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

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.

38 pages, 12 figures

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• Spin-independent origin of the strongly enhanced effective mass in a dilute 2D electron system
• Magnetic Ordering of Nuclear Spins in an Interacting 2D Electron Gas
• Electrical resistivity near Pomeranchuk instability in two dimensions
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• Non-analytic behavior of 2D itinerant ferromagnets
• Spin Susceptibility of Interacting Two-dimensional Electrons with Anisotropic Effective Mass
• Temperature dependence of the spin susceptibility of a clean Fermi gas with repulsion
• Temperature dependence of spin susceptibility in two-dimensional Fermi liquid systems
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