Specific heat of sodium-vanadium bronzes NaxV2O5 between 0.5 and 50 K

The specific heat of NaxV2O5, x=0.2, 0.25, 0.3, 0.36, and 0.41, and of pure V2O5 single crystals, was measured between 0.5 and 50 K in zero magnetic field as well as in fields of different intensities up to 2.8 T. The specific heat of pure V2O5 shows a well-defined maximum in CT3; this indicates the presence of low-lying modes which can be described by Einstein oscillators. The lowest Einstein frequency E obtained from the specific-heat data is 76 cm-1 while the Debye temperature D=164 K. The addition of sodium to V2O5 enhances the specific heat below 7 K considerably. The excess specific heat is linear in temperature and is magnetic field dependent and can be described by a simple model of many three-level systems with spin S=1. However, this model is at the moment not understood theoretically. This is the same difficulty encountered in spin-glasses which also contain an excess specific heat rather linear in temperature over a considerable temperature range.