Nonanalytic paramagnetic response of itinerant fermions away and near a ferromagnetic quantum phase transition

TL;DR

This paper investigates the nonanalytic magnetic response of itinerant fermions near a ferromagnetic quantum phase transition, revealing how low-energy processes and non-Fermi-liquid behavior influence the nature of the transition.

Contribution

It demonstrates that nonanalytic |M|^3 terms dominate the thermodynamic potential near a QCP, leading to a first-order transition, and extends the Eliashberg approach to finite magnetic fields.

Findings

Nonanalytic |M|^3 term in thermodynamic potential.

Near QCP, |M|^{7/2} behavior indicates non-Fermi-liquid effects.

First-order transition precedes spiral instability in long-range interaction models.

Abstract

We study nonanalytic paramagnetic response of an interacting Fermi system both away and in the vicinity of a ferromagnetic quantum phase transition (QCP). Previous studies found that (i) the spin susceptibility scales linearly with either the temperature $T$ or magnetic field H in the weak-coupling regime; (ii) the interaction in the Cooper channel affects this scaling via logarithmic renormalization of prefactors of the $T$, |H| terms, and may even reverse the signs of these terms at low enough energies. We show that Cooper renormalization becomes effective only at very low energies, which get even smaller near a QCP. However,even in the absence of such renormalization, generic (non-Cooper) higher-order processes may also inverse the sign of T,|H| scaling. We derive the thermodynamic potential as a function of magnetization and show that it contains, in addition to regular terms, a non-analytic |M|^3 term, which becomes M^4/T at finite $T$. We show that regular (M^2, M^4, ...) terms originate from fermions with energies of order of the bandwidth, while the non-analytic term comes from low-energy fermions. We consider the vicinity of a ferromagnetic QCP by generalizing the Eliashberg treatment of the spin-fermion model to finite magnetic field, and show that the |M|^3 term crosses over to a non-Fermi-liquid form |M|^{7/2} near a QCP. The prefactor of the |M|^{7/2} term is negative, which indicates that the system undergoes a first-order rather than a continuous transition to ferromagnetism. We compare two scenarios of the breakdown of a continuous QCP: a first-order instability and a spiral phase. In a model with a long-range interaction in the spin channel, we show that the first-order transition occurs before the spiral instability.