Abstract
New modes of the magnetic-flux penetration in superconducting quantum interference devices (SQUID's) with ferromagnetic junctions are predicted theoretically. Characteristic multinode anharmonicity of the current-phase relation implies the coexistence of stable and metastable $0$ and $\ensuremath{\pi}$ states for a large interval of strength of the ferromagnetic barrier influence at low temperature. As a consequence, the coexistence of integer and half-integer fluxoid configurations appears in both rf and dc SQUID's and generates two flux jumps per one external flux quantum. In dc SQUID's, new flux jumps are manifested as two dips in the critical current dependence on the external magnetic flux.
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