Magnetic Field Dependence of Low Temperature Specific Heat Jump in Superconducting Crystal

Specific heat of a crystal is the sum of electronic specific heat, which is the specific heat of conduction electrons, and lattice specific heat, which is the specific heat of the lattice. Since properties such as crystal structure and Debye temperature do not change even in the superconducting state, the lattice specific heat may remain unchanged between the normal and the superconducting state. The difference of specific heat between the normal and superconducting state may be caused only by the electronic specific heat difference between the normal and superconducting states. Critical temperature, at which transition occurs, becomes lower than $T_{c0}$ under the influence of a magnetic field. It is well known that specific heat also changes abruptly at this critical temperature, but magnetic field dependence of jump of specific heat has not yet been developed theoretically. In this paper, specific heat jump of superconducting crystals at low temperature is derived as an explicit function of applied magnetic field H by using the thermodynamic relations of A. C. Rose-Innes and E. H. Rhoderick. The derived specific heat jump is compared with experimental data for superconducting crystals of $MgCNi_3$, $LiTi_2O_4$ and $Nd_{0.5}Ca_{0.5}MnO_3$. Our specific heat jump function well explains the jump up or down phenomena of superconducting crystals.

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