Odd Triplet Superconductivity in Superconductor-Ferromagnet Multilayered Structures

We demonstrate that in multilayered superconductor-ferromagnet structures a noncollinear alignment of the magnetizations of different ferromagnetic layers generates a triplet superconducting condensate which is odd in frequency. This triplet condensate coexists in the superconductors with the conventional singlet one but decays very slowly in the ferromagnet, which should lead to a large Josephson effect between the superconductors separated by the ferromagnet. Depending on the mutual direction of the ferromagnetic moments, the Josephson coupling can be both of 0 and of $\pi$ type.

Figure 1

Schematic diagram of a $S/F$ multilayered structure. On top: the magnetization $\mathbf{M}$ in different $F$ layers. The $\mathbf{M}$ vector drawn by solid lines corresponds to chiralities of the same sign. Opposite chirality is obtained if, for example, the magnetization of the right $F$ layer is rotated in the opposite direction (dashed line).

Figure 2

The normalized absolute value of the SC (dashed line) in the $S$ and the $F$ layers. The solid line represents the absolute value of the TC in the $F$ layer. Note that the SC (TC) is an even (odd) function of $x$. Here $d_S/{\xi }_T=d_S/{\xi }_S=0.3$, $d_S/{\xi }_J=5$, $\gamma =0.1$, and $\sin \alpha =0.5$. We have assumed a finite $SF$ interface resistance and set ${\gamma }_b=0.5$.