Vortex lattice disorder in ${\text{YBa}}_2{\text{Cu}}_3{\text{O}}_{7-\delta }$ probed using $\beta \text{-NMR}$

$\beta$-detected NMR $\left(\beta \text{-NMR}\right)$ has been used to study vortex lattice disorder near the surface of the high-$T_C$ superconductor ${\text{YBa}}_2{\text{Cu}}_3{\text{O}}_{7-\delta }$ (YBCO). The magnetic-field distribution from the vortex lattice was detected by implanting a low-energy beam of highly polarized ${{}^8\text{L}\text{i}}^{+}$ into a thin overlayer of silver on optimally doped, twinned, and detwinned YBCO samples. The resonance in Ag broadens significantly below the transition temperature $T_C$ as expected from the emerging field lines of the vortex lattice in YBCO. However, the lineshape is more symmetric and the dependence on the applied magnetic field is much weaker than expected from an ideal vortex lattice, indicating that the vortex density varies across the face of the sample, likely due to pinning at twin boundaries. At low temperatures the broadening from such disorder does not scale with the superfluid density.

Figure 1

(Color online) (a) Simulation of $p\left(B\right)$ in an applied field of 52 mT at a distance 90 nm from the superconductor using Eq. (5) convoluted with a Lorentzian of width ${\Delta }_{\text{D}}$. (b) The broadening of $p\left(B\right)$ versus the applied field. Solid lines represent $\sigma$ from Eq. (6) in the bulk, and 40 and 90 nm away from the superconductor. Long dashed line shows $\sigma$ at 90 nm from Eq. (9) for $D=4\mu \text{m}$ and $f=0.1$. Inset: sketch of a possible vortex arrangement including vortex trapping at twin boundaries spaced by $D$ and a regular triangular vortex lattice elsewhere. (c) $\sigma \left(T\right)$ (normalized at $T=0$), from Eq. (9) for $B_0=52\text{mT}$, $z=-90\text{nm}$, and $f=0.1$, is plotted against $T/T_C$ for different values of $D$. A $d$-wave temperature dependence of $\lambda \left(T\right)$ is used. (Ref. 37) In all figures $\lambda \left(0\right)=150\text{nm}$.

Figure 2

(Color online) Implantation profiles of ${{}^8\text{L}\text{i}}^{+}$ at energies of (a) 5 keV into 60 nm of Ag with the mean at 40 nm away from YBCO film and (b) 8 keV into 120 nm of Ag with the mean at 90 nm away from YBCO crystals, as calculated via TRIM.SP. (Ref. 45) Solid lines are phenomenological fits.

Figure 3

(Color online) $\beta \text{NMR}$ resonances in Ag/YBCO (crystal I) at temperatures 100, 80, 20, and 4.5 K measured in a magnetic field $B_0$ of 52.3 mT applied along YBCO $c$ axis. The solid lines are best fits using a Lorentzian.

Figure 4

(Color online) The vortex-related broadening below $T_C$, ${\Delta }_{\text{sc}}\left(T\right)=\Delta \left(T\right)-{\Delta }_{\text{ns}}$ of the twinned (full symbols) and detwinned (opaque squares) YBCO crystals in an applied field $B_0$. $\Delta \left(T\right)$ is the linewidth at temperature $T$ of the Lorentzian fits and ${\Delta }_{\text{ns}}$ is the constant linewidth in the normal state. Solid lines represent a fit using ${\Delta }_{\text{DVL}}=2.355\sigma$ where $\sigma$ is given in Eq. (9) and $D$ and $f$ are varied to fit the data. A $d$-wave temperature dependence of $\lambda \left(T\right)$ in YBCO is used, (Ref. 37) where $\lambda \left(0\right)=150\text{nm}$.

Figure 5

(Color online) Comparison of the field distributions in the three samples taken at temperatures 100 K (top panel), 5 K (crystals), and 10 K (film). The $x$ axis is shifted by $B_0$, the applied field which is 52.3 (51.7) mT for the crystals (film). Solid lines are Lorentzian fits and dashed lines are the simulation described in the text.

Figure 6

(Color online) Superconducting broadening ${\Delta }_{\text{sc}}\left(T\right)$ of $\beta \text{-NMR}$ resonance spectra at temperatures $\sim 4.5–10\text{K}$ in the three samples. The experimental broadening is compared with the linewidth of an ideal VL ${\Delta }_{\text{VL}}$ (dashed lines) and ${\Delta }_{\text{DVL}}$ of a disordered VL (solid lines), which are both weighted by the ${{}^8\text{L}\text{i}}^{+}$ profile given in Fig. 2.