Lattice symmetries and regular states in classical frustrated antiferromagnets

Details Lattice symmetries and regular states in classical frustrated antiferromagnets Lattice symmetries and regular states in classical frustrated antiferromagnets

2011-01-06

arxiv.org/abs/1101.1212v1

Phys. Rev. B 83, 184401 (2011)

Physics

Condensed Matter

Strongly Correlated Electrons

15 pages, 12 figures, 1 table

Scientific paper

10.1103/PhysRevB.83.184401

We consider some classical and frustrated lattice spin models with global O(3) spin symmetry. There is no general analytical method to find a ground-state if the spin dependence of the Hamiltonian is more than quadratic (i.e. beyond the Heisenberg model) and/or if the lattice has more than one site per unit cell. To deal with these situations, we introduce a family of variational spin configurations, dubbed "regular states", which respect all the lattice symmetries modulo global O(3) spin transformations (rotations and/or spin flips). The construction of these states is explicited through a group theoretical approach, and all the regular states on the square, triangular, honeycomb and kagome lattices are listed. Their equal time structure factors and powder-averages are shown for comparison with experiments. All the well known N\'eel states with 2 or 3 sublattices appear amongst regular states on various lattices, but the regular states also encompass exotic non-planar states with cubic, tetrahedral or cuboctahedral geometry of the T=0 order parameter. Whatever the details of the Hamiltonian (with the same symmetry group), a large fraction of these regular states are energetically stationary with respect to small deviations of the spins. In fact these regular states appear as exact ground-states in a very large range of parameter space of the simplest models that we have been looking at. As examples, we display the variational phase diagrams of the J1-J2-J3 Heisenberg model on all the previous lattices as well as that of the J1-J2-K ring-exchange model on square and triangular lattices.

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