Metamagnetism and Lifshitz transitions in models for heavy fermions

We investigate metamagnetic transitions in models for heavy fermions by considering the doped Kondo lattice model in two dimensions. Results are obtained within the framework of dynamical mean field and dynamical cluster approximations. Universal magnetization curves for different temperatures and Kondo couplings develop upon scaling with the lattice coherence temperature. Furthermore, the coupling of the local moments to the magnetic field is varied to take into account the different Landé factors of localized and itinerant electrons. The competition between the lattice coherence scale and the Zeeman energy scale allows for two interpretations of the metamagnetism in heavy fermions: Kondo breakdown or Lifshitz transitions. By tracking the single-particle residue through the transition, we can uniquely conclude in favor of the Lifshitz transition scenario. In this scenario, a quasiparticle band drops below the Fermi energy which leads to a change in topology of the Fermi surface.

Figure 1

$T_{\mathrm{coh}}$-scaled magnetization $M(g_f/g_c,T/T_{\mathrm{coh}},B/T_{\mathrm{coh}})$ for (a) two-orbital DMFT and (b) four-orbital DCA. The respective coherence temperatures are (a) $T_{\mathrm{coh}}(g_f/g_c=1,J/t=1.6)=0.094t$, $T_{\mathrm{coh}}(g_f/g_c=1,J/t=1.4)=0.057t$, and $T_{\mathrm{coh}}(g_f/g_c=1,J/t=1.3)=0.044t$; (b) $T_{\mathrm{coh}}(g_f/g_c=1,J/t=1.6)=0.10t$ and $T_{\mathrm{coh}}(g_f/g_c=1,J/t=2.0)=0.18t$.

Figure 2

The magnetic field value of the second Lifshitz transition, $B_{\mathrm{L}2}(g_f/g_c)$, agrees well with $B_{\mathrm{L}2}(g_f/g_c)\propto {(g_f/g_c)}^{-1}$.

Figure 3

Static MF results for the magnetization $M$ and single-particle residue $Z_{\sigma }$.

Figure 4

The imaginary part of Matsubara self-energies $\mathrm{Im}{\Sigma }_{\sigma =\downarrow ,\uparrow }^{\mathrm{DMFT}}\left(i{\omega }_n\right)$ at values of the magnetic field close to $B=B_{\mathrm{L}2}$.

Figure 5

Single-particle spectral function $A_{\sigma }(\mathbf{k},\omega )$ across the MMT at the lowest temperature, $\beta t=200$ (magnetic field values are indicated by arrows in Fig. 6). The narrow distribution of spectral weight close to the Fermi energy (dashed line) indicates that Kondo coherence remains across the MMT.

Figure 6

Magnetization $M$ and single-particle residue $Z_{\sigma }^{\mathrm{DMFT}}$ across the MMT. (The arrows refer to the single-particle spectra of Fig. 5.)

Figure 7

Magnetization $M$ and single-particle residues $Z_{\sigma }$ from two-orbital (DMFT) calculations and four-orbital (DCA) calculations. The $k$ vectors ${\mathbf{K}}_1=(0,0)$ and ${\mathbf{K}}_2=(\pi ,\pi )$ denote the relevant DCA patches.