Higher order spin interactions mediated by the substrate

Abstract

Since the seminal works in the fifties it has been known that a bath of non-interacting electrons mediates an interaction between local moments (such as nuclear spins or magnetic impurities) coupled to distant sites of the lattice. Recent efforts in simultaneous control of multi-qubit arrays rely on defining quantum dots in environments which likewise contain electrons capable of mediating effective interactions. It is therefore interesting to analyze systems with more than two impurities in higher orders of perturbation theory. Here we derive and discuss the significance of the effective spin interactions between four impurities in fourth order of the coupling between the impurities and the substrate, mediated by conduction electrons of a two-dimensional square lattice. This effective interaction resembles the ring exchange -- a coupling of four spins appearing in perturbative treatment of the Hubbard model. Despite it being a higher-order effect, it can dramatically influence the magnetic ordering. We show that as an effective interaction between impurity spins, the ring exchange can also compete with the more familiar two-spin interactions.

9 pages,5 figures

References in corpus (11)

• RKKY in half-filled bipartite lattices: graphene as an example
• Effective spin model for the spin-liquid phase of the Hubbard model on the triangular lattice
• Phase Diagram of a Spin Ladder with Cyclic Four Spin Exchange
• Spin Bose-Metal and Valence Bond Solid phases in a spin-1/2 model with ring exchanges on a four-leg triangular ladder
• Demonstration of three- and four-body interactions between trapped-ion spins
• Kondo versus indirect exchange: the role of the lattice and the actual range of RKKY interactions in real materials
• Competition between Kondo screening and indirect magnetic exchange in a quantum box
• Exact diagonalization study of the Hubbard-parametrized four-spin ring exchange model on a square lattice
• Ring-Exchange Interaction Effects on Magnons in Dirac Magnet CoTiO${}_3$
• Vanishing RKKY interactions in Ce-based cage compounds
• RKKY to Kondo crossover in Helical Edge of a Topological Insulator

Cited by in corpus (2)

• Magnetic order through Kondo coupling to quantum spin liquids
• Dynamic-RKKY induced time-reversal symmetry breaking and chiral spin liquids