Magnetic susceptibility of cerium: An LDA$+$DMFT study

The magnetic properties of Ce in the $\alpha$ and $\gamma$ phase are calculated within the local-density approximation and dynamical mean-field theory (LDA$+$DMFT) approach. The magnetic susceptibility in these two phases shows a similar behavior over a wide temperature range: a Curie-Weiss law at high temperatures, indicating the presence of local moments, followed by a maximum in a crossover regime, and a saturation characteristic of a state with screened local moments at low temperature. The difference in experimentally observable magnetic properties is caused by the shift of the susceptibility to higher temperatures in the $\alpha$ phase compared to the $\gamma$ phase.

Figure 1

Uniform magnetic susceptibility $\chi \left(T\right)$ for Ce-$\alpha$. Inset (a): enlarged view of $\chi \left(T\right)$ in the low-temperature region. Inset (b): inverse magnetic uniform susceptibility ${\chi }^{-1}\left(T\right)$.

Figure 2

Imaginary part of the self-energy for all 14 $4f$ orbitals at $T=129$ K ($\beta =90$ eV${}^{-1}$) in Ce-$\alpha$. Due to the crystal-field splitting, they form three different sets of curves denoted as $t_{1u}$, $t_{2u}$, and $a_{2u}$. The inset shows the low-energy behavior of $\mathrm{Im}\Sigma \left(i{\omega }_n\right)$. For one of the curves, exact positions of Matsubara frequencies and linear extrapolation (dashed line) to zero are shown.

Figure 3

Local magnetic susceptibility ${\chi }_0\left(T\right)$ and inverse local magnetic susceptibility ${\chi }_0^{-1}\left(T\right)$ for Ce-$\alpha$.

Figure 4

Uniform magnetic susceptibility $\chi \left(T\right)$ and inverse magnetic uniform susceptibility ${\chi }^{-1}\left(T\right)$ for Ce-$\gamma$, inset (a).

Figure 5

Local magnetic susceptibility ${\chi }_0\left(T\right)$ and inverse magnetic local susceptibility ${\chi }_0^{-1}\left(T\right)$ for Ce-$\gamma$.

Figure 6

Imaginary part of the self-energy for all 14 $4f$ orbitals at $T=64$ K in Ce-$\gamma$. Due to the crystal-field splitting, they form three different sets of curves denoted as $t_{1u}$, $t_{2u}$, and $a_{2u}$. The inset shows the low-energy behavior of $\mathrm{Im}\Sigma \left(i{\omega }_n\right)$. For one of the curves, exact positions of Matsubara frequencies and linear extrapolation (dashed line) to zero are shown.

Figure 7

Top panel: spectral function for the Ce-$\alpha$ phase calculated for $\beta =90$ eV${}^{-1}\sim 130$ K. Bottom panel: spectral function for the Ce-$\gamma$ phase calculated for $\beta =180$ eV${}^{-1}\sim 65$ K.