  We report evidence for the existence of a supercurrent of magnons in a magnon
Bose-Einstein condensate prepared in a room temperature yttrium-iron-garnet
magnetic film and subject to a thermal gradient. The magnon condensate is
formed in a parametrically populated magnon gas, and its temporal evolution is
studied by time-, frequency- and wavector-resolved Brillouin light scattering
spectroscopy. It has been found that local heating in the focal point of a
probing laser beam enhances the temporal decrease in the density of the freely
evolving magnon condensate after the termination of the pumping pulse, but it
does not alter the relaxation dynamics of the gaseous magnon phase. This
phenomenon is understood as the appearance of a magnon supercurrent within the
condensate due to a temperature- and, consequently, magnetisation-gradient
induced phase gradient in the condensate wave function.
