Generic Long-Range Order-Parameter Correlations in Metallic Quantum Magnets

TL;DR

This paper demonstrates that in all metallic magnets, the coupling to conduction electrons causes the order-parameter susceptibility to be long-ranged at zero temperature, significantly affecting the nature of magnetic quantum phase transitions across various classes.

Contribution

It provides a universal analysis showing long-range correlations in metallic magnets and their impact on the order of quantum phase transitions, based on simple single-particle and renormalization-group considerations.

Findings

Long-range correlations modify the transition from second to first order in most 3-d systems.

In non-centrosymmetric ferromagnets with strong spin-orbit coupling, the transition order changes in 2-d but not in 3-d.

In helimagnets and antiferromagnets, the effect is weaker and does not alter the transition order if the wave number is large.

Abstract

It is shown that in all types of metallic magnets the coupling of the order parameter to the conduction electrons leads to an order-parameter susceptibility that is long-ranged at zero temperature. This is true for all known classes of ferromagnets, and also for antiferromagnets and spin-density wave systems, helimagnets, magnetic nematics, and altermagnets. The consequences for the magnetic quantum phase transition vary between different classes of magnets. In almost all 3-d systems with a homogeneous magnetization, as well as in magnetic nematics and in altermagnets, the long-ranged correlations generically modify the nature of the magnetic quantum phase transition from second order to first order. The only exception are non-centrosymmetric ferromagnets with a strong spin-orbit interaction, where the correlations change the order of the transition in 2-d systems, but not in 3-d ones. In helimagnets, spin-wave systems, and Neel antiferromagnets their effect is even weaker and does not change the order of the transition if the ordering wave number is sufficiently large, except in flat-band systems. In systems with quenched disorder the transition generically is of second order, but the correlations modify the critical behavior. These conclusions are reached by very simple considerations that are based entirely on the single-particle excitations in the nonmagnetic phase and their modifications by a field conjugate to the order parameter, augmented by renormalization-group considerations.