# Incommensurate magnetic order and phase separation in the two-dimensional Hubbard model with nearest and next-nearest neighbor hopping

## TL;DR

This study maps the magnetic phases of the 2D Hubbard model with complex hopping, revealing phase separation and incommensurate order, which could explain magnetic behaviors in cuprates and ruthenates.

## Contribution

It provides a detailed phase diagram including incommensurate and phase-separated states, highlighting the importance of phase separation in understanding magnetic properties.

## Key findings

- First-order transitions lead to phase separation between magnetic phases.
- Phase separation significantly affects the phase diagram near half-filling.
- Results suggest magnetic phase coexistence explains behaviors in cuprates and ruthenates.

## Abstract

We consider the ground state magnetic phase diagram of the two-dimensional Hubbard model with nearest and next-nearest neighbor hopping in terms of electronic density and interaction. We treat commensurate ferro- and antiferromagnetic, as well as incommensurate (spiral) magnetic phases. The first-order magnetic transitions with changing chemical potential, resulting in a phase separation (PS) in terms of density, are found between ferromagnetic, antiferromagnetic and spiral magnetic phases. We argue that the account of PS has a dramatic influence on the phase diagram in the vicinity of half-filling. The results imply possible interpretation of the unusual behavior of magnetic properties of one-layer cuprates in terms of PS between collinear and spiral magnetic phases. The relation of the results obtained to the magnetic properties of ruthenates is also discussed.