Odd triplet superconductivity in superconductor-ferromagnet structures with a narrow domain wall

TL;DR

This paper investigates how narrow domain walls in superconductor-ferromagnet structures induce both short-range and long-range odd triplet superconducting correlations, affecting Josephson currents and the density of states.

Contribution

It provides analytical solutions for Green's functions describing short-range and long-range triplet components in SF structures with narrow domain walls, highlighting their dependence on magnetic properties.

Findings

Long-range triplet component amplitude depends on exchange energy and scattering time.

Josephson current can be positive or negative depending on magnetic chirality.

Density of states contributions differ for short-range and long-range components.

Abstract

We study the proximity effect in superconductor-ferromagnet (SF) structure with a narrow domain wall (DW) at the SF interface. The width of the domain wall is assumed to be larger than the Fermi wave length, but smaller than other characteristic lengths (for example, the ''magnetic'' length). The transmission coefficient is supposed to be small so that we deal with a weak proximity effect. Solving the linearized Eilenberger equation, we find analytical expressions for quasiclassical Green's functions. These functions describe the short-range (SR) condensate components, singlet and triplet with zero projection of the total spin on the quantization z-axis, induced in F due to the proximity effect as well as long-range odd triplet component (LRTC) with a nonzero projection of the total spin of Cooper pairs on the $z$% -axis. The amplitude of the LRTC essentially depends on the product $h\tau $ and increases with increasing the exchange energy $h$ ($\tau $ is the elastic scattering time). We calculate the Josephson current in SFS junction with a thickness of the F layer much greater than the penetration length of the SR components. The Josephson critical current caused by the LRTC may be both positive and negative depending on chirality of the magnetic structure in F. The density of states (DOS) in a diffusive SF bilayer is also analyzed. It is shown that the contributions of the SR and LR components to the DOS in F have a different dependence on the thickness $d$ of the F layer (nonmonotonous and monotonous).