Direct Observation of the Oxygen Isotope Effect on the In-Plane Magnetic Field Penetration Depth in Optimally Doped ${\mathrm{Y}\mathrm{B}\mathrm{a}}_2{\mathrm{C}\mathrm{u}}_3{\mathrm{O}}_{7-\delta }$

We report the first direct observation of the oxygen-isotope (${}^{16}\mathrm{O}/{}^{18}\mathrm{O}$) effect on the in-plane penetration depth ${\lambda }_{ab}$ in a nearly optimally doped ${\mathrm{Y}\mathrm{B}\mathrm{a}}_2{\mathrm{C}\mathrm{u}}_3{\mathrm{O}}_{7-\delta }$ film using the novel low-energy muon-spin rotation technique. Spin-polarized low-energy muons are implanted in the film at a known depth $z$ beneath the surface and precess in the local magnetic field $B(z)$. This feature allows us to measure directly the profile $B(z)$ of the magnetic field inside the superconducting film in the Meissner state and to make a straightforward determination of ${\lambda }_{ab}$. A substantial isotope shift $\Delta {\lambda }_{ab}/{\lambda }_{ab}=2.8(1.0)\%$ at 4 K is observed, implying that the in-plane effective supercarrier mass $m_{ab}^{*}$ is oxygen-isotope dependent with $\Delta m_{ab}^{*}/m_{ab}^{*}=5.5(2.0)\%$. These results are in good agreement with magnetization measurements on powder samples.

Figure 1

Magnetic field penetration profiles $B(z)$ on a logarithmic scale for a ${}^{16}\mathrm{O}$ substituted (closed symbols) and a ${}^{18}\mathrm{O}$ substituted (open symbols) ${\mathrm{Y}\mathrm{B}\mathrm{a}}_2{\mathrm{C}\mathrm{u}}_3{\mathrm{O}}_{7-\delta }$ film measured in the Meissner state at 4 K and an external field of 9.2 mT, applied parallel to the surface of the film. The data are shown for implantation energies 3, 6, 10, 16, 22, and 29 keV starting from the surface of the sample. Solid curves are best fits by Eq. (3). Error bars are smaller than the size of symbols. The inset shows schematically the distribution of the screening current in a thin anisotropic superconducting slab of thickness $2t$ in a magnetic field applied parallel to the flat surface. The screening current $J$ flows preferably parallel to the $ab$ planes, giving rise to an exponential field decay along the crystal $c$ axis. Because of twinning in the $ab$ plane ($a$ and $b$ axes are not distinguishable) the so-called in-plane magnetic penetration depth ${\lambda }_{ab}$ is measured.

Figure 2

Temperature dependence of ${\lambda }_{ab}^{-2}$ normalized by ${}^{16}\lambda _{ab}^{-2}(0)$ for ${}^{16}\mathrm{O}$ and ${}^{18}\mathrm{O}$ substituted ${\mathrm{Y}\mathrm{B}\mathrm{a}}_2{\mathrm{C}\mathrm{u}}_3{\mathrm{O}}_{7-\delta }$ fine powder samples as obtained from low-field SQUID magnetization measurements. The inset shows the low-temperature region between 10 and 60 K. The reproducibility of the oxygen exchange procedure was checked by the back exchange (crosses).