FiniteU-induced competing interactions, frustration, and quantum phase transition in a triangular-lattice antiferromagnet

Abstract

The 120 0 ordered antiferromagnetic state of the Hubbard model on a triangular lattice presents an interesting case of U -controlled competing interactions and frustration. The spin stiffness is found to vanish at U * stiff ≈ 6 and the spin-wave energy ωM at q M = (2π/3, 0) etc. is found to vanish at U * M ≈ 6.8 due to competing spin couplings generated at finite U . The loss of magnetic order due to the magnetic instability at qM yields a first-order quantum phase transition in the insulating state at U = U * M . Implications of the quantum spin disordered insulator to the spin-liquid state and Mott transition in the organic systems κ − (BEDT − TTF)2X are discussed. Effects of hole and electron doping on magnetic ordering and spin stiffness are also examined.

Magnetic excitations, phase diagram and order-by-disorder in the extended triangular-lattice Hubbard model

“…2(a) shows a typical structure factor S (q, ω) evaluated in the 120 • ordered phase away from the phase boundaries. The ordering wavevector is at the K points in the BZ, and spectral weight vanishes at the Γ point in agreement with previous results [45], in which only the t = 0 case was studied. This coplanar but non-collinear state has three spin excitation modes; at low energies the susceptibility matrix is approximately diagonal in global coordinates µ = x, y, z, allowing us to characterize each of these modes as having either purely inplane (S x , S y ) or out-of-plane (S z ) character.…”

“…We also confirmed a strong particle-hole asymmetry, as was seen for the t = 0 model in Ref. [45], but since a full study of the doping dependent phase diagram is beyond the scope of this work we concentrate on the case of half-filling for the remainder.…”

“…However, the following numerical studies provided clear evidence for a long-range 120 • antiferromagnetic (AFM) order in the strong coupling limit [40][41][42][43][44]. Away from strong coupling, a spin stiffness analysis based on a mean-field approximation indicates a loss of 120 • magnetic order at U ∼ 6t [45]. An intermediate QSL phase (the so-called weak-Mott insulator) might additionally be stabilized for moderate Hubbard interaction U ∼ 8t, as indicated by the variational cluster approximation (VCA) [46], path-integral renormalization group analysis [47], and series expansions [48].…”

Interaction-driven topological insulators on the kagome and the decorated honeycomb lattices

“…The same antiferromagnetic state has also been found on the triangular lattice. [62][63][64] The further-neighbor interaction is decoupled in a similar way:…”

Spin-orbit coupling induced magnetic anisotropy and large spin wave gap in NaOsO3

“…Due to the presence of spin mixing terms in the Hamiltonian (equations (1) and (2)), spin is not a good quantum number, and we therefore use the general method to investigate spin waves [13]. In the (π, π, π) AFM ground state 0 Y ñ | of the three-orbital model, we consider the time-ordered transverse spin fluctuation propagator in the composite orbital-sublattice basis:…”