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We study how a population of spin waves can be characterized from theanalysis of the electrical microwave noise delivered by an inductive antennaplaced in its vicinity. The measurements are conducted on a syntheticantiferromagnetic thin stripe covered by a micron-sized antenna that feeds aspectrum analyser after amplification. The antenna noise contains twocontributions. The population of incoherent spin waves generates a fluctuatingfield that is sensed by the antenna: this is the "magnon noise". The antennanoise also contains the contribution of the electronic fluctuations: theJohnson-Nyquist noise. The latter depends on all impedances within themeasurement circuit, which includes the antenna self-inductance. As a result,the electronic noise contains information about the magnetic susceptibility ofthe stripe, though it does not inform on the absolute amplitude of the magneticfluctuations. For micrometer-sized systems at thermal equilibrium, theelectronic noise dominates and the pure magnon noise cannot be determined. Ifin contrast the spinwave bath is not at thermal equilibrium with themeasurement circuit, and if the spin wave population can be changed then onecould measure a mode-resolved effective magnon temperature provided specificprecautions are implemented.

Measuring a population of spin waves from the electrical noise of an inductively coupled antenna