Commensurate-incommensurate transitions in magnetic bubble arrays with periodic line pinning

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Abstract
We report direct observations of commensurate-incommensurate phase transitions as a function of bubble concentration in a two-dimensional magnetic bubble array subject to periodic line pinning. The pinning lines consist of lithographically produced parallel permalloy bars. Temperature is simulated by an ac magnetic field. The structure function shows a smooth migration of Bragg peaks with density indicating a second order (or weakly first order) commensurate-incommensurate-commensurate transition as the local orientation of the array rotates continuously. We have also identified a commensurate smectic phase.