$\alpha$-$\gamma$ transition in cerium: Magnetic form factor and dynamic magnetic susceptibility in dynamical mean-field theory

The nature of the elemental cerium phases, undergoing an isostructural volume collapse transition, cannot be understood using conventional solid-state concepts. Using the combination of density functional theory and dynamical mean-field theory, we study the magnetic properties of both the $\alpha$ and the $\gamma$ phases. We compute the magnetic form factor and show that it is very close to the free ion behavior in both the local moment $\gamma$ phase as well as the more itinerant $\alpha$ phase, in agreement with neutron scattering experiments. In sharp contrast, the dynamic local magnetic susceptibility of the two phases is strikingly different. In the $\gamma$ phase, the sharp low energy peak due to local moment formation and consequently low Kondo temperature dominates the spectra. In $\alpha$ phase two broad peaks can be identified, the first is due to Kondo screening and the second is due to Hund's coupling. This shows that hybridization plays a central role in the $\alpha$-$\gamma$ transition in cerium, and that from the point of view of magnetic properties, the $4f$ electrons are strongly correlated in both phases.

Figure 1

Momentum transfer dependence of the normalized magnetic form factor F${}_M^2$(Q) of $\alpha$-Ce and $\gamma$-Ce. Blue circles show experimental data taken from Ref. [16].

Figure 2

Imaginary part of the local dynamic magnetic susceptibility, Im$\chi \left(\omega \right)$, for $\alpha$ and $\gamma$ cerium (yellow dotted and red dashed lines, respectively). The inset shows the static susceptibility $\chi (q,\omega =0)$ of $\alpha$ cerium as a function of $q$ in the first Brillouin zone. Note that the $q$ goes from the points (0,0,0) to (1,1,$-1$) in 12 uniform steps.

Figure 3

Difference of $S(q,\omega )$ between $\alpha$ and $\gamma$ phase: Top panel shows DFT + DMFT results. Lower panel shows high-energy neutron inelastic measurements, taken from Ref. [16].