Proximity effects and triplet correlations in Ferromagnet/Ferromagnet/Superconductor nanostructures

Abstract

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 $T_c(\alpha )$ 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, $T_c(\alpha )$ is in general a non-monotonic 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.

14 pages including 11 figures

References in corpus (5)

• Symmetries of Pairing Correlations in Superconductor-Ferromagnet Nanostructures
• Superconducting triplet spin valve
• Spin-dependent Cooper Pair Phase and Pure Spin Supercurrents in Strongly Polarized Ferromagnets
• Odd Triplet Pairing in clean Superconductor/Ferromagnet heterostructures
• Induced Triplet Pairing in clean s-wave Superconductor/Ferromagnet layered structures

Cited by in corpus (6)

• Controlled suppression of superconductivity by the generation of polarized Cooper pairs in spin valve structures
• Odd-frequency superconducting states with different types of Meissner response: Problem of coexistence
• Angular dependence of superconductivity in superconductor / spin valve heterostructures
• Proximity Induced Vortices and Long-Range Triplet Supercurrents in Ferromagnetic Josephson Junctions and Spin Valves
• Proximity Effects in Conical-Ferromagnet/Superconductor bilayers
• Tunneling Conductance and Spin Transport in Clean Ferromagnet-Ferromagnet-Superconductor Heterostructures