Thermodynamics of spin waves in a quantum Hall ferromagnet

Under sufficiently large magnetic field, graphene exhibits quantum Hall ferromagnetism at partial fillings of the lowest Landau level, where strong Coulomb interaction breaks its SU(4) isospin symmetry. In particular, the ν= ±1 state hosts spin-wave excitations, whose generation and propagation have been studied using transport. In this talk, we present a local thermodynamic measurement of the ν= 1 state in the presence of magnons using a scanning single electron transistor (SET). Our electronic compressibility measurements show that pumping magnons into the bulk results in a reduction of the ν=1 gap, and allow us to extract numerous thermodynamic quantities including the magnon density, chemical potential, and average skyrmion spin. Our methods furnish an entirely novel means of probing strongly-interacting electronic phases by using electrically-addressable charge-neutral excitation, which is likely to be applicable to a variety of systems with strong interaction, in particular twisted van der Waals heterostructures with flat bands.