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Two-stage melting of disordered vortex-line lattice in Bi2Sr2CaCu2O8+δ
Physica B 284}288 (2000) 803}804
Two-stage melting of disordered vortex-line lattice in Bi Sr CaCu O >B
Ryoko Sugano *, Toshiyuki Onogi , Kazuto Hirata, Masashi Tachiki Advanced Research Laboratory, Hitachi, Ltd., Hatoyama, Saitama 350-0395, Japan National Research Institute for Metals, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan
Abstract We study vortex matter phase diagram of Bi Sr CaCu O , by using Monte Carlo simulation based on Law >B rence}Doniach model. Introducing strong point-like disorder, we "nd two successive phase transformations from the strongly pinned vortex glass to pancake vortex gas via an intermediate weakly pinned glass, when temperature is increased. The "rst one is identi"ed as an intra-layer depinning transition as pre-melting, which subdivides the glass phase into two phases. The intermediate glass melts with inter-layer decoupling of vortex lines, implying the loss of interlayer long-range coherence. These two-phase boundaries agree with recent experimental data. 2000 Published by Elsevier Science B.V. All rights reserved. Keywords: Bragg glass; Flux lines; Bi-2212; Strong point disorder
Recent study of the vortex penetration for Bi Sr CaCu O (BSCCO) crystals through the sur >B face barrier revealed the existence of a phase-separating line well below the melting line [1]. This line may be related with depinning from the point disorder associated with the oxygen defects. In this paper, we study the e!ects of strong point-like disorder on the vortex phase diagram, based on the Lawrence}Doniach model. We have performed the Monte Carlo simulation with N vortex lines penetrating T through N layers in the presence of point pins at "nite X temperature ¹, as in Ref. [2]. Pancake vortex coordinates +r (z), form the ith vortex line (i"1,2,2, N ). The G T in-plane inter-vortex interaction is given by a modi"ed Bessel function e dK ("r "/j ) with the magnetic pen GH ?@ etration depth j (¹)"j (0)(1!(¹/¹ ). We choose ?@ ?@ j (0)"2000 As , the coherence length m (0)"10 As , ?@ ?@ layer thickness d"10 As , and the e!ective mass anisotropy c"(M /M "100. We also set N "16 and ?@ T N "40, where periodic unit cells with image potentials X are used on each layer. The point pin is modeled [3,4] by the cylindrical potential well with a radius c "m (0) ?@
* Corresponding author.
and depth ; (¹)"(e d/2)ln[1#(c /(2m (¹))]. We ?@ used four random pin con"gurations for the sample average with the density of pins by 7;10/cm. Fig. 1 shows the ¹-dependent behavior of the in-plane vortex #uctuation *r "1"r !r "2 /a (a " VW G X G X G X (U /B) for various "elds B. *r sharply bend and cross VW each other at ¹ K30 K for the whole "eld range. This suggests that vortices are easy to wander above ¹ , implying depinning, whereas almost all vortices are frozen below ¹ . Around this depinning temperature ¹ , *r takes a much smaller value of under 0.03 for all VW "elds than the Lindemann melting criteria. This suggests the occurrence of a depinning transition before the melting transition. The Bragg peak G becomes unstable above ¹ . Fig. 2 shows the ¹-dependence of G and the speci"c heat C . In contrast to a constant behavior ¹(¹ , T with increasing ¹, G grows rapidly, above ¹ . Then it suddenly drops and almost vanishes at ¹ (¹ . At %
a melting temperature ¹ , C has a peak as a function
T of ¹. Error bars of G also grow above ¹ (¹ .
Above ¹ , c-axis vortex #uctuation *r "1"r !
XX G X 1r 2 "2 /a exhibits a rapid growth in the ¹-dependG X X G X ence, implying the loss of the c-axis coherence. Bragg glass below ¹ in the low-"eld regime is transformed into weakly pinned (soft) glass at ¹ , then melts to %
0921-4526/00/$ - see front matter 2000 Published by Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 2 1 0 3 - 1
804
R. Sugano et al. / Physica B 284}288 (2000) 803}804
Fig. 1. ¹-dependence of *r for the VW B"125,200,250,320,400,640,800,1000,1600,2500 G.
"eld Fig. 3. Calculated vortex phase diagram. ¹ ; solid circle, ¹ ;
open circle, ¹ ; open triangle, B ; open rectangle. % %
Fig. 3 is a calculated vortex phase diagram. An almost vertical depinning line ¹ divides the vortex solid phase into two phases, strongly pinned glass and soft glass, at higher "eld. At lower "eld, with increasing ¹, the Bragg glass depins at ¹ , and melts into the liquid phase at ¹ ,
via the soft glass phase above ¹ . % Fig. 2. Temperature dependence of G and C at 500 G. T
decoupled liquid at ¹ . On the other hand, with increas ing B, G decreases and vanishes at B (¹). When % ¹(¹ , B (¹) seems almost independent of ¹. B % dependence of *r shows a kink-like anomaly near B , XX % suggesting a reduction of c-axis coherence. This B (¹) % line may correspond to the 2D}3D crossover "eld observed in BSCCO single crystals [5]. Above B and % below ¹ , a strongly pinned glass phase may appear, distinguished from the low-"eld Bragg glass and from the soft glass phase in the intermediate temperature regime. In the soft glass phase, even the small applied currents may cause the vortex #ow and the induced voltage.
Acknowledgement This work was supported by Joint Research Promotion System on Computational Science and Technology (Science and Technology Agency, Japan).
References [1] [2] [3] [4] [5]
D.T. Fuchs et al., Phys. Rev. Lett. 80 (1998) 4971. R. Sugano et al., Phys. Rev. Lett. 80 (1998) 2925. D.R. Nelson, V.M. Vinokur, Phys. Rev. Lett. 68 (1992) 2398. D.R. Nelson, V.M. Vinokur, Phys. Rev. B 48 (1993) 13 060. T. Tamegai et al., Physica C 213 (1993) 33.
Two-stage melting of disordered vortex-line lattice in Bi Sr CaCu O >B
Ryoko Sugano *, Toshiyuki Onogi , Kazuto Hirata, Masashi Tachiki Advanced Research Laboratory, Hitachi, Ltd., Hatoyama, Saitama 350-0395, Japan National Research Institute for Metals, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan
Abstract We study vortex matter phase diagram of Bi Sr CaCu O , by using Monte Carlo simulation based on Law >B rence}Doniach model. Introducing strong point-like disorder, we "nd two successive phase transformations from the strongly pinned vortex glass to pancake vortex gas via an intermediate weakly pinned glass, when temperature is increased. The "rst one is identi"ed as an intra-layer depinning transition as pre-melting, which subdivides the glass phase into two phases. The intermediate glass melts with inter-layer decoupling of vortex lines, implying the loss of interlayer long-range coherence. These two-phase boundaries agree with recent experimental data. 2000 Published by Elsevier Science B.V. All rights reserved. Keywords: Bragg glass; Flux lines; Bi-2212; Strong point disorder
Recent study of the vortex penetration for Bi Sr CaCu O (BSCCO) crystals through the sur >B face barrier revealed the existence of a phase-separating line well below the melting line [1]. This line may be related with depinning from the point disorder associated with the oxygen defects. In this paper, we study the e!ects of strong point-like disorder on the vortex phase diagram, based on the Lawrence}Doniach model. We have performed the Monte Carlo simulation with N vortex lines penetrating T through N layers in the presence of point pins at "nite X temperature ¹, as in Ref. [2]. Pancake vortex coordinates +r (z), form the ith vortex line (i"1,2,2, N ). The G T in-plane inter-vortex interaction is given by a modi"ed Bessel function e dK ("r "/j ) with the magnetic pen GH ?@ etration depth j (¹)"j (0)(1!(¹/¹ ). We choose ?@ ?@ j (0)"2000 As , the coherence length m (0)"10 As , ?@ ?@ layer thickness d"10 As , and the e!ective mass anisotropy c"(M /M "100. We also set N "16 and ?@ T N "40, where periodic unit cells with image potentials X are used on each layer. The point pin is modeled [3,4] by the cylindrical potential well with a radius c "m (0) ?@
* Corresponding author.
and depth ; (¹)"(e d/2)ln[1#(c /(2m (¹))]. We ?@ used four random pin con"gurations for the sample average with the density of pins by 7;10/cm. Fig. 1 shows the ¹-dependent behavior of the in-plane vortex #uctuation *r "1"r !r "2 /a (a " VW G X G X G X (U /B) for various "elds B. *r sharply bend and cross VW each other at ¹ K30 K for the whole "eld range. This suggests that vortices are easy to wander above ¹ , implying depinning, whereas almost all vortices are frozen below ¹ . Around this depinning temperature ¹ , *r takes a much smaller value of under 0.03 for all VW "elds than the Lindemann melting criteria. This suggests the occurrence of a depinning transition before the melting transition. The Bragg peak G becomes unstable above ¹ . Fig. 2 shows the ¹-dependence of G and the speci"c heat C . In contrast to a constant behavior ¹(¹ , T with increasing ¹, G grows rapidly, above ¹ . Then it suddenly drops and almost vanishes at ¹ (¹ . At %
a melting temperature ¹ , C has a peak as a function
T of ¹. Error bars of G also grow above ¹ (¹ .
Above ¹ , c-axis vortex #uctuation *r "1"r !
XX G X 1r 2 "2 /a exhibits a rapid growth in the ¹-dependG X X G X ence, implying the loss of the c-axis coherence. Bragg glass below ¹ in the low-"eld regime is transformed into weakly pinned (soft) glass at ¹ , then melts to %
0921-4526/00/$ - see front matter 2000 Published by Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 2 1 0 3 - 1
804
R. Sugano et al. / Physica B 284}288 (2000) 803}804
Fig. 1. ¹-dependence of *r for the VW B"125,200,250,320,400,640,800,1000,1600,2500 G.
"eld Fig. 3. Calculated vortex phase diagram. ¹ ; solid circle, ¹ ;
open circle, ¹ ; open triangle, B ; open rectangle. % %
Fig. 3 is a calculated vortex phase diagram. An almost vertical depinning line ¹ divides the vortex solid phase into two phases, strongly pinned glass and soft glass, at higher "eld. At lower "eld, with increasing ¹, the Bragg glass depins at ¹ , and melts into the liquid phase at ¹ ,
via the soft glass phase above ¹ . % Fig. 2. Temperature dependence of G and C at 500 G. T
decoupled liquid at ¹ . On the other hand, with increas ing B, G decreases and vanishes at B (¹). When % ¹(¹ , B (¹) seems almost independent of ¹. B % dependence of *r shows a kink-like anomaly near B , XX % suggesting a reduction of c-axis coherence. This B (¹) % line may correspond to the 2D}3D crossover "eld observed in BSCCO single crystals [5]. Above B and % below ¹ , a strongly pinned glass phase may appear, distinguished from the low-"eld Bragg glass and from the soft glass phase in the intermediate temperature regime. In the soft glass phase, even the small applied currents may cause the vortex #ow and the induced voltage.
Acknowledgement This work was supported by Joint Research Promotion System on Computational Science and Technology (Science and Technology Agency, Japan).
References [1] [2] [3] [4] [5]
D.T. Fuchs et al., Phys. Rev. Lett. 80 (1998) 4971. R. Sugano et al., Phys. Rev. Lett. 80 (1998) 2925. D.R. Nelson, V.M. Vinokur, Phys. Rev. Lett. 68 (1992) 2398. D.R. Nelson, V.M. Vinokur, Phys. Rev. B 48 (1993) 13 060. T. Tamegai et al., Physica C 213 (1993) 33.