Determination of the magnetic field penetration depth in superconducting yttrium barium copper oxide: Deviations from the Bardeen-Cooper-Schrieffer laws

We have measured the low-field magnetization for a number of fine powders of ${\mathrm{Y}}_1{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ and applied a standard formula to determine the magnetic field penetration depth $\lambda \mathrm{}\left(T\right)\mathrm{}$ in the superconducting state. Consistent values of $\lambda \mathrm{}\left(0\right)\mathrm{}$ and similar temperature dependences $\lambda \mathrm{}\left(T\right)\mathrm{}$ are obtained for average particle diameters ranging from 1.1 to 9 μm. At low temperatures $\lambda \mathrm{}\left(T\right)\mathrm{}$ is not Bardeen-Cooper-Schrieffer-like, instead a $T^2$ law is observed. The implications of this result are discussed.