Quantum magnetism of iron-based ladders: Blocks, spirals, and spin flux

Motivated by increasing experimental evidence of exotic magnetism in low-dimensional iron-based materials, we present a comprehensive theoretical analysis of magnetic states of the multiorbital Hubbard ladder in the orbital-selective Mott phase (OSMP). The model we used is relevant for iron-based compounds of the ${A\mathrm{Fe}}₂{X}₃$ family (where $A=\mathrm{Cs}$, Rb, Ba, K are alkali metals and $X=\mathrm{S}$, Se are chalcogenides). To reduce computational effort, and obtain almost exact numerical results in the ladder geometry, we utilize a low-energy description of the Hubbard model in the OSMP---the generalized Kondo-Heisenberg Hamiltonian. Our main result is the doping vs interaction magnetic phase diagram. We reproduce the experimental findings on the ${A\mathrm{Fe}}₂{X}₃$ materials, especially the exotic block magnetism of ${\mathrm{BaFe}}₂{\mathrm{Se}}₃$ (antiferromagnetically coupled $2\ifmmode\times\else\texttimes\fi{}2$ ferromagnetic islands of the $\ensuremath{\uparrow}\ensuremath{\uparrow}\ensuremath{\downarrow}\ensuremath{\downarrow}$ form). As in recent studies of the chain geometry, we also unveil block magnetism beyond the $2\ifmmode\times\else\texttimes\fi{}2$ pattern (with block sizes varying as a function of the electron doping) and also an interaction-induced frustrated block-spiral state (a spiral order of rigidly rotating ferromagnetic islands). Moreover, we predict new phases beyond the one-dimensional system: a robust regime of phase separation close to half filling, incommensurate antiferromagnetism for weak interaction, and a quantum spin-flux phase of staggered plaquette spin currents at intermediate doping. Finally, exploiting the bonding/antibonding band occupations, we provide an intuitive physical picture giving insight into the structure of the phase diagram.