Vortex Dynamics at the Transition to the Normal State in YBa 2 Cu 3 O 7-δ Films

Transcription

1 Vrtex Dynamics at the Transitin t the Nrmal State in YBa 2 Cu 3 O 7- Films P.Bernstein a), J.F.Hamet a), M.T.Gnzález b,*) and M.Ruibal Acuña b) a) CRISMAT-ENSICAEN (UMR-CNRS 6508) F14050 Caen cedex 4, France b) LBTS, Departament de Física da Materia Cndensada Universidade de Santiag de Cmpstela E15782, Spain Abstract - We prpse a descriptin f the vrtex dynamics fr YBa 2 Cu 3 O 7- films. Accrding t this descriptin : i) the vrtex mtin is thermally activated alng the twin bundaries f the films; ii) pinning is due t intersectins f twin bundaries and iii) the transitin t the nrmal state is due t vrtex depinning. The predictins f this descriptin are cmpared t data published by Gnzález et al. [Phys.Rev.B68, (2003)]. Manuscript received April 2, 2007; revised May 1, 2007; Reference N.: (ST1) I. VORTEX DYNAMICS IN THE CRITICAL STATE In the physics f YBCO films, the rle f extended planar defects, such as lw angle grain bundaries and twin bundaries (TBs), has been discussed fr a lng time [1,2]. Many authrs have pinted ut that since the width f these planar defects is in the range f ξ ab (T), the supercnducting cherence length in the a-b planes f YBCO, sme type f Jsephsn behavir culd be expected [3, 4]. In this cntributin, we discuss the flux-pinning cntributin f twinning in epitaxially grwn YBCO films (see als Ref.[5] ). Accrding t electrn micrscpy bservatins, the TBs can stretch ver several micrmeters in this type f samples [6]. Different types f measurements suggest that the TBs planes act as grves channeling the vrtices [7,8], but the TBs are highly disrdered at the scale f a few interatmic distances, as revealed by High Reslutin Electrn Micrscpy [9,10]. It is reasnable t suppse that the mdulatin f the TBs width by disrdered areas has a strng effect n their Jsephsn behavir. We suggest that the separatin between the supercnducting banks f the TBs can be lcally large enugh with respect t ξ ab (T) t cause a disruptin f the tunneling current. This results in the splitting f the TBs int rws f Jsephsn weak links with length (see Fig.1). Cnsideratins n the vrtices and TBs energies and the fact that disrdered areas are als certainly included in the weak links alng the TBs suggest that, in the critical state, the weak link energy is equal t k B T. Then, each weak link, whatever its length, carries the same net current that is equal t I J 2πk BT = (1) φ 1

2 where φ is the flux quantum. An experimental verificatin f this predictin is reprted belw. Cnsequently, the critical current takes the frm : I w cr = I J (2) where w is the width f the investigated sample. Anther cnsequence f Eq.(1) is that the amplitude f the vrtex screening current flwing acrss each weak link is als equal t I J, since a current amplitude smaller than I J is in the range f the current thermal fluctuatins [11]. Dissipatin ccurs thrugh thermally activated vrtex mtin alng the TBs. Magnetic susceptibility measurements suggest that vrtex pinning ccurs at the TBs intersectins [12]. Fig.2a represents schematically tw perpendicular vrtex rws in the vicinity f a TB intersectin. The upper vrtex in the vertical rw can mve frward ver distance nly if screening current lines enter bth its cre and the cre f the first vrtex in the hrizntal rw (see Fig.2b). The crrespnding energy barrier takes the frm (Τ 1 ) ξ ab (T 1 ) ξ ab (T 2 ) ξ ab (Τ 2 ) T 1 T 2 Fig.1 : Schematic representatin f a twin bundary sectin at tw different temperatures (T 1 <T 2 ) and sketch f the dependence n temperature f the cherence length, ξ ab. The rectangular peaks represent disrdered areas ( r defects) lying alng the TB that change lcally its width. The tunnneling current is disrupted wherever the effective separatin between the supercnducting banks is much larger than the cherence length. As a result the TBs cnsist f rws f weak links bunded by large disrdered areas (at the atmic scale). The thick dashed lines represent the limits f these weak links. Since at temperature T 1 the cherence length is shrter than at temperature T 2, mre defects r disrdered areas are large enugh t disrupt the supercnducting current at T 1 than at T 2. Cnsequently, the weaks links are shrter at T 1 than at T 2. T 1 T 2 T U = 2 I νφ = 4πνk T (3) J B where νφ is the flux carried by each vrtex, with υ > 1 when the vrtex carries mre than ne flux quantum. 2

3 (a) I J I J Fig.2 : a) Schematic representatin f vrtices lcated alng tw intersecting twin bundaries. The thick lines, the grey areas and the ellipses represent the twin bundaries, the vrtex cres and the screening current lines, respectively; b) the first vrtex in the vertical rw can mve frward ver distance nly if screening currents I J, represented by the dashed arrws, enters bth its cre and the cre f the first vrtex in the hrizntal rw. (b) II. TRANSITION TO THE NORMAL STATE Depinning f an individual vrtex line ccurs if the ttal frce acting n the vrtex is equal t the maximum value f the pinning energy gradient [13]. Accrding t Brandt, [14,15] the pinning energy is an elastic energy. Then, the maximum intensity f frce F r can be written as U F = J creνφd = 2 (4). In Eq.(4), J cre is the current density carried by the vrtex cre when depinning ccurs. Frm Eqs.(1-4), we have J = 4 J and I = 4I (5) cre cr cre since current I J flws acrss the weak links in the critical state. J F r 3

4 Let s cnsider a sketch f the vrtices lying in the vicinity f the annihilatin line alng a TB. In the critical state (Fig.3a) and in absence f any external field, the TB is cmpletely penetrated by the vrtices and the antivrtices. The mean distance between the vrtex cres is equal t 2λ and there is n vrtex interactin. When each weak link carries current 3I J, the mean distance between neighbring vrtices is equal t 2λ/3. The ttal screening current flwing acrss the vrtex cres is equal t zer, except acrss the cres f the vrtices lcated at ±λ/3 that carry a screening current equal t 2I J due t their next neighbrs (see Fig.3c). Hwever, due t its first and secnd neighbring vrtices, the weak link lcated n the annihilatin line carries a ttal screening current that is equal t 4I J, the depinning value. As the current ges n increasing, mre weak links carry current 4I J and we expect a sudden vrtex depinning when current 4I J flws acrss the cres f the vrtices neighbring the TBs intersectins in the vicinity f the annihilatin line. It is reasnable t assume that this brutal depinning prcess ignites a thermal runaway and the transitin t the nrmal state. III. COMPARISON TO EXPERIMENTAL RESULTS a -5λ -3λ -λ λ 3λ 5λ 2I b 2I -λ/2 λ/2 c 2I J 4I λ/3 λ/3 Fig.3 : Schematic representatin f the vrtices and antivrtices lying alng a twin bundary in the vicinity f the annihilatin line : (a) each weak link carries current I J (critical state); (b) each weak link carries current 2I J ; (c) each weak link carries current 3I J. The ellipses represent screening current lines and the grey areas in the ellipses represent the vrtex 4 cres. The thick hrizntal lines and the vertical line represent the twin bundary and the annihilatin line, respectively. Only the screening currents flwing acrss the weak links lcated n the annihilatin line and at the vrtex cres are shwn (full arrws).

5 The wrk carried ut by the frce due t the transprt current acting n a vrtex line that mves ver distance takes the frm W = Jνφd. Accrding t the Kim-Andersn mdel, in the flux creep regime we have U k T W Vα e B sinh (6) k BT where V is the vltage at the terminals f the sample. Then, the length can be determined frm the current-vltage curves. The inset in Fig.4 shws the values fr tw films respectively 190nm and 150nm thick measured by Gnzàlez et al. [16 ]. As expected, (see Fig.1) the values increase as the temperature increases. At a given temperature, an estimatin f I wl, the current flwing acrss the weak links in the critical state, can be btained with Eq.(2) frm the experimental values f I cr and. The main part f Fig.4 shws the values calculated fr bth samples. Except near T c, the experimental I wl values are in the range f 2πk BT I J =, as predicted by the mdel. Fig.5 shws J*(T), the current density at the φ transitin t the nrmal state measured by Gnzàlez et al. n bth samples, as well as the w values calculated suppsing that the current at the transitin takes the frm I* = 3I J. There is a very gd agreement between calculated and measured values in the whle range 4x10-6 3x10-6 I wl (A) 2x10-6 1x (m) T(K) T(K) Fig.4: Current I wl = J cr d carried in the critical state by each weak link f the 190nm (circles) and the 150nm (squares) thick films measured by Gnzàlez et al., as a functin f the temperature. The slid line shws the 2πk predicted values BT I wl = (Eq.1). The inset shws the values. φ f the measurements, althugh J* is different frm 3J cr near T c [17]. 5

6 10 7 J (A/cm 2 ) d=190nm J* experimental J* calculated 3xJ cr Fig.5: Experimental and calculated current densities at the transitin t the nrmal state fr the 190nm and the 150nm films measured by Gnzález et al. The experimental and calculated values are very near 3J cr except near T c J (A/cm 2 ) 10 5 d=150nm J* experimental J* calculated 3xJ c T(K) IV. SUMMARY We have prpsed a descriptin accunting fr the behavir f twinned YBCO films in the critical state and at the transitin t the nrmal state. Accrding t this mdel, the vrtices are in mtin alng the TBs that, due t disrder, behave as rws f weak links. Vrtex pinning ccurs at the TBs intersectins. All the weak links carry the same current I J (T) in the critical state. The transitin t the nrmal state ccurs when each weak link carries current 3I J. It is triggered by vrtex depinning at the TBs intersectins neighbring the annihilatin line. The mdel predictins are in gd agreement with the data measured by Gnzàlez et al.[16]. 6

7 References and Ntes [1] G.Deutscher and K.A.Müller, Phys. Rev. Lett., vl.59, pp , [2] G. Deutscher, IBM J. Res. Dev., vl.33, pp , [3] A.Gurevitch and L.D.Cley, Phys. Rev.B, vl.50, pp , [4] E. Mezzetti, R. Gerbald, G. Ghig, L. Gzzelin, B. Minetti, C. Camerling, A.Mnac, G. Cuttne, and A. Rvelli, Phys. Rev. B, vl.60, pp , [5] P.Bernstein and J.F.Hamet, J.Appl.Phys., vl.95, pp , [6] J.-L. Maurice, O. Durand, M. Druet and J.-P. Cntur, Thin Slid Films, vl.319, pp , [7] M.Oussena, P.A.J.de Grt, S.J.Prter, R.Gagnn and L.Taillefer Phys. Rev. B, vl. 51, pp , [8] H. Pastriza, S. Candia, and G. Nieva, Phys.Rev.Lett.,vl.83, pp , [9] Y.Zhu, M.Suenaga, J.Taft and D.O.Welch, Phys.Rev.B, vl.44, pp ,1991. [10] C.Gupil, F.Warmnt, M.Hervieu, J.F.Hamet and Ch.Simn, Phys.Rev.B, vl.60, pp , [11] Since in the critical state the ttal current carried by a weak link is als equal t I J, the transprt current is equal t zer acrss the weak links carrying the screening current f an islated vrtex if screening and transprt currents have the same directin. It is equal t 2I J acrss the weak links where they flw in ppsite directins. [12] S.Berger, D-G.Crété, J-P.Cntur, K.Buzehuane and J.L.Maurice, Phys.Rev.B vl.63, pp , [13] Ch.Gupil, T.Auarun, D.Thpart, J.F.Hamet and Ch.Simn, Phys.Rev.B, vl.54, pp , [14] E.H.Brandt, Phys.Rev.Lett. vl. 69, pp , [15] E.H.Brandt, Z.Phys.B, vl. 80, pp , [16] M.T.Gnzález, J.Viña, S.R.Currás, J.A.Veira, J.Maza and F.Vidal, Phys.Rev.B, vl.68, pp , [17]The reasns that J 3Jcr in the vicinity f T c are detailed in : P. Bernstein et al., Physica C (2007), di: /j.physc (in press) 7