We report the results of a study of superconducting proximity effects in clean ferromagnet/ferromagnet/superconductor (${\mathrm{F}}_1{\mathrm{F}}_2\mathrm{S}$) heterostructures, where the pairing state in S is a conventional singlet $s$-wave. We numerically find the self-consistent solutions of the Bogoliubov-de Gennes (BdG) equations and use these solutions to calculate the relevant physical quantities. By linearizing the BdG equations, we obtain the superconducting transition temperatures $T_c$ as a function of the angle $\alpha$ between the exchange fields in ${\mathrm{F}}_1$ and ${\mathrm{F}}_2$. We find that the results for $T_c\left(\alpha \right)$ in ${\mathrm{F}}_1{\mathrm{F}}_2\mathrm{S}$ systems are clearly different from those in ${\mathrm{F}}_1\mathrm{S}{\mathrm{F}}_2$ systems, where $T_c$ monotonically increases with $\alpha$ and is highest for antiparallel magnetizations. Here, $T_c\left(\alpha \right)$ is in general a nonmonotonic function, and often has a minimum near $\alpha \approx {80}^{\circ }$. For certain values of the exchange field and layer thicknesses, the system exhibits reentrant superconductivity with $\alpha$: it transitions from superconducting to normal, and then returns to a superconducting state again with increasing $\alpha$. This phenomenon is substantiated by a calculation of the condensation energy. We compute, in addition to the ordinary singlet pair amplitude, the induced odd triplet pairing amplitudes. The results indicate a connection between equal-spin triplet pairing and the singlet pairing state that characterizes $T_c$. We find also that the induced triplet amplitudes can be very long ranged in both the S and F sides and characterize their range. We discuss the average density of states for both the magnetic and the S regions, and its relation to the pairing amplitudes and $T_c$. The local magnetization vector, which exhibits reverse proximity effects, is also investigated.

• Received 11 May 2012

DOI:https://doi.org/10.1103/PhysRevB.86.014523