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.

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

References in corpus (11)

• Spin-lattice coupling in frustrated antiferromagnets
• Pyrochlore Antiferromagnet: A Three-Dimensional Quantum Spin Liquid
• Spin Driven Jahn-Teller Distortion in a Pyrochlore system
• Electronic Orbital Currents and Polarization in Mott Insulators
• Breathing Pyrochlore Lattice Realized in A-Site Ordered Spinel Oxides LiGaCr4O8 and LiInCr4O8
• Antiferromagnetic Quantum Spins on the Pyrochlore Lattice
• Frustrated Heisenberg antiferromagnet on a pyrochlore lattice
• Novel Phase Transitions in the Breathing Pyrochlore Lattice: 7Li-NMR on LiInCr4O8 and LiGaCr4O8
• Magnetic Phase Diagram of the Breathing Pyrochlore Antiferromagnet LiGa1-xInxCr4O8
• Ground-state selection and spin-liquid behaviour in the classical Heisenberg model on the breathing pyrochlore lattice
• Order by disorder and gauge-like degeneracy in quantum pyrochlore antiferromagnet

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