Degenerate perturbation theory of quantum fluctuations in a pyrochlore antiferromagnet

Abstract

We study the effect of quantum fluctuations on the half-polarized magnetization plateau of a pyrochlore antiferromagnet. We argue that an expansion around the easy axis limit is appropriate for discussing the ground state selection amongst the classically degenerate manifold of collinear states with a 3:1 ratio of spins parallel/anti-parallel to the magnetization axis. A general approach to the necessary degenerate perturbation theory is presented, and an effective quantum dimer model within this degenerate manifold is derived for arbitrary spin $s$. We also generalize the existing semiclassical analysis of Hizi and Henley [Phys. Rev. B {\bf 73}, 054403 (2006)] to the easy axis limit, and show that both approaches agree at large $s$. We show that under rather general conditions, the first non-constant terms in the effective Hamiltonian for $s\ge 1$ occur only at {\sl sixth} order in the transverse exchange coupling. For $s\ge 3/2$, the effective Hamiltonian predicts a magnetically ordered state. For $s\le 1$ more exotic possibilities may be realized, though an analytical solution of the resulting quantum dimer model is not possible.

References in corpus (3)

• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Monte Carlo study of half-magnetization plateau and magnetic phase diagram in pyrochlore antiferromagnetic Heisenberg model
• Effective Hamiltonian for the Pyrochlore antiferromagnet: semiclassical derivation and degeneracy

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