2008/11/30 by Dmitrii L. Maslov, Andrey V. Chubukov
Physics and Astronomy · #Advanced Condensed Matter Physics #Physics of Superconductivity and Magnetism #Rare-earth and actinide compounds #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.79.075112
published as Phys. Rev. B v. 79, 075112 (2009) · 38 pages, 12 figures
arxiv created 2008/12/06 · openalex publication_date 2009/02/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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 \ensuremathχ 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, \ensuremath|H\ensuremath| 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, \ensuremath|H\ensuremath| scaling. We derive the thermodynamic potential as a function of magnetization and show that it contains, in addition to regular terms, a nonanalytic \ensuremath|M\ensuremath|3 term, which becomes M4∕T at finite T. We show that regular (M2,M4,…) terms originate from fermions with energies of order of the bandwidth, while the nonanalytic 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 \ensuremath|M\ensuremath|3 term crosses over to a non-Fermi-liquid form \ensuremath|M\ensuremath|7∕2 near a QCP. The prefactor of the \ensuremath|M\ensuremath|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; the latter may arise from the nonanalytic dependence of \ensuremathχ on the momentum. In a model with a long-range interaction in the spin channel, we show that the first-order transition occurs before the spiral instability.