Thermal expansion of coexistence of ferromagnetism and superconductivity

The temperature dependence of thermal expansion of coexistence of ferromagnetism and superconductivity below the superconducting transition temperature T-c up arrow of a majority spin conduction band is investigated. Majority spin and minority spin superconducting gaps exist in the coexistent state. We assume that the Curie temperature is much larger than the superconducting transition temperatures. The free energy that Linder et al. [Phys. Rev. B76, 054511 (2007)] derived is used. The thermal expansion of coexistence of ferromagnetism and superconductivity is derived by the application of the method of Takahashi and Nakano [J. Phys.: Condens. Matter 18, 521 (2006)]. We find that we have the anomalies of the thermal expansion in the vicinity of the superconducting transition temperatures.