A Kinetics Driven Commensurate–Incommensurate Transition

Abstract

We study the steady-state structure of an interface in an Ising system on a square lattice with a nonuniform external field. This structure exhibits a commensurate–incommensurate transition driven by the velocity of the interface. The nonuniform field has a profile with a fixed shape which is designed to stabilize a flat interface, and is translated with velocity ve . For small velocities, the interface is stuck to the profile and is rippled with a periodicity which may be either commensurate or incommensurate with the lattice parameter of the square lattice. For a general orientation of the profile, the local slope of the interface locks into one of infinitely many rational directions, producing a devil's staircase structure. These lock-in or commensurate structures disappear as ve increases through a kinetics driven commensurate–incommensurate transition. For large ve , the interface becomes detached from the field profile and coarsens with Kardar–Parisi–Zhang (KPZ) exponents. The complete phase diagram and the multifractal spectrum corresponding to these structures have been obtained numerically together with several analytic results concerning the dynamics of the rippled phases. Our work has technological implications in crystal growth and the production of surfaces with desired surface morphologies.