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The heat-capacity and magnetization measurements under high pressure havebeen carried out in a ferromagnetic superconductor UGe$_2$. Both measurementswere done using a same pressure cell in order to obtain both data for onepressure. Contrary to the heat capacity at ambient pressure, an anomaly isfound in the heat capacity at the characteristic temperature $T^{*}$ where themagnetization shows an anomalous enhancement under high pressure where thesuperconductivity appears. This suggests that a thermodynamic phase transitiontakes place at $T^{*}$ at least under high pressure slightly below $P_{c}^{*}$where $T^{*}$ becomes zero. The heat-capacity anomaly associated with thesuperconducting transition is also investigated, where a clear peak of $C/T$ isobserved in a narrow pressure region ($\Delta P \sim 0.1$ GPa) around$P_{c}^{*}$ contrary to the previous results of the resistivity measurement.Present results suggest the importance of the thermodynamic critical point$P_{c}^{*}$ for the appearance of the superconductivity.Comment: 4 pages, 4 figures, to appear in Phys. Rev. B, Rapid Communication

physical review. b, condensed matter and materials physics

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Heat-capacity anomalies atTscandT*in the ferromagnetic superconductor