Vortex order–disorder transition in relaxation and field-sweep measurements B. Kalisky a, * , A. Shaulov a , D. Bhattacharya a,1 , T. Tamegai b , Y. Yeshurun a a Department of Physics, Institute of Superconductivity, Bar-Ilan University, Ramat-Gan 52900, Israel b Department of Applied Physics, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan Abstract Time evolution of the induction profile across a Bi 2 Sr 2 CaCu 2 O 8þd crystal was magneto-optically recorded in two experiments: during ramping the external magnetic field or after a sudden application of the field. The results of these experiments reveal a front-like propagation or retreat of a transient disordered vortex state, respectively. Analysis of the front velocity shows that while the retreat is continuously decelerated, the propagation is accelerated, approaching a constant velocity when the front induction reaches the vortex order–disorder phase transition field B od . The latter observation suggests a method for determining the value of B od , eliminating transient state effects. Ó 2004 Elsevier B.V. All rights reserved. Keywords: Vortex phase transitions; Transient vortex state; Annealing time Recent studies of the vortex order–disorder phase transition in Bi 2 Sr 2 CaCu 2 O 8þd (BSCCO) showed that proper characterization of this transition must take into account effects of transient disordered vortex states [1–4]. In this paper we show how these transient states manifest themselves in two commonly used magnetic measurement techniques––field sweep at a certain rate and relaxation over a certain time period after abrupt application of a field (rise time < 50 ms). Measurements were carried out on a 1.55 · 1.25 · 0.05 mm 3 BSCCO single crystal (T c ¼ 92 K), using a magneto-optical (MO) imaging system coupled to a 40- ms/frame CCD camera. The MO images were generated using an iron-garnet indicator with in-plane anisotropy. Magneto-optical snapshots of the local induction dis- tribution across the sample were taken at T ¼ 21 K, under fields 140–840 G, applied parallel to the crystal c axis. In relaxation measurements, after a sudden applica- tion of the field (rise time < 50 ms), images were collected over a time period of 4 s every 40 ms and over an additional time period of 26 s every 300 ms. In the field sweep experiment, MO images of the induction distri- bution were collected while the external field was ramped at a constant rate of 4–1600 G/s. Fig. 1 illustrates a typical result obtained in a relax- ation experiment with a field step of 480 G. Following the abrupt increase in the external field, a transient disordered vortex state exists throughout the entire sample [1]. Subsequently, the thermodynamically fa- vored quasi-ordered phase nucleates at the center of the sample where the field is minimal, and thus the lifetime of the transient state is shortest. Coexistence of quasi- ordered and transient disordered vortex states is indi- cated by a ‘‘break’’ in the local induction profile, separating between the low j ordered phase near the center and the high j disordered phase near the edge [5]. Growth of the quasi-ordered state, and concurrent re- treat of the transient disordered state, is demonstrated by a movement of the break towards the sample edge, as shown in Fig. 1. The inset to this figure illustrates that as the induction B f at the break approaches the transition field B od , the velocity, v f , of the front drops down. Only * Corresponding author. Tel.: +972-3-531-8607/7325; fax: +972-3-535-3298. E-mail address: ph50@mail.biu.ac.il (B. Kalisky). 1 Permanent address: Electroceramics Division, Central Glass and Ceramic Research Institute, Calcutta 700 032, India. 0921-4534/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2004.02.121 www.elsevier.com/locate/physc Physica C 408–410 (2004) 382–383