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

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.