Probing the Order Parameter and thec-Axis Coupling of High-TcCuprates by Penetration Depth Measurements

We have measured the low-temperature $\left(T\right)$ dependence of the anisotropic penetration depth $\lambda \left(T\right)$ of magnetically aligned powders of $\mathrm{HgBa}{}_2\mathrm{Ca}{}_{n-1\mathrm{}}\mathrm{Cu}{}_n{\mathrm{O}}_{2n+2+\delta }$ ( $n=1\mathrm{}$ and 3) down to 1.2 K. For both members the $T$ dependence of the in-plane penetration depth ${\lambda }_{\mathrm{ab}}\left(T\right)$ is strongly linear, whereas the out-of-plane component ${\lambda }_c\left(T\right)$, for $n=1\mathrm{}$ and 3, varies as $T^5$ and $T^2$, respectively. For comparison, we also report ${\lambda }_c\left(T\right)$ data for grain-aligned $\mathrm{YBa}{}_2\mathrm{Cu}{}_3{\mathrm{O}}_{7-\delta }$ ( $\delta =0.0\mathrm{}$ and 0.43) which vary as $T$ and $T^2$, respectively. The results are discussed in terms of $d_{x^2-y^2}-$wave symmetry of the order parameter in cuprates.