Nature of the Quantum Phase Transition in Clean, Itinerant Heisenberg Ferromagnets

TL;DR

This paper develops a comprehensive theory for quantum phase transitions in clean, itinerant Heisenberg ferromagnets, revealing that fluctuations induce either first or second-order transitions depending on spatial dimensions, aligning with experimental data.

Contribution

It introduces a generalized mean-field theory accounting for soft particle-hole excitations, predicting fluctuation-induced first and second-order quantum ferromagnetic transitions.

Findings

Standard mean-field theory fails for d ≤ 3 due to soft modes.

Transition can be first or second-order depending on parameters.

In d=3, the second-order transition exhibits mean-field behavior with logarithmic corrections.

Abstract

A comprehensive theory of the quantum phase transition in clean, itinerant Heisenberg ferromagnets is presented. It is shown that the standard mean-field description of the transition is invalid in spatial dimensions $d\leq 3$ due to the existence of soft particle-hole excitations that couple to the order parameter fluctuations and lead to an upper critical dimension $d_c^+ = 3$. A generalized mean-field theory that takes these additional modes into account predicts a fluctuation-induced first-order transition. In a certain parameter regime, this first-order transition in turn is unstable with respect to a fluctuation-induced second-order transition. The quantum ferromagnetic transition may thus be either of first or of second-order, in agreement with experimental observations. A detailed discussion is given of the stability of the first-order transition, and of the critical behavior at the fluctuation-induced second-order transition. In $d=3$, the latter is mean field-like with logarithmic corrections to scaling, and in $d<3$ it can be controlled by means of a $3-\epsilon$ expansion.