Pairing Symmetry and Flux Quantization in a Tricrystal Superconducting Ring of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">Y</mml:mi><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Ba</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Cu</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mrow><mml:mn>7</mml:mn><mml:mo>−</mml:mo><mml:mi>δ</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>

We have used the concept of flux quantization in superconducting $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ 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, $\frac{{\ensuremath{\Phi}}_{0}}{2}=\frac{h}{4e}$ has been observed in the 3-junction ring, but not in the 2-junction rings. These results are consistent with $d$-wave pairing symmetry.

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