Spin gap and superconductivity in the ground state of the two-dimensional Hubbard model

Three aluminum polycations, Al13 (epsilon)-Keggin Johansson-type, Al13 M?gel-type and Al30 (delta)-Taulelle-type have been measured by 27Al solid state NMR, using MAS and 3QMAS spectroscopies. The number of inequivalent aluminum obtained by these high resolution NMR experiments leads to a comparison with their respective XRD results obtained on single crystal. In all three cases, the inequivalent sites measured by NMR and deduced from the XRD measurement show apparent discrepancies. It is, therefore, shown that the choice of the space group has to be made in such a way that both diffraction and NMR measurement can be brought to a consistent description of the sample considered. In the case of Al30 (delta)-Taulelle, a new refinement of diffraction results has been performed changing the space group from C2/c to Cc leading to consistent results between XRD and NMR.