From itinerant to local-moment antiferromagnetism in Kondo lattices: Adiabatic continuity versus quantum phase transitions

Motivated by both experimental and theoretical activities, we discuss the fate of Kondo screening and possible quantum phase transitions in antiferromagnetically ordered phases of Kondo lattices. While transitions with topological changes of the Fermi surface may occur, we demonstrate that an entirely continuous evolution from itinerant to local-moment antiferromagnetism (i.e., from strong to negligible Kondo screening) is possible as well. This situation is in contrast to that in a nonsymmetry-broken situation where a quantum phase transition toward an exotic metallic spin-liquid state necessarily accompanies the disappearance of Kondo screening. We discuss criteria for the existence of topological transitions in the antiferromagnetic phase as well as implications for theoretical scenarios and for current experiments.

Figure 1

(Color online) Fermi surfaces (left) and band structures (right) for a mean-field Kondo-lattice model, Eq. (3), on a two-dimensional (2D) rectangular lattice, with $n_c=0.5$ and bare band dispersions as given in the text. The dashed lines show the boundary of the reduced Brillouin zone of the antiferromagnet with $\vec{Q}=\left(\pi /2,0\right)$. (a) Bare $c$ band. (b) Paramagnetic heavy Fermi liquid (FL), $V=0.3$. (c) Antiferromagnetic Fermi liquid (AF) with (c1) $V=0.29$, $M_s={10}^{-4}$, and $m_s={10}^{-5}$ (no changes occur for $M_s,m_s\to 0$) and (c2) $V=0.01$, $M_s=0.1$, and $m_s={10}^{-2}$. From (b) to (c1), the system undergoes a standard SDW transition, whereas (c2) is close to a “local-moment” antiferromagnet [i.e., obtained by backfolding of the band structure from (a), together with a fully gapped $f$ band]. Note that (c) has two completely filled bands after backfolding.

Figure 2

Schematic zero-temperature phase diagram of the Kondo-Heisenberg model ${\mathcal{H}}_{\text{KLM}}+{\mathcal{H}}_I$ as a function of the dimensionless ratio $T_{\text{K}}/I$ (formed from Kondo and intermoment exchange energy scales) and the amount of quantum fluctuations (e.g., due to frustration). The solid lines show continuous phase transitions associated with the onset of antiferromagnetism and deconfinement/topological order. In the absence of antiferromagnetism, the deconfinement transition is equivalent to a Kondo breakdown or $f$ Mott transition. The shaded area denotes the crossover from itinerant to local-moment AF; in this region FS-topology-changing transitions may occur depending on the type of magnetic order and the FS topology, see Appendix . (The structure of the phase boundaries follows from Refs. 8, 9.) A scenario of deconfined criticality modifies the phase diagram (Ref. 10), see text.

Figure 3

(Color online) Fermi surfaces as in Fig. 1, but now for a situation with a $2\times 2$ AF unit cell as described in the text. (a) Bare $c$ band. (b) Paramagnetic heavy FL, $V=0.45$. (c) AF Fermi liquid with (c1) $V=0.44$, $M_s={10}^{-4}$, and $m_s={10}^{-5}$ and (c2) $V=0.01$, $M_s=0.1$, and $m_s={10}^{-2}$.