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

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 N{é}el antiferromagnets their effect is even weaker and does not change the order of the transition if the ordering wave number is sufficiently large. 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.

Figures (13)

• Figure 1: Electron-electron interaction in (a) the particle-hole channel and (b) the particle-particle channel.
• Figure 2: Field splitting of the Fermi surface in a FM based on a Landau Fermi liquid. The sheets of the Fermi surface are labeled by the spin projection.
• Figure 3: Schematic phase diagram in the $T$-$r$ plane showing the boundary between the ferromagnetic (FM) and the paramagnetic (PM) phase. A line of second-order transitions (blue double line) meets a line of first-order transition (green single line) at the tricritical point $(T_{\text{tc}},r=0)$. The quantum phase transition is of first order and located at $(T=0, r_1)$.
• Figure 4: Field splitting of the Fermi surface in a FM based on a Dirac Fermi liquid. The sheets of the Fermi surface are labeled by the chirality index $\alpha$ and the Stoner splitting index $\sigma$, not by the spin projection.
• Figure 5: Schematic Fermi surface of a non-centrosymmetric FM with a strong spin-orbit interaction. The sheets cannot be labeled by the spin projection.