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and these two length scales become equivalent around 0.6 mT. Any vortex cluster is unlikely to be observed above 0.6 mT. In fact Moshchalkov et al. 5 have reported no clearly visible vortex clusters at 1.0 mT. The observations 

∗ Corresponding author: vic- tor.moshchalkov@fys.kuleuven.be 1 

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In conclusion, scanning SQUID microscopy shows that in high quality MgB$_{2}$ single crystals vortices line up lo- cally at very low vortex densities and grow into vortex clusters with increasing applied field. The average dis- tances between nearest neighboring vortices forming clus- ters are practically independent of the applied field B , in contrast to the conventional (1/ B ) 1 / 2 behavior. The sim- ulations of a vortex system of a type-1.5 superconductor indeed reproduce these observations. Our experimental data, as well as consistency between experiment and the simulations, clearly demonstrates that high quality MgB$_{2}$ single crystals lie in the type-1.5 regime. 

This work was supported by Methusalem Funding by the Flemish government, the Flemish FWO, the Bel- gian Interuniversity Attraction Poles (IAP), the ESF- NES “Nanoscience and Engineering in Superconductiv- ity” Programmes, and JSPS core-to-core NES program. 

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