Detecting Spin Fractionalization in a Spinon Fermi Surface Spin Liquid: Prediction and Application for YbMgGaO$_4$

Continuing the recent proposal of the spinon Fermi surface U(1) spin liquid state for YbMgGaO$_4$ in Yao-Dong Li, {\it et al}, arXiv:1612.03447 and Yao Shen, et al, Nature 2016, we explore the experimental consequences of the external magnetic fields on this exotic state. Specifically, we focus on the weak field regime where the spin liquid state is preserved and the fractionalized spinon excitations remain to be a good description of the magnetic excitations. From the spin-1/2 nature of the spinon excitation, we predict the unique features of spinon continuum when the magnetic field is applied to the system. Due to the small energy scale of the rare-earth magnets, our proposal for the spectral weight shifts in the magnetic fields can be immediately tested by inelastic neutron scattering experiments. Several other experimental aspects about the spinon Fermi surface and spinon excitations are discussed and proposed. Our work provides a new way to examine the fractionalized spinon excitation and the candidate spin liquid states in the rare-earth magnets like YbMgGaO$_4$.