Inverse melting is the process in which a crystal reversibly transforms int
o a liquid or amorphous phase when its temperature is decreased. Such a pro
cess is considered to be very rare(1), and the search for it is often hampe
red by the formation of non-equilibrium states or intermediate phases(2). H
ere we report the discovery of first-order inverse melting of the lattice f
ormed by magnetic flux lines in a high-temperature superconductor. At low t
emperatures, disorder in the material pins the vortices, preventing the obs
ervation of their equilibrium properties and therefore the determination of
whether a phase transition occurs. But by using a technique(3) to 'dither'
the vortices, we were able to equilibrate the lattice, which enabled us to
obtain direct thermodynamic evidence of inverse melting of the ordered lat
tice into a disordered vortex phase as the temperature is decreased. The or
dered lattice has larger entropy than the low-temperature disordered phase.
The mechanism of the first-order phase transition changes gradually from t
hermally induced melting at high temperatures to a disorder-induced transit
ion at low temperatures.