Spinon resonance of two-dimensional U(1) spin liquids with Fermi surface.

We investigate signatures of spin liquids with spinon Fermi surfaces in electron spin resonance experiments. We focus on the magnetic field (h) and temperature (T) dependence of the linewidth η of the resonance peak in the ESR absorption spectrum. We show that in the presence of DM interaction, the linewidth is determined by the low-energy U(1) gauge fluctuations resulting in a characteristic η ~ h^2/3 scaling at T=0 and a more complicated behavior T/h + T^2/3 f(h/T), with an explicit form of the scaling function f(x), at finite T. We find that exchange anisotropy results in a weaker h and T dependence of η. We discuss relevance of our findings to experiments on the spin liquid candidate κ-ET and related materials.