Direct Observation of Superheating and Supercooling of Vortex Matter
X.S. Ling, S.R. Park, and B.A. McClain, Department of Physics, Brown University
S.-M. Choi, NCNR/CHRNS and University of Maryland
D.C. Dender and J.W. Lynn, NCNR
A current question of fundamental interest concerns whether a vortex solid-liquid transition exists in type-II superconductors. The peak effect, where the critical current exhibits a peak rather than decreasing monotonically with increasing temperature, has been found to occur at the same temperature as a magnetization jump, which suggests a melting of the vortex lattice. However, there has been no direct structural evidence indicating whether there is indeed an underlying phase transition, and if so, whether it is solid-to-solid, solid-to-liquid, or even liquid-to-liquid in origin.
To investigate these issues, SANS measurements combined with simultaneous magnetic susceptibility measurements  have been performed in the peak effect regime in a Nb single crystal. Metastable supercooled vortex liquid and superheated vortex solid phases have been observed, providing direct structural evidence for a first-order vortex solid-liquid transition associated with the peak effect.
The peak-effect regime for the Nb crystal was determined in situ by measuring the characteristic dip in the temperature dependence of the real-part of the ac magnetic susceptibility , as shown in Fig. 1(a) for H = 3.75 kOe . The pronounced diamagnetic dip in (T) of the ac susceptibility corresponds to a strong peak effect in the critical current.
Figure 1. Peak effect and (H-T) phase diagram of Nb. a) ac magnetic susceptibility for Hdc = 3.75 kOe (field-cooled). Hac = 3.3 Oe and 1 kHz. Inset: global H-T phase diagram for the Nb crystal used in this study. (b) Expanded view of the H-T phase diagram (shaded box in a). Two observed SANS images of the field-cooled vortex states are shown.
For each (T,H), SANS patterns were measured for different thermal histories. At sufficiently low temperatures the SANS images show sharp Bragg peaks with six-fold symmetry, independently of the thermal history. An example is shown in the inset of Fig. 1(b) for H = 3.75 kOe and T = 3.50 K. However, the vortex pattern starts to show striking history dependence as the peak-effect regime is approached. For example, if the crystal is cooled in an applied magnetic field (FC, field-cooled), the vortex patterns show nearly isotropic rings in the peak-effect regime (right inset in Fig. 1(b)). In contrast, if the crystal is field-cooled to a low temperature (~ 2 K) and then warmed back up, sharp Bragg spots are observed for all temperatures up to the superconduction transition temperature Tc2 indicated in Fig. 1. Shown in the top panel of Fig. 2 are the ZFC and FC images at (3.75 kOe, 4.40 K), which is just below To(3.75 kOe)= 4.50 K. The images in the mid panel are for (4.00 kOe, 4.40 K), which is 0.10 K above Tp(4.0 kOe)= 4.30 K. The intensities at the radial maximum for the mid panel SANS data are plotted in the lower panel. The sharp Bragg spots for the ZFC state indicate a vortex lattice with long-range-order (LRO), while the very broad spots for the FC state signify a disordered phase with short-range-order.
Figure 2. History-dependent SANS patterns at 4.40 K. The SANS images of the ZFC and FC vortex states for H = 3.75 kOe (top panel: below the onset of the peak effect) and H = 4.00 kOe (mid panel: near the upper end of the peak-effect regime). The thick arrows indicate how the SANS images evolve after applying a small ac magnetic field. The lower panel shows the intensity data at the radial maximum as a function of the azimuthal angle for the ZFC and FC SANS data (H = 4 kOe).
The observed hysteresis suggests a first-order vortex solid-liquid (or glass) transition. A controversial issue is the location of the underlying equilibrium phase transition to the position of the peak effect. One interpretation places the conjectured vortex solid-liquid transition Tm at Tp, consistent with the recent experiments in YBCO. Another widely held view is based on the classical Lindemann criterion which would place Tm at Tc2(H) for Nb, provided the vortex-lattice elastic moduli remain well-behaved. In this scenario, the FC disordered phase seen here (as well as in [2,3]) is a supercooled liquid and the thermodynamic ground state is an ordered solid across the entire peak-effect regime. The third scenario places Tm at or below the onset of the peak effect.
To experimentally determine the ground state and approximate value of Tm, the susceptibility coil was used to shake the vortex assembly, using SANS to observe how the vortex structure evolves. The data show that above Tp the Bragg peaks start to disappear within the first 102 sec of the shaking experiment, demonstrating that the equilibrium state is disordered. Similiarly, the FC disordered states for T < Tp are metastable and the ordered ZFC state is the ground state, opposite to that for T > Tp. In the < Tp regime, though, the metastability is obviously stronger since a much larger ac field is needed to change the metastable state.
The conclusion drawn from these measurements is that for T > Tp the ordered ZFC vortex lattice is a superheated state and the ground state of the vortex system is a disordered vortex liquid, while for T < Tp the ground state is a vortex Bragg solid and the disordered FC state is a supercooled vortex liquid. A thermodynamic phase transition must therefore have taken place, with Tm Tp. These results also imply the absence of superheating in conventional transport experiments with a large drive current, which solves a longstanding puzzle in which the history dependence of the nonlinear resistance always vanishes at Tp(H); only with extremely low drive currents may one then observe the subtle effects of superheating in transport.
This work was recently highlighted in Physical Review Focus, January 19, 2001.
 X.S. Ling, S.R. Park, B.A. McClain, S.-M. Choi, D.C. Dender, J.W. Lynn Phys. Rev. Lett 86, 712 (2001).
 J.W. Lynn, et al., Phys. Rev. Lett. 72, 3413 (1994).
 P.L. Gammel, et al. Phys. Rev. Lett. 80, 833 (1998).