A hysteresis loop is observed for the first time in the de Haas-van Alphen (dHvA) effect of beryllium at low temperatures and quantizing magnetic field applied parallel to the hexagonal axis of the single crystal. The irreversible behavior of the magnetization occurs at the paramagnetic part of the dHvA period in conditions of Condon domain formation arising by strong enough dHvA amplitude. The resulting extremely nonlinear response to a very small modulation field offers the possibility to find in a simple way the Condon domain phase diagram. From a harmonic analysis, the shape and size of the hysteresis loop is constructed.

Using a set of micro Hall probes for the detection of the local induction, the inhomogeneous Condon domain structure has been directly observed at the surface of a pure silver single crystal under strong Landau quantization in magnetic fields up to 10 T. The inhomogeneous induction occurs in the theoretically predicted part of the Condon domain phase diagram. Information about size, shape, and orientation of the domains is obtained by analyzing Hall probes placed along and across the long sample axis and by tilting the sample. On a beryllium surface the induction inhomogeneity is almost absent although the expected induction splitting here is at least 10 times higher than in silver.

We demonstrate experimentally and theoretically that the dissipative state of superconducting samples with a periodic array of holes at high current densities consists of flux rivers resulting from a short-range attractive interaction between vortices. This dynamically induced vortex-vortex attraction results from the migration of quasiparticles out of the vortex core (kinematic vortices). We have directly visualized the formation of vortex chains by scanning Hall probe microscopy after freezing the dynamic state by a field cooling procedure at a constant bias current. Similar experiments carried out in a sample without holes show no hint of flux river formation. We shed light on this nonequilibrium phenomena modeled by timedependent Ginzburg-Landau simulations. Self-organization and its associated pattern morphologies belong to the most striking phenomena in nature. Usually periodic, such features are often the result of competing interactions. One of the most common structures is stripe patterns, which are found in magnetic, colloidal, or biological systems [1]. In most of them, the longrange (dipolarlike) repulsion is balanced by a short-range attraction, with an origin specific to each system. An interesting analogue can be found in superconductivity. Although this state of matter is magnetophobic, the magnetic field can penetrate (type-II) superconductors in the form of vortices with each bearing a flux quantum È 0 . Since the magnetic energy increases when vortices approach each other [2], their interaction is purely repulsive, and they form a triangular lattice. However, an attractive component in the vortex-vortex interaction may appear even in type-II superconductors. For example, such phenomenon is observed in anisotropic superconductors with a magnetic field tilted away from the principal symmetry axes [3][4][5], or as a result of the nonlocal relationship between supercurrents and vector potential in clean and low-materials [6]. Another example can be found in the case of type-1.5 superconductors where two weakly coupled order parameters, each of which belong to a different type of superconductivity, coexist in the same material [7,8]. In all cases when vortex attraction is present, a vortex chain formation is observed.However, the formation of vortex chains in isotropic type-II superconductors is still energetically unfavorable due to purely repulsive interactions [9]. The only instance where vortex chains are predicted to attract each other in type-II isotropic superconductors is when they are out of equilibrium. Namely, in an applied dc drive, fast moving vortices due to a Lorentz force create an excess of quasiparticles behind themselves generating a wake of depleted order parameter [10,11]. This effect gives rise to the socalled kinematic vortices characterized by a very anisotropic vortex core elongated in the direction of motion [11]. Under these circumstances, vortices attract the following vortices and interconnect into a ''vortex river.'' This directional interaction between kinematic vorti...