RKKY interaction in Layered Superconductors with Anisotropic Pairing

The RKKY interaction between rare-earth (RE) ions in high-$T_c$ superconductors is considered at $T\ll T_c$. It is shown that this interaction consists of two terms: conventional oscillating one and the positive term, which is proportional to the gap function and decreases in the $2D$ case inversely proportional to the distance. In the antiferromagnetic state of the RE subsystem this positive interaction gives rise for frustrations which diminishes the Neel temperature. In the case of strongly anisotropic gap function this frustration produces two different values of the effective nearest neighbor exchange coupling between RE ions along the $a$ and $b$. This anisotropy has been established experimentally in Ref.\cite{6,7,8}.