The alternating current (ac) Josephson effect in a time-independent
spatially-inhomogeneous setting is manifested by the occurrence of Josephson
oscillations - periodic macroscopic phase-induced collective motions of the
quantum condensate. So far, this phenomenon was observed at cryogenic
temperatures in superconductors, in superfluid helium, and in Bose-Einstein
condensates (BECs) of trapped atoms. Here, we report on the discovery of the ac
Josephson effect in a magnon BEC carried by a room-temperature ferrimagnetic
film. The BEC is formed in a parametrically populated magnon gas in the spatial
vicinity of a magnetic trench created by a dc electric current. The appearance
of the Josephson effect is manifested by oscillations of the magnon BEC density
in the trench, caused by a coherent phase shift between this BEC and the BEC in
the nearby regions. Our findings advance the physics of room-temperature
macroscopic quantum phenomena and will allow for their application for data
processing in magnon spintronics devices