Thermodynamic nature of the 0-PI quantum transition in superconductor-ferromagnet-superconductor trilayers

In structures made up of alternating superconducting and ferromagnet layers (S/F/S heterostructures), it is known that the macroscopic quantum wavefunction of the ground state changes its phase difference across the F--layer from 0 to PI under certain temperature and geometrical conditions, whence the name "0-PI" for this crossover. We present here a joint experimental and theoretical demonstration that the "0-PI" is a true thermodynamic phase transition: microwave measurements of the temperature dependence of the London penetration depth in Nb/Pd_0.84Ni_0.16/Nb trilayers reveal a sudden, unusual decrease of the density of the superconducting condensate (square modulus of the macroscopic quantum wavefunction) with decreasing temperature, which is predicted by the theory here developed as a transition from the 0- to the PI-state. Our result for the jump of the amplitude of the order parameter is the first thermodynamic manifestation of such temperature-driven quantum transition.