Nonuniform superconductivity due to the orbital magnetic effect in ad-wave superconductor in a magnetic field

A type-II superconductor with d-wave pairing interactions with anisotropy due to the crystal lattice is studied. A kind of nonuniform superconductivity due to the orbital magnetic effect with a spatially oscillating order parameter is found to occur under appropriate conditions on the coupling constants and the direction of the magnetic field. It is found that the state depends on the direction of the magnetic field strongly. The spin magnetic effect on this nonuniform superconducting state is also examined. The relevance to the recent experimental result in heavy fermion ${\mathrm{UPd}}_2$ ${\mathrm{Al}}_3$ system is discussed. © 1996 The American Physical Society.