Theory of Self-Induced Vortex State in Ferromagnetic Superconductors

We have developed the quasi-classical formalism for a self-induced vortex state in ferromagnetic superconductors. By combining the spatially averaged approximation of the superconductivity with the phenomenological form of the ferromagnetism, we demonstrate the thermodynamic properties of the p-wave triplet equal-spin-pairing state with the spontaneous vortex lattice. The occurrence condition for the self-induced vortex state is discussed within this formalism. The comparison of the calculated quantities with the observed ones indicates that the self-induced vortex state indeed occurs in UCoGe, and its pairing symmetry seems to be the A2-type with a small spin difference in the gap magnitudes. In the vicinity of the ferromagnetic quantum critical point with a large uniform susceptibility, it is possible to exhibit the type-II to the type-I transition in the magnetization process.