Melting of a confined monolayer of magnetized beads

We present an experimental model system to study two-dimensional phase transitions. This system is composed of a monolayer of millimetric beads interacting through shor range magnetic dipole-dipole interactions. As the system is athermal, a mechanical agitation is used to produce an erratic motion of the beads. The two-dimensional melting scenario predicted by the Kosterlitz-Thouless-Halperin-Nelson-Young theory is observed. Each phase (liquid-hexatic-solid) has been highlighted with the use of both static and dynamic order parameters. Translational and orientational order are, respectively, estimated through the pair correlation function g(r) and both orientational correlation function g(6)(r) and its temporal counterpart g(6)(t). We observe two transitions by tuning the applied magnetic field H. First, a loss of translational order without loss of orientational order is observed. This is the signature of the transition from the solid phase to the so-called "hexatic" phase. Finally, the orientational order disappears, leading to a liquidlike structure.