Magnetic order through Kondo coupling to quantum spin liquids

TL;DR

This paper investigates how magnetic order can emerge in localized spins coupled to Kitaev-type spin liquids, revealing diverse magnetic phases mediated by fractionalized excitations in various models.

Contribution

It introduces and analyzes three toy models showing how fractionalized excitations in spin liquids induce different magnetic orders in coupled localized spins.

Findings

Short-range interactions in the Kitaev model preserve the spin-liquid ground state.

Long-range RKKY interactions in the Yao-Lee model lead to antiferromagnetic order.

Square-lattice model exhibits diverse magnetic phases, including dimerized and Ising antiferromagnetic states.

Abstract

We study the emergence of magnetic order in localized spins that interact solely through their coupling to a Kitaev-type spin liquid. Using three toy models -- the Kitaev model, the Yao-Lee model, and a square-lattice generalization of the Kitaev model -- we calculate the effective exchange Hamiltonians mediated by the fractionalized excitations of these spin liquids. This setup is analogous to a Kondo lattice model, where conduction electrons are replaced by itinerant Majorana fermions. In the Kitaev model, our results show that the lowest-order perturbation theory generates short-range interactions with modified couplings and extending to sixth order introduces longer-range interactions while preserving the quantum spin-liquid ground state. Models involving more Majorana flavors on honeycomb and square lattices exhibit more complex behavior. The honeycomb Yao-Lee model with three flavors of itinerant Majorana fermions generates long-range RKKY-type interactions, leading to antiferromagnetic order and partial gapping of the Majorana fermion spectrum. In contrast, the square-lattice model produces a combination of anisotropic short- and long-range interactions, which can give rise to either a dimerized quantum paramagnetic state or an Ising antiferromagnet, depending on the parameters. These results illustrate the rich variety of magnetic orders that can be mediated by Kitaev-type spin liquids.