  We study how a population of spin waves can be characterized from the
analysis of the electrical microwave noise delivered by an inductive antenna
placed in its vicinity. The measurements are conducted on a synthetic
antiferromagnetic thin stripe covered by a micron-sized antenna that feeds a
spectrum analyser after amplification. The antenna noise contains two
contributions. The population of incoherent spin waves generates a fluctuating
field that is sensed by the antenna: this is the "magnon noise". The antenna
noise also contains the contribution of the electronic fluctuations: the
Johnson-Nyquist noise. The latter depends on all impedances within the
measurement circuit, which includes the antenna self-inductance. As a result,
the electronic noise contains information about the magnetic susceptibility of
the stripe, though it does not inform on the absolute amplitude of the magnetic
fluctuations. For micrometer-sized systems at thermal equilibrium, the
electronic noise dominates and the pure magnon noise cannot be determined. If
in contrast the spinwave bath is not at thermal equilibrium with the
measurement circuit, and if the spin wave population can be changed then one
could measure a mode-resolved effective magnon temperature provided specific
precautions are implemented.
