Theory of self-induced vortex state in ferromagnetic superconductors

We have developed a quasi-classical formalism for a self-induced vortex state in ferromagnetic superconductors. By combining the spatially averaged approximation of superconductivity with the phenomenological free energy of ferromagnetism, we demonstrate the thermodynamic properties of the p-wave triplet equal-spin-pairing state with a 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 of the A₂ type with a small spin difference in gap magnitude. In the vicinity of the ferromagnetic quantum critical point with a large uniform susceptibility, it is possible to exhibit a type-II to type-I transition in the magnetization process.