  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.
