − andthat it saturates at H ≃ . | H | ≤
80 mT can only be of minor influ-ence on the domain structure, since the variations of mag-netic moment of the substrate are expected to be about4.5% from the saturated magnetization (5 . · A/m).The location of the domain walls and their shape weredetermined by magnetic force microscopy (MFM), priorto the preparation of the Al bridge. The expected am-plitude of the z − component of the nonuniform magneticfield, B , exceeds the upper critical field H c of such Alfilms even at low temperatures (see below). The cross-shaped Al microbridge (50 nm thick) was fabricated bymeans of e-beam lithography, molecular beam epitaxyand lift-off etching (the top image in Fig. 1). The width w of the ”arms” of the microbridge was equal to 30 µ mand limited by the width of the magnetic domains. Fourcontact pads, labelled in Fig. 1 as I–IV, were used for theinjection of the dc bias current I and for the measurementof the voltage drop V for two different cases: along thedomain wall ( V k ) using the electrodes I and II and acrossthe domain walls ( V ⊥ ) using the electrodes III and IV.This symmetrical form of the superconducting elementwas intentionally chosen in order to have the possibilityto compare the I − V characteristics in two perpendiculardirections for the same magnetic landscape.Figure 2 shows the level curves of the dc resistance ofthe sample, V k ( H, T ) /I = 0 . R n and V ⊥ ( H, T ) /I =0 . R n , R n being the normal-state resistance, I =100 µ A. These lines can be commonly interpreted as thedependence of the superconducting critical temperature T c on H . In spite of some inessential differences, bothphase transition lines T k c ( H ) and T ⊥ c ( H ) have symmetri-cal maxima of similar amplitudes, and they are character-ized by almost the same slope dT c /dH . In our opinion,this indicates that the nucleation of superconductivity,responsible for an initial deviation of the electrical re-sistance from its normal value, is almost isotropic (i.e.independent on the direction in which the bias currentwas injected and the voltage drop was recorded). Tak-ing the position of the T c maxima and comparing theslope dT c /dH with that for the regime of surface super-conductivity dT c /dH ≃ . T c /H (0) c , we estimate theamplitude of the nonuniform field B ≃
52 mT, the up- −80 −60 −40 −20 0 20 40 60 800.50.70.91.11.3 µ H, mT T c , K T ||c T ⊥ c T ||c T ⊥ c FIG. 2: (color online) The phase transition lines T c ( H ) es-timated according to the criterium V ( H, T c ) /I = 0 . R n forthe measurements of magnetotransport using the contacts Iand II (along the domain wall, red circles) and the contacts IIIand IV (across the domain walls, blue squares). I = 100 µ Ais the dc bias current and R n is the normal state resistance. per critical field µ H (0) c ≃ . T = 0, and themaximal critical temperature T c ≃ .
35 K. These valuesappear to be typical for pure Al films and bridges [8].However deeper in the superconducting state in the H − T plane the transport properties of the S/F hybridsystem become essentially anisotropic. Figure 3 illus-trates this, showing the dependencies of the resistance R k = V k /I (top row) and R ⊥ = V ⊥ /I (bottom row) as afunction of H and I , derived from the isothermal I − V curves at constant H value. As expected the total resis-tance of the sample goes to zero only for the parallel ge-ometry when I flows along domain walls [Fig. 3 (a)–(c)].Indeed, the stripe-type domain structure allows to forma continuous path for the supercurrents at | H | ≃ B ,connecting the electrodes I and II. It is easy to see thatthe maximal critical current corresponds to the most ef-fective compensation, when one part of the bridge is sub-jected to zero local magnetic field, B z = µ H + b z ≃ B z ≃ B induces the normal state in the otherpart. Taking I max = 1035 µ A and the sample’s cross-section S = 1 . · − cm , one can estimate the criti-cal current density j c = 2 I max /S ≃ . · A/cm at T = 500 mK, which can be interpreted as the depin-ning current density. Apparently, an increase of temper-ature reduces the size of the area of zero resistance in the H − I plane. By contrast, alternating superconductingand normal (N) regions, induced by the magnetic tem-plate, act as a series of resistors if I is injected perpen-dicular to the S-N interfaces. Consequentially, the for-mation of superconductivity above the reverse domainsroughly halves the total resistance of the sample at lowtemperatures: min V ⊥ /I ≃ R n / µ H, mT I, m A R || (H,I) at T=500 mK(a) Ohms−80 −40 0 40 80−1−0.500.51 012345 R ⊥ (H,I) at T=500 mK µ H, mT I, m A (d) Ohms−80 −40 0 40 80−1−0.500.51 012345R || (H,I) at T=900 mK µ H, mT I, m A (b) Ohms−80 −40 0 40 80−1−0.500.51 012345 R ⊥ (H,I) at T=900 mK µ H, mT I, m A (e) Ohms−80 −40 0 40 80−1−0.500.51 012345R || (H,I) at T=1300 mK µ H, mT I, m A (c) Ohms−80 −40 0 40 80−1−0.500.51 012345 R ⊥ (H,I) at T=1300 mK µ H, mT I, m A (f) Ohms−80 −40 0 40 80−1−0.500.51 012345 FIG. 3: (Color online) The dc resistance R of the superconducting bridge as a function of the external magnetic field H andthe biased dc current I , measured along the domain wall [panels (a)–(c)] and across the domain wall [panels (d)–(f)]. (a) and(d) T = 500 mK, (b) and (e) T = 900 mK, (c) and (f) T = 1300 mK. Solid black lines are the curves of constant resistance: R ( H, I ) = 0 .
5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0 and 4.5 Ohm. Note that the color scales of all plots are identical. a giant anisotropy of resistivity: min R ⊥ / min R k > (Fig. 4), which is in agreement with that obtained for anetwork of parallel magnetic domains in permalloy films[17, 18, 19, 20].In summary, we demonstrated that a 1D domain struc-ture in a ferromagnetic substrate can induce a giant anisotropy of the electrical transport of S films that areplaced on top of the substrate. This effect is causedby the appearance of superconducting channels that runalong the underlying magnetic domains. We also studiedthe H - and T dependence of the critical current throughsuch an individual channel. (a) T=500 mK, I=600 µ A (b) T=500 mK, I=100 µ A R / R m a x −80 −40 0 µ H, mT µ H, mTR || R ⊥ R || R ⊥ FIG. 4: (Color online) Giant resistance anisotropy illus-trated by cross-sections of R || ( H, I ) [panel (a) in Fig. 3] and R ⊥ ( H, I ) [panel (d) in Fig. 3] taken at T = 500 mK and I = 600 µ A (a) and I = 100 µ A (b). Red circles (blue squares)correspond to the resistivity along (across) the domain wall.
The authors are grateful to A.S. Mel’nikov, A.A.Fraerman and R. Kramer for stimulating discussions.This work was supported by the Methusalem Fundingof the Flemish Goverment, NES – ESF program, theBelgian IAP, the Fund for Scientific Research – Flan-ders (F.W.O.–Vlaanderen), the Russian Fund for BasicResearch, RAS under the program ”Quantum physicsof condensed matter” and the Presidential grant MK-4880.2008.2. [1] A.I. Buzdin, Rev. Mod. Phys. , 935 (2005).[2] I.F. Lyuksyutov and V.L. Pokrovsky, Adv. Phys. , 67(2005).[3] M. V´elez, J.I. Mart´ın, J.E. Villegas, A. Hoffmann, E.M.Gonz´alez, J.L. Vicent, and I.K. Schuller, Journ. Magn. Magn. Mater. , 2547–2562 (2008).[4] A.Yu. Aladyshkin, A.V. Silhanek, W. Gillijns, and V.V.Moshchalkov, Supercond. Sci. Tech. , 053001 (2009).[5] M. Lange, M.J. van Bael, Y. Bruynseraede, and V.V.Moshchalkov, Phys. Rev. Lett. , 197006 (2003).[6] A.Yu. Aladyshkin, A.I. Buzdin, A.A. Fraerman, A.S.Melnikov, D.A. Ryzhov, A.V. Sokolov, Phys. Rev. B ,184508 (2003).[7] Z. Yang, M. Lange, A. Volodin, R. Szymczak, and V.V.Moshchalkov, Nature Mater. , 793 (2004).[8] W. Gillijns, A.Yu. Aladyshkin, A.V. Silhanek, and V.V.Moshchalkov, Phys. Rev. B , 060503(R) (2007).[9] D.J. Morgan and J.B. Ketterson, Phys. Rev. Lett. ,3614(1998).[10] M.J. Van Bael, K. Temst, V.V. Moshchalkov, and Y.Bruynseraede, Phys. Rev. B , 14674 (1999).[11] M. Lange, M.J. van Bael, V.V. Moshchalkov, and Y.Bruynseraede, Appl. Phys. Lett. , 322 (2002).[12] J.I. Mart´ın, M. V´elez, J. Nogu´es, and I.K. Schuller, Phys.Rev. Lett. , 1929 (1997).[13] Y. Jaccard, J.I. Mart´ın, M.-C. Cyrille, M. V´elez, J.L.Vicent, and I.K. Schuller, Phys. Rev. B , 8232 (1998).[14] A. Hoffmann, P. Prieto, and I.K. Schuller, Phys. Rev. B , 6958 (2000).[15] D.Y. Vodolazov, B.A. Gribkov, S.A. Gusev, A.Yu.Klimov, Yu.N. Nozdrin, V.V. Rogov, and S.N.Vdovichev, Phys. Rev. B , 064509 (2005).[16] M. Morelle and V.V. Moshchalkov, Appl. Phys. Lett. ,172507 (2006).[17] V. Vlasko-Vlasov, U. Welp, G. Karapetrov, V. Novosad,D. Rosenmann, M. Iavarone, A. Belkin, and W.-K. Kwok,Phys. Rev. B , 134518 (2008).[18] A. Belkin, V. Novosad, M. Iavarone, J. Fedor, J.E. Pear-son, A. Petrean-Troncalli, and G. Karapetrov, Appl.Phys. Lett. , 072510 (2008).[19] A. Belkin, V. Novosad, M. Iavarone, J. Pearson, and G.Karapetrov, Phys. Rev. B , 180506 (2008).[20] V.K. Vlasko-Vlasov, U. Welp, A. Imre, D. Rosenmann,J. Pearson, and W.K. Kwok, Phys. Rev. B , 214511(2008).[21] M.V. Miloˇsevi´c, G. Berdiyorov, and F.M. Peeters, Phys.Rev. Lett.95