We report on muon spin rotation measurements of the internal magnetic field distribution $n\left(B\right)$ in the vortex solid phase of $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y$ (YBCO) single crystals, from which we have simultaneously determined the hole-doping dependences of the in-plane Ginzburg-Landau (GL) length scales in the underdoped regime. We find that $T_c$ has a sublinear dependence on $1∕{\lambda }_{ab}^2$, where ${\lambda }_{ab}$ is the in-plane magnetic penetration depth in the extrapolated limits $T\to 0$ and $H\to 0$. The power coefficient of the sublinear dependence is close to that determined in severely underdoped YBCO thin films, indicating that the same relationship between $T_c$ and the superfluid density is maintained throughout the underdoped regime. The GL coherence length ${\xi }_{ab}$ (vortex core size) is found to increase with decreasing hole-doping concentration and to exhibit a field dependence that is explained by proximity-induced superconductivity on the CuO chains. Both ${\lambda }_{ab}$ and ${\xi }_{ab}$ are enhanced near $\frac{1}{8}$ hole doping, supporting the belief by some that stripe correlations are a universal property of high-$T_c$ cuprates.

• Received 20 June 2007

DOI:https://doi.org/10.1103/PhysRevB.76.134518