Temperature-induced 0−π coexistence in clean superconductor-ferromagnet-superconductor Josephson junctions

Abstract

A clean ballistic superconductor-ferromagnet metal-superconductor (SFS) junction is studied within the quasiclassical theory of superconductivity. We show that the temperature-induced coexistence of the 0 and π states and the transition 0−π results from the temperature-induced transition between stable and metastable states of the junction. The π shift occurs in small but finite critical intervals {Zc} of the magnetic barrier influence parameter Z=2dh/ℏv0, where h is the exchange energy and d the barrier thickness. The width of {Zc} and the coexistence temperature T0π depend also on the reduced barrier thickness d¯=d/ξ0, where ξ0 is the zero-temperature superconducting coherence length. The interval {Zc} increases with d¯. For T≠T0π the junction is in the 0 or π state. In contrast to the dirty case, the critical current Ic depends monotonously on temperature, changing the sign but not the magnitude at the transition point. The nonvanishing critical current Ic(T0π) is related to the existence of the second harmonic in the current-phase relation, which could be observed experimentally.

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