2D magnetic nanoparticles are known to lead to numerous structures, experimentally '¹' and theoretically '²'. Here we want to focus on the case of magnetic nanoparticles in a strong perpendicular magnetic field which aligns all magnetic dipoles. Then the dipole dipole interaction is repulsive as well as the hard core interaction, and a confinement is required to stabilize the structure. These interactions are simulated by means of a Monte-Carlo computation. The energetic difference between a triangular lattice of perpendicular dipoles and a square lattice with the same density is quite weak. Thus the solidification temperature of confined perpendicular dipoles is expected to be very low. This is confirmed by numerical simulations which show that the solid phase contains triangular lattice parts as well as many defects as known in a Wigner glass. As a matter of fact this liquid-solid transition reveals to be a freezing one because of the continuous variation of energy per particle through the transition. In the solid phase, heating is linked with localized particle displacements towards a more irregular structure.
'¹' F. Kun et al., Phys. Rev. E 64, 061503, (2001).
'²' A. Ghazali and J.-C.S. Levy, Phys. Rev. B 67, 064409, (2003).

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