Two-Dimensional Melting of Magnetic Bubble Arrays: A Continuous Hexatic-To-Liquid Transition
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TWO-DIMENSIONAL MELTING OF MAGNETIC BUBBLE ARRAYS: A CONTINUOUS HEXATIC-TO-LIQUID TRANSITION R. SESHADRI AND R. M. WESTERVELT Division of Applied Sciences and Department of Physics Harvard University, Cambridge, MA 02138 ABSTRACT Arrays of two-dimensional magnetic bubbles in thin garnet films undergo a hexatic-toliquid transition as a function of bubble density controlled by an applied spatially uniform dc bias magnetic field that opposes the magnetization in the bubbles. The phase transition is driven by topological point defects. The bubbles are observed directly using optical microscopy and digital imaging techniques. In the presence of a linear gradient in the dc bias magnetic field the hexatic-to-liquid transition occurs spatially in the direction of the gradient. As the system goes from hexatic to liquid, a continuous decrease in bubble density accompanied by a continuous disordering of the array is observed along the gradient direction. This continuous disordering persists even after the system is allowed to equilibrate for very long periods of time, indicating that the hexatic-to-liquid transition is continuous at equilibrium. Dynamics of topological defects observed in the gradient field correspond to those observed in the uniform field. INTRODUCTION In two-dimensions the melting transition that transforms a crystal, with quasi-longrange translational order and long-range orientational order, into an isotropic liquid, with shortrange orientational and translational order, occurs via the unbinding of topological defects [1-6]. Building on the ideas of Kosterlitz and Thouless [3], Halperin and Nelson [4-5] and Young [6] suggested that melting in two-dimensional systems at equilibrium occurs via two continuous transitions. The first transition transforms the crystal into a hexatic, with quasi-long-range orientational order and short-range translational order, as dislocation pairs continuously unbind into free dislocations accompanied by the loss of translational order. Halperin and Nelson suggested that a second transition that is mediated by the continuous unbinding of dislocations or disclination pairs into free disclinations accompanied by the loss of orientational order transforms the hexatic into an isotropic liquid. Most experiments that study this melting process, with notable exceptions [7-9], are limited by the inability to directly observe the arrays and the defect dynamics. Computational studies that permit such observations are limited by small numbers of particles, periodic boundary conditions and short equilibration times. Recently, Chudnovsky showed that in the presence of microscopic disorder in the system the crystal phase is absent and a hexatic glass is the most ordered phase [10]. Therefore, in the presence of microscopic disorder the scenario for two-dimensional melting is as follows: a hexatic glass becomes a hexatic, which then becomes a liquid when the system looses orientational order as it undergoes the continuous dislocation unbinding transition. A hexatic vortex glass has been imag
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