Ferromagnetism in ${\mathrm{UGe}}_2$: A microscopic model

The Anderson lattice model is used to explain the principal features of the heavy fermion compound ${\mathrm{UGe}}_2$ by means of the generalized Gutzwiller approach (the statistically consistent Gutzwiller approximation method). This microscopic approach successfully reproduces the magnetic and electronic properties of this material, in qualitative agreement with experimental findings from magnetization measurements, neutron scattering, and de Haas–van Alphen oscillations. Most importantly, it explains the appearance, sequence, character, and evolution in an applied magnetic field of the observed in ${\mathrm{UGe}}_2$ ferromagnetic and paramagnetic phases as an effect of a competition between the $f-f$ electron Coulomb interaction energy and $f$-conduction electron hybridization.

Figure 1

Top: Phase diagram on the plane total filling–hybridization strength for the zero field, containing both FM and PM phases for $U=5$. The color scale denotes total spin polarization $m$. Phases are divided by the dashed and the solid lines. Dashed lines denote the second-order transition, whereas the solid denotes the first-order transition with the critical points, CP. Fine dashed lines mark how the phase borders would change for $U=8$. (a)–(c) depict a schematic spin-resolved density of states corresponding to the phase sequence appearing along the solid vertical line (from bottom to top).

Figure 2

(a) Magnetization as a function of hybridization strength for the band filling $n=1.6$, and the Coulomb repulsion $U=5$. Both phase transitions induced by the hybridization change are of first order. (b) Corresponding experimental results from Ref. [4]. (c) $f$-orbital filling as a function of hybridization. (d) Square of DOS at the Fermi level vs $\left|V\right|$ through the phase sequence. Inset: Experimentally measured $T^2$-term coefficient $A$ of the resistivity vs pressure from Ref. [18].

Figure 3

(a) Phase diagram on the applied field–hybridization strength plane for $n=1.6$ and $U=5$. The color scale denotes total spin polarization. The dashed lines mark the phase stability thresholds for $U=8$. In the inset we show experimental results [4]. (b) Magnetization vs applied field for selected hybridization strengths when the system is entering into the FM1 to FM2 phase-transition regime. (c) Evolution of orbital-resolved magnetization with the field for low hybridization, $\left|V\right|=0.5$ (mimicking ambient pressure). Note the very small $c$-electron polarization up to $h\simeq 0.1$.