Spin fluctuations and ferromagnetic order in two-dimensional itinerant systems with Van Hove singularities

TL;DR

This paper investigates the conditions for ferromagnetism in 2D electron systems near Van Hove singularities, highlighting the importance of spin fluctuations and comparing different theoretical approaches.

Contribution

It provides a quasistatic analysis of ferromagnetic criteria in 2D systems with Van Hove singularities, emphasizing the role of incommensurate spin fluctuations and refining the critical interaction estimate.

Findings

Spin excitations are positively defined for sufficiently large Hubbard U.

Critical interaction Uc exceeds the Stoner criterion near Van Hove filling.

Incommensurate spin fluctuations influence the ferromagnetic quantum phase transition.

Abstract

The quasistatic approach is used to analyze the criterion of ferromagnetism for two-dimensional (2D) systems with the Fermi level near Van Hove (VH) singularities of the electron spectrum. It is shown that the spectrum of spin excitations (paramagnons) is positively defined when the interaction between electrons and paramagnons, determined by the Hubbard on-site repulsion U, is sufficiently large. Due to incommensurate spin fluctuations near the ferromagnetic quantum phase transition, the critical interaction Uc remains finite at VH filling and exceeds considerably its value obtained from the Stoner criterion. A comparison with the functional renormalization group results and mean-field approximation which yields a phase separation is also performed.