Reentrant Square to Rhombic Vortex Lattice Transition in

Re-entrant Square to Rhombic Vortex Lattice Transition in V 3 Si • D. Mc. K. Paul, S. Crowe, Warwick • M. Yethiraj, D. K. Christen, A. A. Gapud, ORNL • C. Dewhurst, R. Cubitt, ILL • L. Porcar, NIST • A. Gurevich, University of Wisconsin

Non-local case: equal field contours are not circular around the core of the flux line Non-locality: Effects of the finite spatial extent of a Cooper pair ξ (coherence length) Coherence length and Penetration depth diverge as temperature approaches Tc

The lattice symmetry can change as a function of field (and hence distance between vortices)

V 3 Si: Type-II Superconductor • Cubic! No mass anisotropy • Upper Critical Field= 21 Tesla • Lower Critical Field= 0. 05 Tesla • Coherence length 35 Å • Penetration depth 1050 Å • Tc = 16. 4 K • Excellent test system for non-local effects • Long mean free path >300Å => clean sample • No evidence of structure in the superconducting gap

Original Work demonstrated the vortex lattice in V 3 Si was distorted from hexagonal and there was a tendency to become less distorted as the temperature increased. Low temperature distortions are well explained by non-locality effects.

What we were looking for: Changes in morphology as Hc 2 and Tc are approached to test various theories of non-locality, also some clues as to what might be happening in the borocarbides. Start with a square lattice and see if it becomes hex again ?

V 3 Si: B//100 I Tesla Temperature Diffraction Study T = 11 K T = 12. 5 K T = 14 K

Explanation of Diffraction Images based on Domains

First Order Transition in Vortex Lattice Morphology at low temperature and H || 100 The opening angle departs from 60° as the field is increased till the lattice transforms to one with square symmetry. The region of coexistence and lack of any continuous structural evolution suggests a first order transition.

Phase Diagram with B//100 • At low fields, the FLL has • 6 -fold symmetry. As the field is increased the lattice transforms to a square one. As the temperature (hence coherence length) is increased, the square symmetry reverts back to hexagonal. Gurevich and Kogan PRL 87 177009 (2001) - Thermal fluctuations

In Lu. Bi 2 B 2 C, a possible “nose” was also observed - Eskildsen et. al, PRL 86, 5148 (2001

Another non-magnetic borocarbide, YNi 2 B 2 C No evidence for anything but similar effects as seen at low temperature

Summary for Borocarbides • What is ‘clear’ is that the VL in the borocarbides does not appear to be a simple Hexagonal lattice even with weak non-locality. • Need to consider both effects, the underlying anisotropies e. g. Fermi surface and gap anisotropy.

Conclusions • • • We clearly observe the change to a hexagonal lattice close to Tc / Hc 2 At low temperatures, effects well explained by nonlocality Phase transitions near Tc and Hc 2 are explained by inclusion of thermal fluctuations Re-entrant boundary for hex-square transition Borocarbides are another story ! we are probably seeing the influence of gap anisotropy or multi-band effects.