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.
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