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Anomalous properties of the magnetization, the crystal dilatation, and other physical quantities observed in the mixed state of compounds such as UPd2Al3 and CeRu2 suggest the occurrence of a new state near H-c2. In such compounds with large spin susceptibility and high H-c2, a new inhomogeneous superconducting state is theoretically predicted to occur in high magnetic fields. In this inhomogeneous state which is shown to be a generalized Fulde-Ferrell-Larkin-Ovchinnikov state, the order parameter is spatially modulated, and planar nodes of the order parameter are periodically aligned perpendicular to the vortices. Various theoretical predictions are compared with experimental results on UPd2Al3 and CeRu2 related to this new superconducting high-field state

Generalized Fulde-Ferrell-Larkin-Ovchinnikov state in heavy-fermion and intermediate-valence systems