  An haloscope of the QUAX--$a\gamma$ experiment composed of an OFHC-Cu cavity
inside an 8.1 T magnet and cooled to $\sim200$ mK was put in operation for the
search of galactic axion with mass $m_a\simeq43~\mu\text{eV}$. The power
emitted by the resonant cavity was amplified with a Josephson Parametric
Amplifier whose noise fluctuations are at the Standard Quantum Limit (SQL).
With the data collected in about 1 h at the cavity frequency $\nu_c=10.40176$
GHz the experiment reached the sensitivity necessary for the detection of
galactic QCD-axion setting the $90\%$ confidence level (CL) limit to the
axion-photon coupling $g_{a\gamma\gamma}<0.639\cdot10^{-13}$ GeV$^{-1}$.
