0 Vortex Clustering : The Origin of the Second Peak in the Magnetisation Loops of Type Two Superconductors [ Short title : Vortex Clustering ]

We study vortex clustering in type II Superconductors. We demonstrate that the “second peak” observed in magnetisation loops may be a dynamical effect associated with a density driven instability of the vortex system. At the microscopic level the instability shows up as the clustering of individual vortices at (rare) preferential regions of the pinning potential. In the limit of quasi-static ramping the instability is related to a phase transition in the equilibrium vortex system. Corresponding author, email: [email protected] 1 When the external magnetic field penetrates a type II superconductor, magnetic vortex lines appear inside the bulk of the sample. These vortex lines are repulsive and quantised each carrying a multiple q of the magnetic flux quantum φ0. The energy per unit length of a vortex line is proportional to q and accordingly one typically expects to have configurations with well separated single quantised vortex lines [1]. We show below, however, that dynamical vortex clustering may become very important: vortices form inhomogeneous spatial structures which become relevant for the evolution of the system. This clustering may for instance cause the “second peak” observed in magnetisation loops and strongly affects the structure of the vortex system, magnetic relaxation, and the distribution of the local magnetic induction as measured in μ spin-relaxation experiments. The understanding of structural properties of vortices, underlying the presence of the “second peak”, is one of the central issues of current research in superconductivity, and is related to fundamental aspects of vortex matter ranging from dynamical behaviour to phase transitions. (see eg. [2, 3]). In a superconducting sample in the presence of an external magnetic field, vortex lines penetrating from the surface into the bulk may be trapped on pinning centres [1, 4] leading to a spatially inhomogeneous vortex distribution and to a net magnetisation of the sample. As the external field is increased the vortex lines are squeezed together and therefore interact more strongly. Such a strong interaction will counteract the pinning forces and thus one expects, as in fact is usually observed, the magnetisation to decrease with increasing external field once vortices have fully penetrated the sample. However, upon further increase of the external field the magnetisation is often observed to increase again [5]. This behaviour leads to the so-called fishtail structure in the magnetisation data for YBCO or the arrowhead structure in equivalent data for BISCCO samples[6, 7]. A similar peak structure has also been observed in low temperature superconductors [8]. The second peak is one of the most important unsolved problems in vortex physics. It has been seen as a signature of a phase transition in the vortex system and its