  Thermodynamic investigations on volborthite (Cu3V2O7(OH)2 2H2O), which
possesses a two-dimensional kagome structure of S-1/2 spins, are presented. The
low-temperature heat capacities of volborthite and its Zn analogue compound
were measured by the relaxation calorimetry technique between 0.8 and 45 K. The
magnetic heat capacity of volborthite is characterized by two contributions of
T-linear and T2 dependences, the former of which is large above 1 K, giving
evidence of dense gapless excitations. We find a distinct kink in Cp T-1 at T*
= 1 K, which demonstrates a thermodynamic phase transition of short-range
nature to a novel ground state as reported in previous 51V-NMR experiments. The
T-linear term becomes smaller but remains finite even in the low-temperature
state below T*, while it is gradually reduced with increasing magnetic field
and vanishes at 5 T, which is close to the critical field for the field-induced
transition observed in the first magnetization step.
