Effective Hamiltonians for some highly frustrated magnets

Abstract

In prior work, the authors developed a method of degenerate perturbation theory about the Ising limit to derive an effective Hamiltonian describing quantum fluctuations in a half-polarized magnetization plateau on the pyrochlore lattice. Here, we extend this formulation to an arbitrary lattice of corner sharing simplexes of $q$ sites, at a fraction $(q-2k)/q$ of the saturation magnetization, with $0<k<q$. We present explicit effective Hamiltonians for the examples of the checkerboard, kagome, and pyrochlore lattices. The consequent ground states in these cases for $k=1$ are also discussed.

10 pages, 2 figures,. Conference proceedings for Highly Frustrated Magnetism 2006

References in corpus (3)

• The phase diagram of the hexagonal lattice quantum dimer model
• Quantum effects in a half-polarized pyrochlore antiferromagnet
• Effective Hamiltonian for the Pyrochlore antiferromagnet: semiclassical derivation and degeneracy

Cited by in corpus (6)

• Highly Frustrated Magnetic Clusters: The kagome on a sphere
• Order from structural disorder in $XY$ pyrochlore antiferromagnet $\mathrm{E}{\mathrm{r}}_2\mathrm{T}{\mathrm{i}}_2{\mathrm{O}}_7$
• Magnetization Process of the Spin-S Kagome-Lattice Heisenberg Antiferromagnet
• Metamagnetic jump in the spin-1/2 antiferromagnetic Heisenberg model on the square-kagome lattice
• Ordered Phases of the Anisotropic Kagome Lattice Antiferromagnet in a Field
• Tunneling-induced restoration of classical degeneracy in quantum kagome ice