Thermodynamic nature of the0–πquantum transition in superconductor/ferromagnet/superconductor trilayers

Abstract

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 π under certain temperature and geometrical conditions, whence the name "0 − π" for this crossover. We present here a joint experimental and theoretical demonstration that the 0 − π is a true thermodynamic phase transition: microwave measurements of the temperature dependence of the London penetration depth in Nb/Pd0.84Ni0.16/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 π−state. Our result for the jump of the amplitude of the order parameter is the first thermodynamic manifestation of such temperature-driven quantum transition.

Фазовые Переходы В Гибридных SFS-структурах С Тонкими Сверхпроводящими Слоями

“…Особенности эффекта близости на SF-границе при-водят также к аномальному поведению экранирующих свойств гибридных структур: немонотонной зависимости эффективной длины проникновения магнитного поля в SF-бислой от толщины ферромагнетика [27][28][29], па-рамагнитному эффекту Мейснера [30][31][32], ухудшению экранирующих свойств SFS-структуры при понижении температуры T [29,33,34]. В случае изучения экрани-рующих свойств гибридных SF структур в качестве исследуемой величины выступает эффективная глубина проникновения магнитного поля , которая вблизи T c определяется средней по объему SF-структуры плотно-стью куперовских пар:…”

Robustness of the0−πtransition against compositional and structural ageing in superconductor/ferromagnetic/superconductor heterostructures

“…Since we have identified the nonmonotonous behavior of ∆λ ef f (T ) as the signature of the 0 − π transition, it is important to rule out possible spurious effects that can mimic this behavior. An extensive discussion has been reported previously, 7 we shortly recall it here. First, several experimental runs were performed, including runs after entirely disassembling and reassembling the microwave resonator: the data completely overlapped.…”

“…In the specific, and much studied [3][4][5][6][7] case of SFS trilayers, the competition between S and F orderings gives rise to two possible superconducting ground states, so-called "0" and "π" states. In the 0 state the superconducting order parameter is depressed in the F layer, but no phase difference exists between the S layers.…”

“…Since the signature of the transition is observed or predicted mostly in phase-interference effects, one might raise some questions about the true nature of the transition. Recently, it has been experimentally observed 7 that the transition has a true thermodynamic nature: surface impedance measurements yielded the temperature dependence of the superfluid density in SFS samples with different d F . In the sample with critical d F thickness, a reentrant jump of the superfluid density was observed, in agreement with theoretical calculations.The experimental behavior was in agreement with theoretical calculations, 7,8 and the extended theoretical treatment 8 confirmed the existence of a jump in superfluid density at the 0 − π, temperature-induced transition.However, while all qualitative features of the theoretical calculations were observed in the measurements of the superfluid density, a few minor quantitative discrepancies existed.…”

“…7). Since aim of this paper is to understand this ageing effect and gather informations from joint electrodynamics, structural and chemical investigation, we performed a preliminary repetition of the measurements on the reference Nb sample, as-grown and after ageing.…”