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The periodic response of magnetoresistance to an externally tunable parameter, such as magnetic field or chemical composition, in the bulk or an artificially designed material has been exploited for technological applications as well as to advance our understanding of many novel effects of solid state physics. Some notable examples are the giant magnetoresistance effect in layered materials, the quantum hall effect in semiconductor heterostructure and the phase coherence of electronic wave function in disordered metals. In recent years, the ability to engineer materials at the nanoscale has played a key role in exploring new phenomenon. Using a system involving periodic Co dots array in direct contact with a surrounding polycrystalline Cu film, we report the observation of giant thermal hysteresis and an anomalous oscillatory magnetoresistance behavior. The unusual aspects of oscillatory magnetoresistance include its observation along only one field scan direction in an intermediate temperature range of 100 K < T < 200 K. Reducing the thickness of the Cu film weakens the magnetoresistance oscillation. These properties suggest a new phenomenon, which could be harnessed for future technological applications., Comment: 5 pages, 4 figures; Topographical Nanoengineering; Magnetoresistance Oscillation, Giant Thermal Hysteresis