Melting of a confined monolayer of magnetized beads

Abstract

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.

Transition from a dissipative to a quasi-elastic system of particles with tunable repulsive interactions

“…In our experiments, the computations of the pair correlation function and of the orientational correlation function (not shown here) lead to qualitatively similar results as in [15]. Finally, the behavior of the collisionless nearly crystalline state at strong enough ε can be understood as follows.…”

“…ν c decreases with ε, vanishes below 0.1 Hz for ε > 10 and is strictly zero for ε > 30. For greater ε, particle displacements become bounded [15]. Indeed, in Fig.…”

“…3). For ε > 30, displacements become progressively constrained by magnetic repelling and the system can be seen as an assembly of confined particles [15]. F then increases with ε, highlighting a heterogeneity of velocities, as particles are individually more or less confined.…”

“…We point out that without taking into account the geometry of the magnetisation and the demagnetising magnetic field, an effective susceptibility χ can be defined [15,18], yield-ing an expression of the magnetic energy proportional to Eq. (1).…”

“…The magnetic potential energy depends on the local configuration of the particles, and therefore it fluctuates in time. Finally, a dimensionless interaction parameter is defined by the ratio ε ≡ E m /E c between the magnetic and kinetic energies [15,18]. When ε is increased, the system undergoes a continuous transition from an inelastic granular gas [ Fig.…”