Long-range effects in superconductor-ferromagnet structures

We analyze the proximity effect in a superconductor/ferromagnet (S/F) structure with a local inhomogeneity of the magnetization in the ferromagnet near the S/F interface. We demonstrate that not only the singlet but also the triplet component of the superconducting condensate is induced in the ferromagnet due to the proximity effect. Although the singlet component of the condensate penetrates into the ferromagnet over a short length $\xi _{h}=\sqrt{D/h}$ ($h$ is the exchange field in the ferromagnet and $D$ the diffusion coefficient), the triplet component, being of the order of the singlet one at the S/F interface, penetrates over a long length $\sqrt{D/\epsilon}$ ($\epsilon$ is the energy). This long-range penetration into the ferromagnet leads to a significant increase of the ferromagnet conductance below the superconducting critical temperature $T_{c}$.