Existence of Saturated Ferromagnetic and Spiral States in 1D Lieb-Ferrimagnetic Models away from Half-Filling

TL;DR

This study investigates ferromagnetic and spiral states in one-dimensional Lieb-ferrimagnetic Hubbard models away from half-filling, revealing conditions under which saturated ferromagnetism appears, influenced by local-loop structures and flat bands.

Contribution

It demonstrates that saturated ferromagnetism can occur in certain Lieb-ferrimagnetic chains away from half-filling, highlighting the role of local-loop structures beyond flat band conditions.

Findings

Ferromagnetic states appear in the PD and OD chains away from half-filling.

Flat band presence alone does not guarantee ferromagnetism.

Local-loop structures significantly influence the emergence of ferromagnetic states.

Abstract

In order to study conditions for the appearance of ferromagnetism in a wide filling region, we investigate numerically three types of one-dimensional Lieb-ferrimagnetic Hubbard models: a periodic diamond (PD) chain, a periodic alternately-attached leg (PAAL) chain and an open diamond (OD) chain. All of these models have a flat band (or equivalently, degenerate single-electron eigenvalues). The PD and OD chains commonly have a local-loop structure. Nagaoka's theorem holds only in the PD chain. At half-filling, it have been rigorously proven that all of these models are ferrimagnet. Away from half-filling, however, quite different magnetic properties are found. In the fillings 1/3< rho_e <1/2, the ground state of the PD chain for a infinitely-large U is the extended ferromagnetic state, that is, the saturated ferromagnetic state or the spiral state for odd or even number of electrons, respectively. In the PAAL chain, on the other hand, there is no magnetic order. Thus, the flat band is found to be not a sufficient condition of the extended ferromagnetic state. We find, moreover, that the saturated ferromagnetism appears in the OD chain, although the Nagaoka theorem does not hold on this chain. This indicates that the local-loop structure plays an important role on the appearance of the extended ferromagnetic state.