Statistical mechanics of magnetic bubble arrays. II. Observations of two-dimensional melting.

Abstract

We report observations of a continuous hexatic-to-liquid melting transition as a function of density in two-dimensional magnetic bubble arrays in garnet films. Bubble arrays can be directly viewed and their motion recorded. The hexatic with orientational order undergoes a phase transition to form an isotropic liquid when dislocations unbind into disclinations. Melting occurs via the formation of progressively larger transient defect clusters that gradually percolate into one another, and eventually span the system destroying orientational order. Observations made in a linear magnetic-field gradient indicate that the transition is continuous. Defect dynamics, concentrations, and mobilities characterize the melting process. At the transition bubble motion goes from constrained in the hexatic to diffusive in the liquid. The transition is described well by a phenomenological criterion: melting occurs when the root mean square of the difference between displacements of adjacent bubbles is \ensuremath{\sim}10% of the average lattice spacing. At higher bubble densities, away from the transition, we observe a hexatic glass characterized by extended orientational order, very few immobile dislocations, and short-range translational order limited by substrate roughness.