Ferromagnetic Josephson junctions can show at equilibrium a $\pi$ phase difference between the superconducting electrodes. We explain this $\pi$ state in an original way by a modified spectrum of Andreev bound states shifted by the exchange energy. A simplified expression for the spectral supercurrent density is calculated and the nonmonotonic temperature dependence of the critical current is discussed. This model accounts for the cancellation of the critical current with temperature observed in a small range of barrier thickness in our ${\mathrm{N}\mathrm{b}/\mathrm{C}\mathrm{u}}_{52}{\mathrm{Ni}}_{48}/\mathrm{Nb}$ junctions. This cancellation corresponds to an inversion of the supercurrent and to a ground-state crossover from a 0 state to a $\pi$ state. This transition is caused both by the thermal distribution of quasiparticles and by the temperature dependence of the exchange energy. The experimental curves are well reproduced by our theoretical expression except for the very small amplitude of the supercurrent attributed to a large spin-flip scattering.

• Received 6 May 2003

DOI:https://doi.org/10.1103/PhysRevB.68.054531