Spin liquid mediated RKKY interaction

We propose an RKKY-type interaction that is mediated by a spin liquid. If a spin liquid ground state exists such an interaction could leave a fingerprint by ordering underlying localized moments such as nuclear spins. This interaction has a unique phenomenology that is distinct from the RKKY interaction found in fermionic systems; most notably the lack of a Fermi surface and absence of the requirement for itinerant electrons, since most spin liquids are insulators. As a working example we investigate the two-dimensional spin-1/2 kagome antiferromagnet (KAFM), although the treatment remains general and can be extended to other spin liquids and dimensions. We find that several different nuclear spin orderings minimize the RKKY-type energy induced by the KAFM but are unstable due to a zero-energy flat magnon band. Despite this we show that a small magnetic field is able to gap out this magnon spectrum for some of the orderings resulting in an intricate nuclear magnetism.