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.