Block Mott insulating state induced by next-nearest neighbor hopping in the S = 3/2 zigzag chain BaCoTe2O7

Abstract

Quasi-one-dimensional correlated electronic multi-orbital 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-fields splitting, the electronic correlations, and strong quantum fluctuations. Recently, the intriguing cobalt zigzag chain system BaCoTe$_2$O$_7$, 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 theory 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 BaCoTe$_2$O$_7$. 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 BaCoTe$_2$O$_7$ provide guidance to experimentalists and theorists working on this zigzag one-dimensional chain and related materials.