Instability of the Quantum-Critical Point of Itinerant Ferromagnets

We study the stability of the quantum-critical point for itinerant ferromagnets commonly described by the Hertz-Millis-Moriya (HMM) theory. We argue that in $D\le 3$ long-range spatial correlations associated with the Landau damping of the order parameter field generate a universal negative, nonanalytic $|q{|}^{(D+1)/2}$ contribution to the static magnetic susceptibility ${\chi }_s(q,0)$, which makes HMM theory unstable. We argue that the actual transition is either towards incommensurate ordering, or first order. We also show that singular corrections are specific to the spin problem, while charge susceptibility remains analytic at criticality.

Figure 1

The two lowest-order diagrams for the corrections to the static spin susceptibility. The self-energy insertion is $\Sigma (p)$; the frequency dependent piece $\Sigma ({\omega }_m)$ is already incorporated into “zero-order” Eliashberg theory.