The magneto-optical Faraday effect in spin liquid candidates

TL;DR

This paper proposes using the magneto-optical Faraday effect to detect the dynamic Hall conductivity in spin liquid candidates, predicting distinct signatures based on the spinon state and feasibility in specific materials.

Contribution

It introduces a novel experimental approach to probe spin liquids via the Faraday effect, predicting specific signatures for different spinon states and estimating experimental detectability.

Findings

Finite Faraday rotation expected for spinons with Fermi surface.

No rotation predicted for massless Dirac spinons.

Feasible detection in specific candidate materials.

Abstract

We propose an experiment to use the magneto-optical Faraday effect to probe the dynamic Hall conductivity of spin liquid candidates. Theory predicts that an external magnetic field will generate an internal gauge field. If the source of conductivity is in spinons with a Fermi surface, a finite Faraday rotation angle is expected. We predict the angle to scale as the square of the frequency rather than display the standard cyclotron resonance pattern. Furthermore, the Faraday effect should be able to distinguish the ground state of the spin liquid, as we predict no rotation for massless Dirac spinons. We give a semiquantitative estimate for the magnitude of the effect and find that it should be experimentally feasible to detect in both $\kappa$-(ET)$_2$Cu$_2$(CN)$_3$ and, if the spinons form a Fermi surface, Herbertsmithite. We also comment on the magneto-optical Kerr effect and show that the imaginary part of the Kerr angle may be measurable.