Sr$_{2}$RuO$_{4}$ (SRO) is the prime candidate for chiral $p$-wave superconductor with critical temperature $T_{c}(SRO)sim$1.5 K. Chiral domains with opposite chiralities $p_{x}pm ip_{y}$ were proposed, but yet to be confirmed. We measure the field dependence of the point contact (PC) resistance between a tungsten tip and the SRO-Ru eutectic crystal, where micrometer-sized Ru inclusions are embedded in SRO with atomic sharp interface. Ruthenium is an $s$-wave superconductor with $T_{c}(Ru)sim$0.5 K, flux pinned near the Ru inclusions can suppress its superconductivity as reflected from the PC resistance and spectra. This flux pinning effect is originated from SRO textit{underneath} the surface and is very strong. To fully remove it, one has to thermal cycle the sample above $T_{c}(SRO)$. This resembles the thermal demagnetization for a ferromagnet, where ferromagnetic domains are randomized above its Curie temperature. Another way is by applying alternating fields with decreasing amplitude, resembling field demagnetization for the ferromagnet. The observed hysteresis in magnetoresistance can be explained by domain dynamics, providing support for the existence of chiral domains. The origin of strong pinning textit{underneath} the surface is also discussed.
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