Absolute values of the London penetration depth in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+y}$ measured by zero field ESR spectroscopy on Gd doped single crystals

Zero-field electron spin resonance (ESR) of dilute Gd ions substituted for Y in the cuprate superconductor ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+y}$ is used as a novel technique for measuring the absolute value of the low-temperature magnetic penetration depth $\lambda \left(\overrightarrow{T}0\right).$ The Gd ESR spectrum of samples with $\approx 1\%$ substitution was obtained with a broadband microwave technique that measures power absorption bolometrically from 0.5 to 21 GHz. This ESR spectrum is determined by the crystal field that lifts the level degeneracy of the spin $7/2{\mathrm{Gd}}^{3+}$ ion and details of this spectrum provide information concerning oxygen ordering in the samples. The magnetic penetration depth is obtained by relating the number of Gd ions exposed to the microwave magnetic field to the frequency-integrated intensity of the observed ESR transitions. This technique has allowed us to determine precise values of $\lambda$ for screening currents flowing in the three crystallographic orientations $(â,$ $\mathrm{b̂},$ and $ĉ)$ in samples of ${\mathrm{Gd}}_x{\mathrm{Y}}_{1-x}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+y}$ of three different oxygen contents $y=0.993\mathrm{}{(T}_c=89\mathrm{}\mathrm{K}),$ $y=0.77\mathrm{}{(T}_c=75\mathrm{}\mathrm{K}),$ and $y=0.52\mathrm{}{(T}_c=56\mathrm{}\mathrm{K}).\mathrm{}$ The in-plane values are found to depart substantially from the widely reported relation $T_c\propto 1/{\lambda }^2.$