Theory of antiferromagnetic Heisenberg spins on breathing pyrochlore lattice

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 $0<J' \ll J$. The ground state has a thermodynamic degeneracy at $J'$=0, and I have studied lattice symmetry breaking associated to lifting this degeneracy. Third-order perturbation in $J'$ 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.