Superconductivity under a ferromagnetic molecular field

Superconductivity under a ferromagnetic molecular field is investigated theoretically based on a one-dimensional electron-band model. By using an exact solution which takes into account infinite numbers of higher harmonics for the Bogoliubov—de Gennes equation, it is demonstrated that the spatially modulated superconducting state with a distorted sinusoidal wave is stabilized in the highfield region. A key feature of the solution is a soliton lattice structure which has a two-energy-gap structure and is accompanied by a spin-density polarization of the conduction electrons. The coexistence phase observed in ${\mathrm{ErRh}}_4$ ${\mathrm{B}}_4$ which consists of ferromagnetism, superconductivity, and a sinusoidally modulated magnetic state, is successfully interpreted in terms of this modulated superconducting state.