Pairing Symmetry and Flux Quantization in a Tricrystal Superconducting Ring of $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$

We have used the concept of flux quantization in superconducting $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ rings with 0, 2, and 3 grain-boundary Josephson junctions to test the pairing symmetry in high-$T_c$ superconductors. The magnetic flux threading these rings at 4.2 K is measured by employing a scanning superconducting quantum interference device microscope. Spontaneous magnetization of a half magnetic flux quantum, $\frac{{\Phi }_0}{2}=\frac{h}{4e}$ has been observed in the 3-junction ring, but not in the 2-junction rings. These results are consistent with $d$-wave pairing symmetry.