Odd triplet superconductivity in a superconductor/ferromagnet structure with a narrow domain wall

We study 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 wavelength 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 ferromagnet (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 superconductor/ferromagnet/superconductor 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).

Figure 1

Schematic picture of a SF bilayer with a domain wall (the shadowed stripe) at the SF interface. The width of the DW is $w$; $v/h,l$ denote the “magnetic” length and the mean free path.

Figure 2

DOS variation $\delta \nu \left(ϵ\right)$ at the outer surface of the F layer vs the normalized energy $ϵ/\Delta$ plotted on the basis of Eqs. (52, 53). The contributions of the SR components, $f_{0,3}$, are shown in (a) and the contributions of the LRTC, $f_1$, is shown in (b). The following values of parameters are used: ${\theta }_h\equiv d/{\xi }_h=1.5$ (solid lines) and ${\theta }_h=1.8$ (dotted lines); $\Gamma /\Delta =0.1$, $d/{\gamma }_F=0.4$, and $K_1=0.6{\varkappa }_h$. The parameters ${\varkappa }_{ϵ}$ and $K_3$ are assumed to be much smaller than ${\varkappa }_h$.

Figure 3

The same graphs as in Fig. 2 with parameters: ${\theta }_h\equiv d/{\xi }_h=1.5$ (solid lines) and ${\theta }_h=1.8$ (dotted lines); $\Gamma /\Delta =0.05$, $d/{\gamma }_F=0.2$, and $K_1=0.6{\varkappa }_h$. The parameters ${\varkappa }_{ϵ}$ and $K_3$ are assumed to be much smaller than ${\varkappa }_h$.