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We report an extensive high-sensitivity search for axion dark matter above 1\, GHz at the Center for Axion and Precision Physics Research (CAPP). The cavity resonant search, exploiting the coupling between axions and photons, explored the frequency (mass) range of 1. 025\, GHz (4. 24\, eV) to 1. 185\, GHz (4. 91\, eV). We have introduced a number of innovations in this field, demonstrating the practical approach of optimizing all the relevant parameters of axion haloscopes, extending presently available technology. The CAPP 12\, T magnet with an aperture of 320\, mm made of Nb₃Sn and NbTi superconductors surrounding a 37-liter ultralight-weight copper cavity is expected to convert DFSZ axions into approximately 10² microwave photons per second. A powerful dilution refrigerator, capable of keeping the core system below 40\, mK, combined with quantum-noise limited readout electronics, achieved a total system noise of about 200\, mK or below, which corresponds to a background of roughly 4 10³ photons per second within the axion bandwidth. The combination of all those improvements provides unprecedented search performance, imposing the most stringent exclusion limits on axion--photon coupling in this frequency range to date. These results also suggest an experimental capability suitable for highly-sensitive searches for axion dark matter above 1\, GHz.
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