Origin of Biquadratic Exchange Interactions in a Mott Insulator as a Driving Force of Spin Nematic Order

Abstract

We consider a series of Mott insulators in unit of two orbitals each hosting spin-1/2 electron, and by pairing two spin-1/2 into spin-1 triplet, derive the effective exchange interaction between the adjacent units via fourth order perturbation theory. It turns out that the biquadratic exchange interaction between spin-1, which is one of the origins of the nematic order, arises only in processes where the four different electrons exchange cyclically along the twisted loop, which we call "twisted ring exchange" processes. We show that the term becomes the same order with the Heisenberg exchange interactions when the on-orbital Coulomb interaction is not too large. Whereas, the inter-orbital Coulomb interactions give rise to additional processes that cancel the twisted ring exchange, and strongly suppresses the biquadratic term. The Mott insulator with two electrons on degenerate two orbitals is thus not an ideal platform to study such nematic orders.

References in corpus (12)

• Strong electronic correlations from Hund's coupling
• Short-ranged RVB physics, quantum dimer models and Ising gauge theories
• Nematic order in square lattice frustrated ferromagnets
• The quadrupolar phases of the S=1 bilinear-biquadratic Heisenberg model on the triangular lattice
• Spin Nematic Phase in S=1 Triangular Antiferromagnets
• Quadrupolar correlations and spin freezing in S = 1 triangular lattice antiferromagnets
• On the origin of biquadratic exchange in spin 1 chains
• Quantum spin nematics, dimerization, and deconfined criticality in quasi-one dimensional spin-1 magnets
• Antiferromagnetic spin-S chains with exactly dimerized ground states
• Dimer-Quadrupolar Quantum Phase Transition in the Quasi-One-Dimensional Heisenberg Model with Biquadratic Interaction
• Berry phase induced dimerization in one-dimensional quadrupolar systems
• Magnetic Phase Diagram of Spin-1/2 Two-Leg Ladder with Four-Spin Ring Exchange

Cited by in corpus (11)

• Orbital and magnetic ordering in single-layer FePS3: A DFT+U study
• Thermodynamic properties of an $S=1/2$ ring-exchange model on the triangular lattice
• Evidence for biquadratic exchange in the quasi-two-dimensional antiferromagnet FePS${}_3$
• Range of biquadratic and triquadratic Heisenberg effective couplings deduced from multiorbital Hubbard models
• Pronounced 2/3 magnetization plateau in a frustrated $S$ = 1 isolated spin-triangle compound: Interplay between Heisenberg and biquadratic exchange interactions
• Spin nematics in frustrated spin-dimer systems with bilayer structure
• Abundant quadrupolar or nematic phases driven by the Heisenberg interactions in a spin-1 dimer system forming a bilayer
• Spin nematics next to spin singlets
• Effective spin model with anisotropic exchange interactions for the spin-orbit coupled Hubbard model at half-filling
• Nematic correlations and nematic Berezinskii-Kosterlitz-Thouless transition in spin-1 kagome lattice antiferromagnets
• Phononic enhancement and detection of hidden spin-nematicity and dynamics in quantum magnets