  Inverse melting, in which a crystal reversibly transforms into a liquid or
amorphous phase upon decreasing the temperature, is considered to be very rare
in nature. The search for such an unusual equilibrium phenomenon is often
hampered by the formation of nonequilibrium states which conceal the
thermodynamic phase transition, or by intermediate phases, as was recently
shown in a polymeric system. Here we report a first-order inverse melting of
the magnetic flux line lattice in Bi2Sr2CaCu2O8 superconductor. At low
temperatures, the material disorder causes significant pinning of the vortices,
which prevents observation of their equilibrium properties. Using a newly
introduced 'vortex dithering' technique we were able to equilibrate the vortex
lattice. As a result, direct thermodynamic evidence of inverse melting
transition is found, at which a disordered vortex phase transforms into an
ordered lattice with increasing temperature. Paradoxically, the structurally
ordered lattice has larger entropy than the disordered phase. This finding
shows that the destruction of the ordered vortex lattice occurs along a unified
first-order transition line that gradually changes its character from
thermally-induced melting at high temperatures to a disorder-induced transition
at low temperatures.
