Weak magnetism and non-Fermi liquids near heavy-fermion critical points

TL;DR

This work proposes that non-Fermi liquid behavior near heavy-fermion quantum critical points arises from the destruction of the large Fermi surface, producing a small Fermi surface FL$^*$ state with a spinon Fermi surface and an emergent U(1) gauge field. It develops a three-dimensional mean-field description, followed by a gauge-fluctuation analysis, showing a direct, possibly second-order transition from FL$^*$ to the heavy FL with a jump in Fermi-volume and non-Fermi liquid criticality; fluctuations can further drive a spin-density-wave instability of the spinon FS, yielding an exotic U(1) SDW$^*$ metal with weak magnetism. The paper derives a log-divergent specific heat in the FL$^*$ and at the critical point, analyzes transport via a quantum Boltzmann equation, and outlines experimental probes (specific heat, thermal and Raman responses, and monopole detection) that could distinguish the U(1) SDW$^*$ state from conventional SDW metals. Overall, it provides a cohesive framework linking Kondo breakdown, emergent gauge dynamics, and weak-moment magnetism to explain universal non-Fermi liquid signatures in heavy-fermion systems.

Abstract

This paper is concerned with the weak-moment magnetism in heavy-fermion materials and its relation to the non-Fermi liquid physics observed near the transition to the Fermi liquid. We explore the hypothesis that the primary fluctuations responsible for the non-Fermi liquid physics are those associated with the destruction of the large Fermi surface of the Fermi liquid. Magnetism is suggested to be a low-energy instability of the resulting small Fermi surface state. A concrete realization of this picture is provided by a fractionalized Fermi liquid state which has a small Fermi surface of conduction electrons, but also has other exotic excitations with interactions described by a gauge theory in its deconfined phase. Of particular interest is a three-dimensional fractionalized Fermi liquid with a spinon Fermi surface and a U(1) gauge structure. A direct second-order transition from this state to the conventional Fermi liquid is possible and involves a jump in the electron Fermi surface volume. The critical point displays non-Fermi liquid behavior. A magnetic phase may develop from a spin density wave instability of the spinon Fermi surface. This exotic magnetic metal may have a weak ordered moment although the local moments do not participate in the Fermi surface. Experimental signatures of this phase and implications for heavy-fermion systems are discussed.

Figures (8)

• Figure 1: Crossover phase diagram for the vicinity of the $d=3$ quantum transition involving breakdown of Kondo screening. $J_K$ is the Kondo exchange in the Hamiltonian introduced in Section \ref{['mft']}. The only true phase transition above is that at the $T=0$ quantum critical point at $J_K = J_{Kc}$ between the FL and FL$^*$ phases. The "slave" boson $b$ measures the mixing between the local moments and the conduction electrons and is also described in Section \ref{['mft']}. The crossovers are similar to those of a dilute Bose gas as a function of chemical potential and temperature, as discussed in Refs. weichmannbook---the horizontal axis is a measure of the boson chemical potential $\mu_b$. The boson is coupled to a compact U(1) gauge field; at $T=0$ this gauge field is in the Higgs/confining phase in the FL state, and in the deconfining/Coulomb phase in the FL$^*$ state. There is no phase transition at $T>0$ between a phase with $\langle b \rangle \neq 0$ and a phase with $\langle b \rangle =0$ because such a transition is absent in a theory with a compact U(1) gauge field in $d=3$compact (the mean-field theories of Sections. \ref{['mft']} and \ref{['mfmag']} do show such transitions, but these will turn into crossovers upon including gauge fluctuations). The compactness of the gauge field therefore plays a role in the crossovers in the "renormalized classical" regime above the FL state (this has not been worked out in any detail here). However, the compactness is not expected to be crucial in the quantum-critical regime. The crossover line displayed between the FL and quantum critical regimes can be associated with the "coherence" temperature of the heavy Fermi liquid. At low $T$, as discussed in the text, there are likely to be additional phases associated with magnetic order (the SDW and SDW$^*$ phases), and these are not shown above but are shown in Fig. \ref{['qcusdw']}; they also appear in the mean-field phase diagram in Fig. \ref{['pht1']}.
• Figure 2: Expected phase diagram and crossovers for the evolution from the U(1) SDW$^*$ phase to the conventional FL. Two different transitions are generically possible at zero temperature: Upon moving from the SDW$^*$ towards the Fermi liquid, the fractionalization is lost first followed by the disappearance of magnetic order. Nevertheless the higher temperature behavior in the region marked 'quantum critical' is non-fermi liquid like, and controlled by the Fermi volume changing transition from FL to FL$^*$. This may be loosely associated to the breakdown of Kondo screening.
• Figure 3: Fermi surface evolution from FL to FL$^*$: close to the transition, the FL phase features two Fermi surface sheets (the cold $c$ and the hot $f$ sheet, see text). Upon approaching the transition, the quasiparticle residue $Z$ on the hot $f$ sheet vanishes. On the FL$^*$ side, the $f$ sheet becomes the spinon Fermi surface, whereas the $c$ sheet is simply the small conduction electron Fermi surface.
• Figure 4: Mean-field phase diagram of $H_{\rm mf}$ (\ref{['mf2']}) on the cubic lattice, as function of Kondo coupling $J_K$ and temperature $T$. Parameter values are electron hopping $t=1$, Heisenberg interaction $J_H=0.1$, decoupling parameter $x=0.2$, and conduction band filling $n_c=0.7$. Thin (thick) lines are second (first) order transitions. The "decoupled" phase is an artifact of the mean-field theory, and the corresponding transitions will become crossovers upon including fluctuations, as will the transition between the FL and U(1) FL$^*$ phases; the transitions surrounding the SDW and SDW$^*$ phases will of course survive beyond mean-field theory.
• Figure 5: Staggered magnetization determined from the mean-field solution $H_{\rm mf}$ (\ref{['mf2']}). Parameter are as in Fig. \ref{['pht1']}, the two curves correspond to two horizontal cuts of the phase diagram in Fig. \ref{['pht1']}. At $T=0$, the first-order character of the SDW--FL transition is clearly seen. Note that smaller values of the decoupling parameter $x$ yield smaller values of the magnetization in the SDW and SDW$^*$ phases.