arXiv:0803.3174v1 [cond-mat.supr-con] 21 Mar 2008 Induced Triplet Pairing in clean s-wave Superconductor/Ferromagnet layered structures Klaus Halterman, 1, ∗ Oriol T. Valls, 2, † and Paul H. Barsic 2, ‡ 1 Physics and Computational Sciences, Research and Engineering Sciences Department, Naval Air Warfare Center, China Lake, California 93555 2 School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455 (Dated: January 6, 2014) We study induced triplet pairing correlations in clean ferromagnet/superconductor/ferromagnet heterostructures. The pairing state in the superconductor is the conventional singlet s-wave, and the angle α between the magnetizations of the two ferromagnetic layers is arbitrary. We use a numerical fully self-consistent solution of the microscopic equations and obtain the time-dependent triplet correlations via the Heisenberg equations of motion. We find that in addition to the usual singlet correlations, triplet correlations, odd in time as required by the Pauli principle, are induced in both the ferromagnets and the superconductor. These time-dependent correlations are largest at times of order of the inverse of the Debye cutoff frequency, ωD, and we find that within that time scale they are often spatially very long ranged. We discuss the behavior of the characteristic penetration lengths that describe these triplet correlations. We also find that the ferromagnets can locally magnetize the superconductor near the interface, and that the local magnetization then undergoes strongly damped oscillations. The local density of states exhibits a variety of energy signatures, which we discuss, as a function of ferromagnetic strength and α. PACS numbers: 74.45.+c, 74.25.Bt, 74.78.Fk I. INTRODUCTION Triplet Cooper pairing is no new phenomenon: it has long been recognized to be responsible for superfluidity 1 in 3 He as well as for superconductivity in some electronic materials. This occurs when the pairing interaction is in a partial wave with odd ℓ. However, recent observations have raised the possibility of induced triplet pairing cor- relations in s-wave superconductors. It is a matter of elementary physics that the Cooper pair wavefunction must be antisymmetric under exchange of the two elec- trons to satisfy the Pauli principle. For spatially symmet- ric s-wave superconductors with decoupled spatial and spin degrees of freedom, the spin singlet pair is the only possible antisymmetric state of an electron pair. Triplet pairing states on the other hand, where the spin state is symmetric, are obviously allowed when the pairing is spatially antisymmetric, such as in p-wave superconduc- tors. Triplet states in systems with s-wave pairing, even in momentum or coordinate space, would naively appear to violate the Pauli principle. However, many years ago Berezinskii proposed 2 a triplet state in superfluid 3 He, which involved spatially symmetric correlations. Berezin- skii’s triplet pairing correlations, involving different-time pairing, did not violate the Pauli principle by virtue of being odd in time, thus allowing a triplet state in a sys- tem with s-wave interactions. While such a state did not turn out to be appropriate to describe superfluidity in 3 He, its consideration has led the way to the study of cases where some sort of time-reversal symmetry break- ing mechanism may allow an odd time triplet state to be induced in systems with spatially symmetric interactions. Interest in exotic triplet pairing arises from many quar- ters. In the case of two component cold atomic gases 3 with short-range s-wave interactions, in which the two species have the same mass but different chemical po- tentials, it may be possible to induce a triplet pairing that breaks time reversal symmetry. In electronic materi- als, an important issue is the possible existence of a long range proximity effect in Superconductor/Ferromagnet (SF) heterostructures. Interest in these heterostructures arises in turn from their possible 4 applications. Of par- ticular interest is that the thermodynamic and transport properties of FSF trilayers are found to depend strongly on the relative orientation of the magnetization in the two F layers. 5,6,7,8 This rather well-understood 9,10,11,12 fact makes these structures candidates as spin valves. There have been no unambiguous observations of in- duced triplet correlations in SF structures involving s- wave superconductors. However, there have been some enticing experimental hints in the form of long ranged proximity induced superconducting behavior in SF mul- tilayers with strong exchange fields. The observed ef- fects are over length scales much larger than those of the usual SF proximity effect and more like the much longer length scales associated with the standard prox- imity effect between a superconductor and a normal non- magnetic metal. These observations include measure- ments in superlattices 13 with ferromagnetic spacers and SQUIDs 14 with ferromagnetic interlayers. Superconduct- ing characteristics, such as a critical temperature and en- hanced sub-gap conductance, have been observed in point contact conductance measurements on s-wave supercon- ductor/half metallic systems. 15 Perhaps most compelling is the observation of a Josephson current through a strong almost half-metallic, ferromagnet. 16 All of these experi- ments indicate long range superconducting correlations that are not destroyed by a strong exchange field: a