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Register a new userSuperconducting critical temperature and singlet and triplet pair functions of superconductor/normal-metal/ferromagnet trilayers
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We calculate the superconducting critical temperature $T_c$, the singlet pair function $Psi^+(x)$, and triplet pair function $Psi^-(x)$ of superconductor/normal metal/ferromagnet (S/N/F) trilayers using the linearized Usadel equation near $T_c$. The Greens function method developed by Fominov $et al.$ for the S/F bilayers is extended to the S/N/F trilayer systems. The S of the trilayers is taken to be an s-wave singlet pairing superconductor, and the S/N and N/F interfaces are modeled in terms of the interface resistances parameterized, respectively, by $gamma_b^{SN}$ and $gamma_b^{NF}$. We present the $T_c$, $Psi^+(x)$, and $Psi^-(x)$ for typical $gamma_b^{SN}$, $gamma_b^{NF}$, and the exchange energy $ E_{ex}$: (a) For a small (large) $gamma_b^{NF}$, $T_c$ of S/N/F trilayers, as $d_N$ is increased, increases (decreases) on the length scale of N coherence length $xi_N$ with a discontinuity at $d_N=0$ due to a boundary condition mismatch. (b) $T_c(d_F)$ shows a non-monotonic behavior like S/F bilayers with a weakened shallow dip. (c) The odd frequency triplet component $Psi^-(x)$, induced by $E_{ex}$ and proximity effects, has a maximum near the N/F interface and decreases on the length scale $xi_{ex}$ in F. It also penetrates into N and S regions on the length scale $xi_N$ and $xi_S$, respectively. Based on these results we make comments on the experimental observation of the odd triplet components and the recent $T_c$ measurements in Nb/Au/CoFe trilayer systems.
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We study the tunneling conductance of a ballistic normal metal / ferromagnet / spin-triplet superconductor junction using the extended Blonder-Tinkham-Klapwijk formalism as a model for a $c$-axis oriented Au / SrRuO$_{3}$ / Sr$_{2}$RuO$_{4}$ junction. We compare chiral $p$-wave (CPW) and helical $p$-wave (HPW) pair potentials, combined with ferromagnet magnetization directions parallel and perpendicular to the interface. For fixed $theta_{M}$, where $theta_{M}$ is a direction of magnetization in the ferromagnet measured from the $c$-axis, the tunneling conductance of CPW and HPW clearly show different voltage dependencies. It is found that the cases where the $d$-vector is perpendicular to the magnetization direction (CPW with $theta_{M} = pi/2$ and HPW with $theta_{M} = 0$) are identical. The obtained results serve as a guide to determine the pairing symmetry of the spin-triplet superconductor Sr$_{2}$RuO$_{4}$.
Ferromagnetic spin valves offer the key building blocks to integrate giant- and tunneling-magnetoresistance effects into spintronics devices. Starting from a generalized Blonder--Tinkham--Klapwijk approach, we theoretically investigate the impact of interfacial Rashba and Dresselhaus spin-orbit couplings on the tunneling conductance, and thereby the tunneling-magnetoresistance characteristics, of ferromagnet/superconductor/ferromagnet spin-valve junctions embedding thin superconducting spacers between the either parallel or antiparallel magnetized ferromagnets. We focus on the unique interplay between usual electron tunnelings -- that fully determine the tunneling magnetoresistance in the normal-conducting state -- and the peculiar Andreev reflections in the superconducting state. In the presence of interfacial spin-orbit couplings, special attention needs to be paid to the spin-flip (unconventional) Andreev-reflection process that is expected to induce superconducting triplet correlations in proximitized regions. As a transport signature of these triplet pairings, we detect conductance double-peaks around the singlet-gap energy, reflecting the competition between the singlet and the newly emerging triplet gap. We thoroughly analyze the Andreev reflections role in connection with superconducting tunneling-magnetoresistance phenomena, and eventually unravel huge conductance and tunneling-magnetoresistance magnetoanisotropies -- easily exceeding their normal-state counterparts by several orders of magnitude -- as another experimentally accessible fingerprint of unconventional Andreev reflections. Our results provide an important contribution to establish superconducting magnetic spin valves as an essential ingredient for future superconducting-spintronics concepts.
The superconducting critical temperature $T_C$ of a superconductor/ferromagnet (S/F) bilayer with spin-flip scatterings at the interface is calculated as a function of the ferromagnet thickness $d_F$ in the dirty limit employing the Usadel equation. The appropriate boundary conditions from the spin-flip scatterings at the S/F interface are derived for the Usadel equation which includes the spin triplet pairing components as well as the spin singlet one. The spin-flip processes induce the spin triplet pairing components with s-wave in momentum and odd symmetry in frequency from the s-wave singlet order parameter $Delta$ of the superconductor region. The induced triplet components alter the singlet order parameter in the superconductor through boundary conditions at the interface and, consequently, change the $T_C$ of an S/F bilayer system. The calculated $T_C(d_F)$, like the case of no spin-flips, shows non-monotonic behavior which typically decreases as $d_F$ is increased from 0 and shows a shallow minimum and then saturates slowly as $d_F$ is further increased. It is well established that as the interface resistance (parameterized in terms of $gamma_b$) is increased, the $T_C$ is increased for a given $d_F$ and the non-monotonic feature in $T_C(d_F)$ is strongly suppressed. As the spin flip scattering (parameterized in terms of $gamma_m$) is increased, on the other hand, the $T_C$ is also increased for a given $d_F$, but the non-monotonic feature in $T_C(d_F)$ is less suppressed or even enhanced, through the formation of the spin triplet components.
In s-wave superconductors the Cooper pair wave function is isotropic in momentum space. This property may also be expected for Cooper pairs entering a normal metal from a superconductor due to the proximity effect. We show, however, that such a deduction is incorrect and the pairing function in a normal metal is surprisingly anisotropic because of quasiparticle interference. We calculate angle resolved quasiparticle density of states in NS bilayers which reflects such anisotropic shape of the pairing function. We also propose a magneto-tunneling spectroscopy experiment which could confirm our predictions.
This work discusses theoretically the interplay between the superconducting and ferromagnetic proximity effects, in a diffusive normal metal strip in contact with a superconductor and a non-uniformly magnetized ferromagnetic insulator. The quasiparticle density of states of the normal metal shows clear qualitative signatures of triplet correlations with spin one (TCS1). When one goes away from the superconduting contact, TCS1 focus at zero energy under the form of a peak surrounded by dips, which show a typical spatial scaling behavior. This behavior can coexist with a focusing of singlet correlations and triplet correlations with spin zero at finite but subgap energies. The simultaneous observation of both effects would enable an unambigous characterization of TCS1.
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