Thermodynamics and phase diagrams of layered superconductor/ferromagnet nanostructures

Abstract

We study the thermodynamics of clean, layered superconductor/ferromagnet nanostructures using fully self-consistent methods to solve the microscopic Bogoliubov-deGennes equations. From these self-consistent solutions the condensation free energies are obtained. The trilayer superconductor/ferromagnet/superconductor junction is studied in particular detail: first-order transitions between 0 and $\ensuremath{\pi}$ states as a function of the temperature $T$ are located by finding where the free energies of the two phases cross. The occurrence of these transitions is mapped as a function of the thickness ${d}_{F}$ of the $F$ layer and of the Fermi wave-vector mismatch parameter $\ensuremath{\Lambda}$. Similar first-order transitions are found for systems with a larger number of layers: examples are given in the seven-layer (three-junction) case. The latent heats associated with these phase transitions are evaluated and found to be experimentally accessible. The transition temperature to the normal state is calculated from the linearized Bogoliubov-deGennes equations and found to be in good agreement with experiment. Thus, the whole three-dimensional phase diagram in $T$, ${d}_{F}$, and $\ensuremath{\Lambda}$ space can be found. The first-order transitions are associated with dips in the transition temperature ${T}_{c}$ to the nonsuperconducting state, which should facilitate locating them. Results are also given for the magnetic moment and the local density of states at the first-order transition.