Annealing of the torn vortex lattice in YBCO crystals

Annealing of the torn vortex lattice in YBCO crystals Laboratorio de Bajas Temperaturas, Depto. de Física, FCEyN, Universidad de Buenos Aires, Argentina. Partially supported by: Fundación Sauberán, UBACyT X200 Victoria Bekeris Gabriela Pasquini Group Members: VictoriaI. Bekeris Carlos E. Acha Gabriela Pasquini Hernán J. Ferrari Graduate Students Alejandro J. Moreno Guillermo A. Jorge Miguel Monteverde Gastón Garbarino Undergraduate Students Claudio E. Chiliotte Victor Bettachini

Key results: Oscillatory dynamics organizes different robust vortex lattice configurations (VLC) in YBCO crystals Scenario Annihilation or creation of VL defects (e.g.dislocations) play a major role in bulk VL response

Key results: Repeated symmetrical shaking - small vortex excursions - heals the VL (annihilation of defects) The lattice attainsHIGHER MOBILITY LOWER PINNING POTENTIAL CURVATURE Temporarily asymmetrical shaking or large vortex excursions tears the VL (creation of defects) The lattice attainsLOWER MOBILITY HIGHER PINNING POTENTIAL CURVATURE

’+ j ’’ (non-linear regime)mobility • High |’| or low ’’ high effective Jc, low mobility - Rac (Campbell regime) effective pinning potential well High |’| low real λac, high curvature of effective pinning wells L Procedure : acsusceptibility measurements probe the VLC - Experimental resultscomparedwithMD calculations

Measuring procedure Initial state “Shaking” magnetic field “Probe” ac field Hdc ~ 3 kOe >> Hac ~ 10 Oe > 10-2Oe < Hac < 1 Oe Hdc ac susceptibility measurement to probe the order of the VL t, N YBa2Cu3O7single crystals I.V. Alexandrov et al. JETP Lett. 48, 493 (1988)

Experimental results in twinned YBa2Cu3O7 single crystals Twinned YBa2Cu3O7 ( 0.56 x 0.6 x 0.02 mm3 ) Tc= 92 K , T= 0.3 K ( 10%-90%) Hac // ĉ ,. Hdc = 3 kOe,  =20 avoiding Bose transition. YBa2Cu3O7 single crystals I.V. Alexandrov et al. JETP Lett. 48, 493 (1988)

Hdc = 2 kOe 87 89 91 T (K) Non-linear and Linear c ac = c´+ i c´´ Linear Hdc = 0 hac= 0.04 Oe Hdc = 2.2 kOe hac= 0.04 Oe Non – linear Peak Effect Hdc = 2.2 kOe hac= 3.4 Oe No clear evidence of PE in linear regime

Non- linear response mobility Hdc = 3 kOe Hdc = 3 kOe Symmetric wave form Asymmetric wave form Sinusoidal, Triangular, Square Sawtooth, with variable asymmetry S.O.V. et al PRL. 86, 504 (2001); PRB. 65 134513(2002).

to increase mobility to order the VL to decrease mobility to disorder the VL Molecular Dynamics Simulations S. O. ValenzuelaPhys. Rev. Lett. 88, 247003 (2002)

Connection between attained mobility and effective pinning potential wells?

In Campbell regime: - du/dt - L u + J x o+FT(t) =0 u: vortex displacement, J: current density, FT(t): thermal force : viscosity, L : Labusch constant curvature effective wells 2c = B 0 / 4  L

Linear c ac = c´+ i c´´ • In a general case: l ac = l R + il I • In Campbell regime it is real, e = l I / l R <<1 (e  0.07) l ac2 =l L2 + B0/ 4  L L = Labusch parameter curvature pinning wells • ac + sample geometry determines l ac E. H. Brandt, Phys.Rev.B 50, 13833 (1994); ibid 49 9024 (1994); ibid 50 4034 (1994). • C. J. van der Beek et al., Phys. Rev. B 48, 3393 (1993) Campbell

D =( Rd/2)1/2 2 R d Normalized real penetration depth, l R / D, for Sy and Asy VLC´s G. Pasquini and V. Bekeris, PRB in press

Annealed (Sy) and torn (Asy) vortex lattice in a warming-cooling process Sy : Reversible T cycle Asy : Irreversible T cycle • Slow ~ 2 hrs. cycle • Tini ~ 87.3 K • T  1.3 K • Meas freq: 30 kHz

Annealed (Sy) and torn (Asy) vortex lattice in a warming-cooling process Sy : Reversible T cycle Asy : Irreversible T cycle • No further disordering as • the PE temperature is reached •  relaxation mechanisms • for  VLC • Same W-C curves (not shown) for ASY at T below onset PE are reversible

Conclusions • Oscillatory dynamics organizes the VL in YBCO crystals in different configurations (VLC) characterized by their mobility and effective pinning potentials wells. • Molecular dynamics relates high (low) mobility with low (high) density of defects (e.g. dislocations). • The system relaxes by thermal activation to more favorable VLC either from “over” ordered or from “over” disordered configurations, probably involving different mechanisms (e.g. elastic, plastic relaxation). • There is no trivial relationship between VL mobility and pinning potential curvature, particularly near the PE region.

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Related researches (incomplete list): U.Yaron et al. PRL 73 2748 (1994). S.N Gordeev et al., Nature 385, 324 (1997). G. Ravikumar et al., PRB 57, R11069 (1998). W. Henderson et al., PRL 81, 2352 (1998). Z.L. Xiao et al., PRL 83, 1664 (1999). S.S Banerjee et al., PRB 59, 6043 (1999). Y. Paltiel et al., Nature 403, 398 (2000). X. Ling et al. PRL 86, 712 (2001). P. Chaddah, PRB 62, 5361 (2000). D. Stamopoulos et al. PRB 66 214521 (2002) M. Chandran cond-mat/0407309. ................

- du/dt - L u + J x o+ FT(t) =0 : viscosity, L : Labusch constant u: vortex displacement, J: current density, FT(t): thermal force ac2= L2 + 0 B / (4  L) = L2 + C2 1 +  = 1+ ´ + j ´´ =∑cn / (n +  )  = R  / 2 ac2

Acknowledgements Paco de la Cruz Yanina Fasano Mariela Menghini Carlos Balseiro Daniel Domínguez Eva Andrei Marcelo Rozenberg Pablo Tamborenea Gustavo Lozano Liliana Arrachea Jorge Kurchan Leticia Cugiliangolo

Annealing of the torn vortex lattice in YBCO crystals