Effective Hamiltonians for some highly frustrated magnets

TL;DR

This paper extends a method of deriving effective Hamiltonians for highly frustrated magnets to arbitrary corner-sharing lattices, providing explicit models for various lattices and analyzing their ground states.

Contribution

It generalizes previous work by formulating effective Hamiltonians for a broad class of lattices at specific magnetization fractions, including explicit examples and ground state discussions.

Findings

Derived effective Hamiltonians for checkerboard, kagome, and pyrochlore lattices.

Analyzed ground states for the case of k=1 in these lattices.

Extended the applicability of degenerate perturbation theory to arbitrary corner-sharing lattices.

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.