Theory of antiferromagnetic Heisenberg spins on breathing pyrochlore lattice

Abstract

Spin-singlet orders are studied for the antiferromagnetic Heisenberg model with spin $S$>1/2 on a breathing pyrochlore lattice, where tetrahedron units are weakly coupled and exchange constants have two values $0<J^{\prime }\ll J$. The ground state has a thermodynamic degeneracy at $J^{\prime }$=0, and I have studied lattice symmetry breaking associated to lifting this degeneracy. Third-order perturbation in $J^{\prime }$ for general spin $S$ shows that the effective Hamiltonian has a form of three-tetrahedron interactions of pseudospins $\tau$, which is identical to that previously derived for $S$=1/2, and I have calculated their matrix elements for general $S$. For this effective Hamiltonian, I have obtained its mean-field ground state and investigated the possibility of lattice symmetry breaking for the cases of $S$=3/2 and $1$. In contrast to the $S$=1/2 case,$\tau$'s response to conjugate field has a $Z_3$ anisotropy in its internal space, and this stabilizes the mean-field ground state. The mean-field ground state has a characteristic spatial pattern of spin correlations related to the lattice symmetry breaking. Spin structure factor $S(q)$ is calculated and found to have symmetry broken parts with amplitudes of the same order as the isotropic part.

To be published in Progress of Theoretical and Experimental Physics. 28 pages, 8 figures

References in corpus (3)

• Electronic Orbital Currents and Polarization in Mott Insulators
• Novel Phase Transitions in the Breathing Pyrochlore Lattice: 7Li-NMR on LiInCr4O8 and LiGaCr4O8
• Magnetic Phase Diagram of the Breathing Pyrochlore Antiferromagnet LiGa1-xInxCr4O8

Cited by in corpus (8)

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• Spin ordering induced by lattice distortions in classical Heisenberg antiferromagnets on the breathing pyrochlore lattice
• Competing quantum spin liquids, gauge fluctuations, and anisotropic interactions in a breathing pyrochlore lattice
• Signatures of a magnetic superstructure phase induced by ultrahigh magnetic fields in a breathing pyrochlore antiferromagnet
• Magnetic properties of a capped kagome molecule with 60 quantum spins
• Phase diagram of the antiferromagnetic $J_1$-$J_2$ spin-$1$ pyrochlore Heisenberg model
• Nematicity Liquid in a Trimerized-Kagome Antiferromagnet