  We present results of the Relic Axion Dark-Matter Exploratory Setup (RADES),
a detector which is part of the CERN Axion Solar Telescope (CAST), searching
for axion dark matter in the 34.67$\mu$eV mass range. A radio frequency cavity
consisting of 5 sub-cavities coupled by inductive irises took physics data
inside the CAST dipole magnet for the first time using this filter-like
haloscope geometry. An exclusion limit with a 95% credibility level on the
axion-photon coupling constant of g$_{a\gamma}\gtrsim 4\times10^{-13}
\text{GeV}^{-1}$ over a mass range of 34.6738 $\mu$eV < $m_a$ < 34.6771 $\mu$eV
is set. This constitutes a significant improvement over the current strongest
limit set by CAST at this mass and is at the same time one of the most
sensitive direct searches for an axion dark matter candidate above the mass of
25 $\mu$eV. The results also demonstrate the feasibility of exploring a wider
mass range around the value probed by CAST-RADES in this work using similar
coherent resonant cavities.
