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.

arXiv comment14 pages including 11 figures

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• Meissner Effect Probing of Odd-Frequency Triplet Pairing in Superconducting Spin Valves
• Proximity Induced Vortices and Long-Range Triplet Supercurrents in Ferromagnetic Josephson Junctions and Spin Valves
• Superconducting spin-valve effect in heterostructures with ferromagnetic Heusler alloy layers
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• Robustness of Spin-Triplet Pairing and Singlet-Triplet Pairing Crossover in Superconductor/Ferromagnet Hybrids
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• Standard, inverse and triplet spin-valve effects in F1/S/F2 systems
• Spin Transport in Half-Metallic Ferromagnet-Superconductor Junctions
• Competitive 0 and π states in S/F multilayers: multimode approach
• Transport in Ferromagnet/Superconductor spin valves
• Tunable superconducting critical temperature in ballistic hybrid structures with strong spin-orbit coupling
• Spin current and spin transfer torque in ferromagnet/superconductor spin valves
• Crossover between standard and inverse spin-valve effect in atomically thin superconductor/half-metal structures
• Superconducting spin valve effect in the Co/Pb/Co heterostructure with insulating interlayers
• Expanding the operational temperature window of a superconducting spin valve
• Classification of magnetic inhomogeneities and $0-\pi$ transitions in superconducting-magnetic hybrid structures
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• Observation of Spin Current Hermiticity
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