Sharp or smooth crossover from quantum to classical behavior in S/F/S Josephson φ₀ junction

We consider quantum-classical escape-rate crossover of nanomagnets sandwiched between two superconductors called Josephson φ₀ junction. Within the frameworks of the instanton technique and the nonlinear perturbation method we obtain the crossover boundary separating the sharp crossover from the smooth one. It is found that the crossover boundary is greatly influenced by the supercurrent as well as the anisotropy constants and the magnetic field. These features are expected to be observable with existing experimental techniques.