Incommensurate spin density wave at a ferromagnetic quantum critical point in a three-dimensional parabolic semimetal

TL;DR

This paper investigates the nature of the ferromagnetic quantum critical point in a 3D semimetal, revealing it is preempted by an incommensurate spin density wave phase influenced by spin-orbit coupling and anisotropies.

Contribution

It demonstrates that the ferromagnetic quantum critical point is masked by an incommensurate spin density wave, analyzing effects of spin-orbit coupling and anisotropies on the ordering wavevector.

Findings

Incommensurate spin density wave preempts the quantum critical point.

The wavevector orientation depends on anisotropies and symmetry considerations.

The idealized model retains O(3) symmetry, guiding the wavevector direction.

Abstract

We explore the ferromagnetic quantum critical point in a three-dimensional semimetallic system with upward- and downward-dispersing bands touching at the Fermi level. Evaluating the static spin susceptibility to leading order in the coupling between the fermions and the fluctuating ferromagnetic order parameter, we find that the ferromagnetic quantum critical point is masked by an incommensurate, longitudinal spin density wave phase. We first analyze an idealized model which, despite having strong spin-orbit coupling, still possesses O(3) rotational symmetry generated by the total angular momentum operator. In this case, the direction of the incommensurate spin density wave propagation can point anywhere, while the magnetic moment is aligned along the direction of propagation. Including symmetry-allowed anisotropies in the fermion dispersion and the coupling to the order parameter field, however, the ordering wavevector instead breaks a discrete symmetry and aligns along either the [111] or [100] direction, depending on the signs and magnitudes of these two types of anisotropy.