  The spin chemical potential characterizes the tendency of spins to diffuse.
Probing the spin chemical potential could provide insight into materials such
as magnetic insulators and spin liquids and aid optimization of spintronic
devices. Here, we introduce single-spin magnetometry as a generic platform for
non-perturbative, nanoscale characterization of spin chemical potentials. We
use this platform to investigate magnons in a magnetic insulator, surprisingly
finding that the magnon chemical potential can be efficiently controlled by
driving the system's ferromagnetic resonance. We introduce a symmetry-based
two-fluid theory describing the underlying magnon processes, realize the first
experimental determination of the local thermomagnonic torque, and illustrate
the detection sensitivity using electrically controlled spin injection. Our
results open the way for nanoscale control and imaging of spin transport in
mesoscopic spin systems.
