Comment on "Instability of the ferromagnetic quantum critical point and symmetry of the ferromagnetic ground state in two-dimensional and three-dimensional electron gases with arbitrary spin-orbit splitting"

TL;DR

This paper critiques recent claims about the nature of quantum phase transitions in spin-orbit coupled metals, emphasizing the importance of proper interaction screening in three-dimensional systems.

Contribution

It clarifies that the conclusion of a first-order transition in 3D magnets with spin-orbit interaction is incorrect when interaction screening is properly considered.

Findings

Proper screening negates the soft modes leading to first-order transitions in 3D magnets.

Claims that electron-electron interactions induce first-order transitions are invalid with correct screening.

The analysis refutes recent assertions about the universality of first-order quantum phase transitions in these systems.

Abstract

Metallic quantum ferromagnets in the absence of quenched disorder are known to generically undergo a first-order quantum phase transition, avoiding the quantum critical point that had originally been expected. This is due to soft modes in the underlying Fermi liquid that lead to long-ranged correlations. These correlations in turn yield a nonanalytic dependence of the free energy on the magnetization even at a mean-field level that results in a fluctuation-induced first-order transition. Kirkpatrick and Belitz [Phys. Rev. Lett. {\bf 124}, 147201 (2020)] have pointed out that one notable exception are non-centrosymmetric metals with a strong spin-orbit interaction. In such materials the spin-orbit interaction gives the relevant soft modes a mass, which inhibits the mechanism leading to a first-order transition. Miserev, Loss, and Klinovaja [Phys. Rev. B {\bf 106}, 134417 (2022)] have claimed that this conclusion does not hold if electron-electron interactions in the particle-particle channel, or 2$\kF$ scattering processes, are considered. They concluded that this interaction channel leads to soft modes that are not rendered massive by the spin-orbit interaction and again lead to a first-order quantum phase transition. In this Comment we show that this conclusion is not correct in three-dimensional magnets if the screening of the interaction is properly taken into account.