Long range order in the classical kagome antiferromagnet: effective Hamiltonian approach

Abstract

Following Huse and Rutenberg [Phys. Rev. B 45, 7536 (1992)], I argue the classical Heisenberg antiferromagnet on the kagomé lattice has long-range spin order of the $\sqrt{3}\times \sqrt{3}$ type (modulo gradual orientation fluctuations of the spins' plane). I start from the effective quartic Hamiltonian for the soft (out of plane) spin fluctuation modes, and treat as a perturbation those terms which depend on the discrete coplanar state. Soft mode correlations, which become the coefficients of a discrete effective Hamiltonian, are estimated analytically.

4pp, no figures. Converted to PRB format, extensive revisions/some reorderings to improve clarity; some cuts

References in corpus (8)

• Dipolar spin correlations in classical pyrochlore magnets
• Power-law spin correlations in pyrochlore antiferromagnets
• Octupolar ordering of classical kagome antiferromagnets in two and three dimensions
• Classical antiferromagnet on a hyperkagome lattice
• Propagation and Ghosts in the Classical Kagome Antiferromagnet
• Order by disorder and gauge-like degeneracy in quantum pyrochlore antiferromagnet
• Effective Hamiltonian for the Pyrochlore antiferromagnet: semiclassical derivation and degeneracy
• Depleted pyrochlore antiferromagnets

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