Spin Orbit Scattering Effect on long-Range Odd Frequency Triplet Pairing in Ferromagnet/Superconductor Bilayers

Abstract

A formulation of triplet proximity effect in a ferromagnet/superconductor bilayer based on the de Gennes correlation function method is presented by extending the Takahashi–Tachiki theory. The inhomogeneous in-plane spiral magnetic order is employed in this approach the superconducting order parameter is a conventional spin singlet s-wave pairing, and the induced triplet pair amplitude arises as a result of the broken time-reversal invariance due to the presence of the rotating exchange field. A new type of triplet condensate still possesses the s-wave state but the symmetry requires an odd frequency parity. We find that the inhomogeneous exchange interaction leads to the appearance of the long-range odd frequency triplet pair amplitude, and the inclusion of the spin orbit scattering affects both short-range and long-range triplet components. The superconducting critical temperature of the diffusive ferromagnet/superconductor sandwiches is determined from the secular equation of the linearized gap equation in order to investigate the behavior of the induced triplet pairing. It is found that the induced long-range triplet component exists which arises from the modulation of the in-plane pair amplitudes in the transverse direction. Moreover, the possibility of the cryptoferromagnetic state is demonstrated in favor of superconductivity and this may explain a possible origin of the magnetically dead layer.