The temperature, T, dependence of the magnetic penetration depth, λ, of grain-aligned ${\mathrm{YBa}}_2{\mathrm{Cu}}_4{\mathrm{O}}_8$ has been measured along the ab plane and c axis. Both ${\lambda }_{\mathrm{ab}}\mathrm{}\left(T\right)\mathrm{}$ and ${\lambda }_c\mathrm{}\left(T\right)\mathrm{}$ vary as $\sqrt{T}$ up to $\sim {0.4T}_c$ implying a square-root density of states at low energy. The results are discussed in terms of a proximity model of alternating stacked superconducting and normal layers.

• Received 21 December 1998

DOI:https://doi.org/10.1103/PhysRevB.59.R6635