Intertwined charge, spin, and pairing orders in doped iron ladders

TL;DR

This study investigates doped iron ladder compounds using a two-orbital Hubbard model, revealing magnetic order changes, hole pairing, and potential precursor states to superconductivity, emphasizing the role of Hund's coupling.

Contribution

It provides the first detailed analysis of intertwined magnetic and pairing orders in doped iron ladders using ab initio parameters and DMRG, highlighting the importance of Hund's coupling.

Findings

Incommensurate magnetic order emerges upon hole doping.

Negative binding energy indicates hole pairing at intermediate U.

Dominance of intra-orbital spin-singlet pairing channel.

Abstract

Motivated by recent experimental progress on iron-based ladder compounds, we study the doped two-orbital Hubbard model for the two-leg ladder BaFe$_2$S$_3$. The model is constructed by using {\it ab initio} hopping parameters and the ground state properties are investigated using the density matrix renormalization group method. We show that the $(\pi,0)$ magnetic ordering at half-filling, with ferromagnetic rungs and antiferromagnetic legs, becomes incommensurate upon hole doping. Moreover, depending on the strength of the Hubbard $U$ coupling, other magnetic patterns, such as $(0,\pi)$, are also stabilized. We found that the binding energy for two holes becomes negative for intermediate Hubbard interaction strength, indicating hole pairing. Due to the crystal-field split among orbitals, the holes primarily reside in one orbital, with the other one remaining half-filled. This resembles orbital selective Mott states. The formation of tight hole pairs continues with increasing hole density, as long as the magnetic order remains antiferromagnetic in one direction. The study of pair-pair correlations indicates the dominance of the intra-orbital spin-singlet channel, as opposed to other pairing channels. Although in a range of hole doping pairing correlations decay slowly, our results can also be interpreted as corresponding to a charge-density-wave made of pairs, a precursor of eventual superconductivity after interladder couplings are included. Such scenario of intertwined orders has been extensively discussed before in the cuprates, and our results suggest a similar physics could exist in ladder iron-based superconductors. Finally, we also show that a robust Hund's coupling is needed for pairing to occur.