From dimensional reduction to tetramerization in mixed ferro-antiferro breathing pyrochlores

Abstract

We study the spin-1/2 nearest-neighbor Heisenberg model on the breathing pyrochlore lattice in the mixed ferro-antiferromagnetic regime, where one tetrahedral sublattice is antiferromagnetic and the other ferromagnetic. The classical ground-state manifold is then that of the nearest-neighbor face-centered-cubic (fcc) antiferromagnet built from composite tetrahedral moments. Classical Monte Carlo simulations and the self-consistent Gaussian approximation show that thermal order-by-disorder lifts its subextensive degeneracy and selects the collinear Type-I state with wave vector $X=(1,0,0)$ through a strongly first-order transition. Pseudofermion functional renormalization group calculations for $S=1/2$ and $S=1$ reveal a nonmagnetic window adjacent to the decoupled antiferromagnetic-tetrahedron limit, beyond which $X$ order reappears. Density matrix renormalization group calculations show that this window is not featureless: the antiferromagnetic tetrahedra develop nearly ideal tetramer correlations, with four bonds carrying $⟨{\mathbf{S}}_i\cdot {\mathbf{S}}_j⟩\simeq -1/2$ and the two opposite bonds $\simeq +1/4$, while the structure factor retains broad maxima at $X$. A third-order effective Hamiltonian in the tetrahedral-singlet manifold explains this: reversing the sign of the inter-tetrahedron coupling converts Tsunetsugu's dimer selection into a uniform tetramer selection, as confirmed by exact diagonalization. A dynamic high-temperature expansion traces how local tetrahedral excitations give way to low-energy $X$-centered spectral weight. Finally, we place density-functional parameters for eight structures of spin-3/2 breathing chromium thiospinels in the classical phase diagram. The mapping reproduces the $\mathbf{k}=(1,0,0)$ order of CuInCr${}_4$S${}_8$, accounts for the absence of order in LiGaCr${}_4$S${}_8$, and predicts Type-I order for LiInCr${}_4$S${}_8$.

38 pages, 23 figures, 6 tables