We report the observation of half-integer magnetic flux quantization in mesoscopic rings of superconducting $beta$-Bi$_2$Pd thin films. The half-quantum fluxoid manifests itself as a $pi$ phase shift in the quantum oscillation of the critical temperature. This result verifies unconventional superconductivity of $beta$-Bi$_2$Pd, in accord with the expectation of a topological superconductor. We also discuss the strong indication that $beta$-Bi$_2$Pd is a spin-triplet superconductor.
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