Cyclotron resonance in a kagome spin liquid candidate material

We propose cyclotron resonance as an optical probe for emergent fractionalized excitations in $\mathrm{U}(1)$ quantum spin liquids, focusing on kagome antiferromagnets. In contrast to conventional systems, where cyclotron resonance directly couples to charged carriers, spinons in spin liquids are charge-neutral and interact only through an emergent gauge field, making direct probing challenging. We identify two key mechanisms by which an external physical electromagnetic field induces emergent electric and magnetic fields, enabling indirect coupling to spinons. Using these mechanisms, we compute the absorption rate of the cyclotron resonance response for Dirac spinons forming Landau levels. Our analysis shows that, although the absorption per layer is small, the absence of a skin-depth limitation in insulating spin liquids allows for cumulative absorption comparable to graphene in realistic sample sizes for the recently discovered spin-liquid candidate material ${\mathrm{YCu}}_{3}{(\mathrm{OH})}_{6}{\mathrm{Br}}_{2}[\mathrm{Br}{}_{1\ensuremath{-}y}{(\mathrm{OH})}_{y}]$. Our proposed cyclotron-resonance measurement is a decisive, practical test for spinon Landau levels, providing quantitative expectations where clear experimental evidence has so far been lacking.