Penetration Depth Measurements of 3D $\mathrm{XY}$ Critical Behavior in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6.95}$ Crystals

We report measurements of the electromagnetic penetration depth $\lambda \mathrm{}\left(T\right)\mathrm{}$ in nominally pure crystals of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6,95}$, for temperatures close to the critical temperature $T_c$. Over the range $\frac{0.001<(T_c-T)}{T_c<0.1\mathrm{}}$, we find that $\lambda \mathrm{}\left(T\right)\mathrm{}\propto {\left(\frac{1-T}{T_c}\right)}^{-y}$ with $y\approx 0.33$, consistent with the critical behavior of the three dimensional $\mathrm{XY}$ model. The measured critical behavior is not affected by the presence of small amounts of Zn impurities, in agreement with the Harris criterion.