Charge and magnetic order in the spin-one-half Falicov-Kimball model with Hund coupling in two dimensions

TL;DR

This study investigates charge and magnetic ordering in the two-dimensional spin-one-half Falicov-Kimball model with Hund coupling, revealing dominant configurations and complex magnetic structures through exact-diagonalization and approximation methods.

Contribution

It provides a comprehensive categorization of ground-state charge and spin configurations in the model, highlighting the main phases and their stability regions.

Findings

Charge phase diagram dominated by phase segregation, stripes, and mixed configurations.

Magnetic phase diagram exhibits a richer variety of superstructures.

Identification of key stable configurations across electron concentrations.

Abstract

The spin-one-half Falicov-Kimball model with spin-dependent on-site interaction between localized ($f$) and itinerant ($d$) electrons is studied by small-cluster exact-diagonalization calculations and a well-controlled approximative method in two dimensions. The results obtained are used to categorize the ground-state configurations according to common features (charge and spin ordering) for all $f$ and $d$ electron concentrations ($n_f$ and $n_d$) on finite square lattices. It is shown that only a few configuration types form the basic structure of the charge phase diagram in the $n_f-n_d$ plane. In particular, the largest regions of stability correspond to the phase segregated configurations, the axial striped configurations and configurations that can be considered as mixtures of chessboard configurations and the full (empty) lattice. Since the magnetic phase diagram is much richer than the charge phase diagram, the magnetic superstructures are examined only at selected values of $f$ and $d$ electron concentrations.