  We develop a phenomenological model to study magnetic hysteresis in two
samples designed as possible perpendicular recording media. A stochastic
cellular automata model captures cooperative behavior in the nucleation of
magnetic domains. We show how this simple model turns broad hysteresis loops
into loops with sharp drops like those observed in these samples, and explains
their unusual features. We also present, and experimentally verify, predictions
of this model, and suggest how insights from this model may apply more
generally.
