  We search for the dark photon dark matter (DPDM) using a cryogenic
millimeter-wave receiver. DPDM has a kinetic coupling with electromagnetic
fields with a coupling constant of $\chi$, and is converted into ordinary
photons at the surface of a metal plate. We search for signal of this
conversion in the frequency range $18\text{--}26.5\,\mathrm{GHz}$, which
corresponds to the mass range $74\text{--}110\,mu\mathrm{eV}/c^2$. We observed
no significant signal excess, allowing us to set an upper bound of $\chi <
(0.3\text{--}2.0)\times 10^{-10}$ at 95\% confidence level. This is the most
stringent constraint to date, and tighter than cosmological constraints.
Improvements from previous studies are obtained by employing a cryogenic
optical path and a fast spectrometer.
