Block Mott insulating state induced by next-nearest-neighbor hopping in the S= 32 zigzag chain BaCoTe2 O7

Quasi-one-dimensional correlated electronic multiorbital systems with either ladder or chain geometries continue attracting considerable interest due to their complex electronic phases arising from the interplay of the hopping matrix, the crystal-field splitting, the electronic correlations (Hubbard repulsion U and Hund coupling JH), and strong quantum fluctuations. Recently, the intriguing cobalt zigzag chain system BaCoTe2O7, with electronic density n=7, was prepared experimentally. Here, we systematically study the electronic and magnetic properties of this quasi-one-dimensional compound from the theoretical perspective. Based on first-principles density functional theory calculations, strongly anisotropic one-dimensional electronic Co 3d bands were found near the Fermi level. By evaluating the relevant hopping amplitudes, we provide the magnitude and origin of the nearest-neighbor (NN) and next-nearest-neighbor (NNN) hopping matrices in BaCoTe2O7. With this information, we constructed a three-orbital electronic Hubbard model for this zigzag chain system, and studied two cases: with only a NN hopping matrix, and with NN plus NNN hopping matrices. Introducing the Hubbard and Hund couplings and studying the model via the density matrix renormalization group method, we constructed the ground-state phase diagram. A robust staggered ↑-↓-↑-↓ antiferromagnetic (AFM) region was found when only the NN hopping matrix in the chain direction was employed. However, for the realistic case where the NNN hopping matrix is also included, the dominant state becomes instead a block AFM ↑-↑-↓-↓ order, in agreement with experiments. The system displays Mott insulator characteristics with three half-filled orbitals, when the block AFM order is stable. Our results for BaCoTe2O7 provide guidance to experimentalists and theorists working on this zigzag one-dimensional chain and related materials.