Magnetic fluctuations and itinerant ferromagnetism in two-dimensional systems with van Hove singularities

TL;DR

This paper investigates the conditions for ferromagnetism in 2D systems with Van Hove singularities, highlighting the importance of incommensurate spin fluctuations and providing a refined criterion beyond the Stoner model.

Contribution

It introduces a quasistatic approach to analyze ferromagnetism near Van Hove singularities, accounting for incommensurate spin fluctuations and deriving finite critical interaction values.

Findings

Critical interactions I_c and U_c are finite and larger than Stoner predictions.

Incommensurate spin fluctuations significantly influence ferromagnetic transition.

Spectrum of spin excitations is positive definite when interactions are sufficiently strong.

Abstract

We use the quasistatic approach to analyze the criterion of ferromagnetism for two-dimensional (2D) systems with the Fermi level near Van Hove singularities (VHS) of the electronic spectrum. It is shown that the spectrum of spin excitations (paramagnons) is positively defined when the interaction I between electrons and paramagnons, which corresponds to the Hubbard on-site repulsion U, is sufficiently large. The critical interactions I_c and U_c remain finite at Van Hove filling and exceed considerably their values obtained from the Stoner criterion due to incommensurate spin fluctuations which are important near the ferromagnetic quantum phase transition. Combining the quasistatic approximation and the equation-of -motion method for the Green functions we obtain the results for the electronic self-energy to first order in the inverse number of spin components.