Superconducting transition in Pb/Co nanocomposites: effect of Co volume fraction and external magnetic field
Y. T. Xing, H. Micklitz, T. G. Rappoport, W. A. Rodrigez, E. Baggio-Saitovitch
aa r X i v : . [ c ond - m a t . s up r- c o n ] J a n Superconducting transition in Pb/Co nanocomposites: effect of Co volume fractionand external magnetic field
Y. T. Xing, H. Micklitz, W. A. Rodrigez, and E. Baggio-Saitovitch
Centro Brasileiro de Pesquisas F´ısicas, Rua Dr. Xavier Sigaud 150, Rio de Janeiro, 22290-180, RJ, Brazil
T. G. Rappoport
Instituto de F´ısica, Universidade Federal do Rio de Janeiro,Cx. P. 68528, 21941-972 , Rio de Janeiro, Brazil (Dated: December 3, 2018)Pb films embedded with homogeneously distributed cobalt (Co) nanoparticles (mean size 4.5 nm)have been prepared. Previous transport investigations have shown that Co particles induce spon-taneous vortices below the superconducting transition temperature (T c ) in zero external magneticfield. In this paper we study in detail the influence of the Co volume franction and an external mag-netic field on the superconducting transition in such composites. The large difference in T c -reductionbetween the as-prepared and annealed samples can be attributed to the different superconductingcoherence lengths and the resulting different diameters of the spontaneous vortices in these samples. PACS numbers:
I. INTRODUCTION
Composite materials with a nanometer scale structure,so-called nanocomposites, are an actual research field insolid state physics. In this way a hybrid of two differ-ent materials with conflicting properties can be artifi-cially fabricated, which usually does not exist in nature.An example for such nanocomposites are systems madefrom superconducting (SC) and ferromagnetic (FM) ma-terials. In such systems the interplay between the mu-tual exclusive cooperative phenomena SC and FM canbe studied and many papers have been published onthis topic . It was found that due to the in-teraction between SC and FM, the external magneticfield can increase the critical parameters of the super-conductor. Other interesting phenomena, such as do-main wall superconductivity , hysteresis pinning , etc,were also found in such kind of nanocomposites. Thereare mainly three types of SC/FM nanocomposites: SCand FM multilayers , FM decorations on tope of SCfilms and SC/FM granular systems. The first system isusually used to study the proximity effect in the SC/FMlayers. The second one is usually used to study the for-mation of vortices and antivortices induced by the FMdecorations, which can have the effect of critical parame-ter enhancement . In the last ones, namely, the gran-ular hybrid systems the collective interactions betweenSC and FM has been studied. The above mentioned hys-teresis pinning, for example, has been discovered in sucha system . Very recently we reported about a SC/FM hy-brid system containing single domain Co particles insidea SC Pb matrix . The magnetic moments of the FM Coparticles induce spontaneous vortices inside the SC ma-trix. The random network of such a spontaneous vortexphase has been studied without and with applied exter-nal magnetic field. In this paper we will report on theeffect of external magnetic field on the superconductingtransition temperature of such Pb/Co nanocomposites. II. SAMPLE PREPARATION
The Pb/Co films were prepared by co-deposition ofwell-defined Co clusters and Pb atoms onto the sapphiresubstrate mounted onto the coldfinger of a rotatable,variable-temperature He cryostat. Sapphire was usedas a substrate in order to have a good thermal contactbetween the sample and the coldfinger and having alsoan insulator which will not give any contribution to thetransport measurements made on the film. Ag contactsfor transport measurements have been deposited on thesubstrate by sputtering and were connected to the mea-surement system before closing the main chamber. TheCo clusters were made in-beam by the so-called inert-gas-aggregation method with an Ar pressure of about 10 − mbar. A He-cryopump sitting between the cluster sourceand the main chamber absorbed the Ar gas. For that rea-son, only well-defined Co clusters and essentially no Aratoms will enter the main chamber. The Pb atoms werethermally evaporated and deposited together with the Coclusters. Since it is well-known that island formation willprevent good quality Pb films if deposited at room tem-perature, the substrate was cooled down to ∼
40 K duringdeposition which is low enough to get homogeneous Pbfilms, but, on the other hand, is high enough to preventdeposition of Ar atoms [p(Ar) at 40 K ∼ − mbar]which have not been absorbed by the He-cryopump and,therefore, enter the main chamber together with the Coclusters. The angle between the matrix and the clusterbeam is 45 o . Due to the different beam directions sampleswith different Co volume fraction could be made withinone deposition process. The deposition rates were con-trolled by three quartz balances in order to monitor therates at different positions of the substrate. The samplefor microstructure study was deposited onto a carbon foilmounted in a Transmission Electron Microscope (TEM)-catcher.After transport measurements on the as-prepared sam-ples they were annealed at 300 K for one hour in orderto decrease the lattice defects, formed in the samples dueto the low-temperature deposition. The transport mea-surements have been repeated on the annealed samplesin order to see the influence of lattice defects. The typi-cal dimensions of the sample for transport and magneticmeasurements were 10 mm × ×
100 nm. Trans-port properties in both zero and non-zero magnetic fieldwere investigated in-situ with a split-coil superconduct-ing magnet ( B ≤ . The magnetic measure-ments were performed with a Quantum Design MPMS-XL SQUID. The sample has been taken from the mainchamber of the cluster source after finishing the trans-port measurements and immediately installed into theSQUID system in order to avoid oxidation. The externalmagnetic field is parallel to the surface of the sample inboth the in-situ magnetotransport and ex-situ magneticmeasurements. In this work we studied three sampleswith different Co cluster volume fraction: sample 1 with2.7 vol%, sample 2 with 3.1 vol% and sample 3 with 3.7vol%. III. RESULTS AND DISCUSSION M ( k A / m ) T (K)
50 Oe FC 50 Oe ZFC
FIG. 1: Magnetization as a function of temperature for thesample with about 3 . vol % Co. A 50 Oe external magneticfield was applied for both zero-field cooling and field coolingmeasurements. The size of the Co nanoparticles was studied with aTEM and the picture can be found elsewhere . The Conanoparticles are very homogeneous in size and shapewith a mean diameter of ∼ b of the Co clusters hasbeen determined in the usual way, namely, by measuringthe magnetization of the sample in a warming-up processafter cooling the sample down in either zero-field (zero-field cooling, ZFC) or in a magnetic field (field cooling,FC). A mean value of T b ∼
25 K (corresponding to thepeak temperature in the ZFC curves) is obtained fromthe experimental data shown in Fig. 1. Measurementof the magnetization as a function of external magnetic field at 8 K, i. e. far below T b , reveal the Co clusters tobe in a ferromagnetic state . T (K) (b) ( m ) (a) FIG. 2: Resistivity as a function of temperature in differentexternal magnetic fields for the as-prepared samples with (a)2 . vol % Co (b) 3 . vol % Co and (c) 3 . vol % Co. The resistivity measurements of all three as-preparedsamples in zero field and for different external magneticfields are shown in Fig. 2. One can see a quite sharpsuperconducting transition at T c with a slight decreaseof T c with increasing Co volume fraction v and a largeshift of T c caused by the external magnetic field. Here wedo not show the as-prepared pure Pb sample because thedifference of T c between the as-prepared and annealedpure Pb film (see below) is very small (about 0.1 K).Annealing the samples at 300 K has a drastic effect onthe normal state resistivity ( ρ N ) and the superconduct-ing transition[see Fig. 3 (a)-(d)]. ρ N drops by a factorof ∼
5. The reason for the large change in ρ N is the fol-lowing: as-prepared samples, deposited at ∼
40 K, willcontain a large number of lattice defects, i.e. the Pb ma-trix will be in a highly disordered state. The electronmean free path, estimated from ρ N within the free elec-tron model, is ∼ l by a factor of ∼
5, i.e.to l ∼ ∼ c and fi-nally drops to zero resistivity ∼ . It has been interpreted as a Pure Pb (a)(d) sample3
T (K) (c) ( m ) sample 2 (b) sample 1 FIG. 3: Resistivity as a function of temperature for differ-ent samples annealed at 300 K in different external magneticfields. (a) pure lead, (b) with 2 . vol % Co, (c) with 3 . vol %Co and (d) with 3 . vol % Co. second-order phase transition in the spontaneous vortexphase from a vortex solid to a vortex liquid state. We willnot focus on this point in the present paper but ratherconcentrate on the superconducting transition into thenormal state occurring at T c . T c ( K ) v (vol% Co) as-prepared after annealing from magnetic measurements after annealing H ext = 0 FIG. 4: Critical temperatures, T c , as a function of Co volumefraction with zero external magnetic field. We have plotted in Fig. 4 the dependence of T c fromthe Co volume fraction v for the three samples and thereference point (pure Pb). An additional T c -point result-ing from magnetic measurements on a sample containing ∼ c -data are consistent with a linear de-pendence of T c with v. The straight lines drawn in Fig. 4 have a slope of dT c /dv = - 0.43 K/vol% Co for theas-prepared sample and dT c /dv = - 0.85 K/vol% Co forthe sample annealed at 300 K. The critical concentra-tion for the disappearance of superconductivity is ∼ ∼ ∼
70 vol% Cu has been found . The T c -reduction forgranular SC systems with non-magnetic particles is duethe proximity effect only, in the case of magnetic par-ticles, however, an additional much stronger reductionoccurs due to the formation of the above mentioned spon-taneous vortices. The radius of these vortices is given bythe superconducting coherence length ξ . For disorderedsuperconductors, having a small electron mean free path l , the coherence length is given within the dirty limit tobe ξ ∝ l / or ∝ ρ N − / . The change in ρ N going fromthe as-prepared to the annealed samples is 5.3 ± ξ should increase by afactor of 2.3 ± c /dv go-ing from the as-prepared to the annealed samples is ∼ c /dv scales with the coherencelength or with the diameter of the spontaneous vortices. as-prepared annealed B c ( T ) sample 1(a)(b) sample 2 as-prepared annealed B c ( T ) (c) sample 3 B c ( T ) T (K) as-prepared annealed
FIG. 5: The on-set T c as a function of external magnetic fieldfor the as-prepared and annealed samples with different Co vol %. Next we will discuss the T c -reduction due to the ap-plied external magnetic field. We have plotted in Fig.5 the critical magnetic field B c as a function of T forall three samples in the as-prepared as well as in the an-nealed state as obtained from Fig. 2 and 3. All B(T)curves show a curvature near T c (B=0) which is not ex-pected for a dirty superconductor. According to the workby Werthamer, Helfand and Hohenberg (so-called WHH-theory) there should be a linear dependence of B c (T)with T near T c with a slope given by( dB c /dT ) T = T c = ( − ek B /π ) N ( E F ) ρ N (1)where N(E F ) is the density of states near the Fermienergy. We have drawn straight lines through the datapoints in Fig. 5 neglecting those for small external fieldsfor obtaining (dB c /dT)-values for all samples in theas-prepared as well as in the annealed state. The ratio[(dB c /dT) as − prepared / (dB c /dT) annealed ] for all threesamples is 4.2 ± ρ N ) as − prepared /( ρ N ) annealed = 5.3 ± c /dT) due to annealingis somewhat smaller than that in ρ N , but essentially inagreement with WHH-theory. Now we have to discusswhy for small external magnetic fields the measured T c -values are smaller than expected from the extrapolatedstraight lines in Fig. 5. Without external magnetic fieldthe spontaneous vortices will form some kind of randomnetwork due to the random orientation of the Co particlemagnetic moments. Applying an external magneticfield above T c will align the magnetic moments [seehysteresis in Fig. 1 (b)] and, therefore, will also alignthe spontaneous vortices. For external fields of the orderof 0.2 T the alignment of the magnetic moments willbe almost saturated and with external fields above thisvalue the deviations of the measured data points fromthe extrapolated straight lines essentially disappear.The interpretation of our T c -data for small externalmagnetic fields, therefore, is as follows: at small externalmagnetic fields the spontaneous vortex state developsfrom a random network to an aligned vortex state whichsomehow compensates the decrease of T c due to theexternal magnetic field; when all magnetic moments of the Co particles are aligned, the spontaneous vortexstate is aligned and when the external magnetic fieldis further increased, B c (T) will follow the WHH-curve,i.e. will show a linear increase of B c (T) with decreasingT. The difference in T c between the measured T c (B=0)values, i.e. the values for a random network of sponta-neous vortices, and the extrapolated values for alignedspontaneous vortices is much larger for the annealedsamples than for the as-prepared samples (see Fig.5), i.e.this difference is increasing with increasing coherencelength or vortex diameter. IV. CONCLUSION
We have shown that the effect of both Co volume frac-tion as well of external magnetic field strongly depends ifthe samples are studied in the as-prepared (at low tem-perature) or in the annealed state. The reason for this isthat the annealing strongly changes the electron meanfree path and, as a consequence, the superconductingcoherence length, which determines the diameter of thespontaneous vortices created by the magnetic momentsof the Co particles. The reduction of T c due to Co parti-cles is much larger than that observed for non-magneticparticles in superconducting films, indicating that the in-fluence of these spontaneous vortices on T c is much largerthan the proximity effect. The T c -reduction due to thesespontaneous vortices seems to scale with the supercon-ducting coherence length or diameter of these vortices.It would be interesting to see if theoretical calculationsregarding the random network of spontaneous vorticescould confirm our experimental result.This work was partially supported by CAPES/DAADcooperation program and the Brazilian agencies CNPq,FAPERJ (Cientistas do Nosso Estado and PRONEX).H. Micklitz acknowledges FAPERJ for financial support. A. I. Buzdin, Rev. Mod. Phys. , 935 (2005). M. Lange, M. J. V. Bael, Y. Bruynseraede, and V. V.Moshchalkov, Phys. Rev. Lett. , 197006 (2003). J. I. Mart´ın, M. V´elez, J. Nogu´es, and I. K. Schuller, Phys.Rev. Lett. , 1929 (1997). L. N. Bulaevskii, E. M. Chudnovsky, and M. P. Maley,Appl. Phys. Lett. , 2594 (2000). L. R. Tagirov, Phys. Rev. Lett. , 2058 (1999). J. E. Villegas, M. I. Montero, C.-P. Li, and I. K. Schuller,Phys. Rev. Lett. , 027002 (pages 4) (2006). R. Laiho, E. L¨ahderanta, E. B. Sonin, and K. B. Traito,Phys. Rev. B , 144522 (2003). Z. Yang, M. Lange, A. Volodin, R. Szymczak, and V. V.Moshchalkov, Nat. Mater. , 793 (2004). A. Palau, H. Parvaneh, N. A. Stelmashenko, H. Wang, J. L.Macmanus-Driscoll, and M. G. Blamire, Phys. Rev. Lett. , 117003 (2007). C. Monton, F. de la Cruz, and J. Guimpel, Physical Review B (Condensed Matter and Materials Physics) , 064508(2007). M. Lange, M. J. V. Bael, A. V. Silhanek, and V. V.Moshchalkov, Phys. Rev. B , 052507 (2005). M. J. Van Bael, K. Temst, V. V. Moshchalkov, andY. Bruynseraede, Phys. Rev. B , 14674 (1999). Y. T. Xing, H. Micklitz, T. G. Rappoport, I. G. Sol´orzano-Naranjo, and E. Baggio-Saitovitch, Phys. Rev. B ,224524 (2008). S. Rubin, M. Holdenried, and H. Micklitz, Eur. Phys. J. B , 23 (1998). I. Sternfeld, V. Shelukhin, A. Tsukernik, M. Karpovski,A. Gerber, and A. Palevski, Phys. Rev. B , 064515(2005). N. R. Werthamer, E. Helfand, and P. C. Hohenberg, Phys.Rev.147