Strong electronic correlations in interstitial magnetic centers of zero-dimensional electride $\beta -{\mathrm{Yb}}_5{\mathrm{Sb}}_3$

Using dynamical mean-field theory, we investigate the correlated nature of quantum-confined electrons localized in the crystal voids of the zero-dimensional electride $\beta \text{−}{\mathrm{Yb}}_5{\mathrm{Sb}}_3$. In this work, maximally localized Wannier functions were used to obtain an analytical description of the half-filled electride electronic states and to establish a high degree of their localization, with the magnetic moment of $1{\mu }_{\mathrm{B}}$ per anionic cavity. We reproduced the Mott metal-insulator transition, obtained the experimentally observed energy gap, and demonstrated the decrease of resistivity with increasing temperature, typical for semiconductors. The Curie-type temperature dependence of the compound's magnetic susceptibility was calculated and found to be in close agreement with experiment. These results obtained prove that the Coulomb correlations between the localized anionic electrons are the source of the observed electronic and magnetic properties of $\beta \text{−}{\mathrm{Yb}}_5{\mathrm{Sb}}_3$.

Figure 1

Band structure of $\beta \text{−}{\mathrm{Yb}}_5{\mathrm{Sb}}_3$ (black lines). The contribution to the Bloch states by the maximally localized Wannier function centered on the tetrahedral interstitial voids is located in the energy window from $-0.8$ to 0.3 eV and is shown in red.

Figure 2

Crystal structure of (a) $\beta \text{−}{\mathrm{Yb}}_5{\mathrm{Sb}}_3$ and isosurface of the spatial distribution of the MLWFs describing the electride state in the ($ab$), ($ac$), and ($bc$) planes in panels (b)–(d), respectively. Panel (d) shows only the atoms making the main contribution to the obtained MLWFs. The yellow and blue colors of the isosurface correspond to the positive and negative parts of the wave function, respectively. The Yb and Sb atoms are shown in dark gray and orange, respectively. Dashed line contours denote the unit-cell boundary.

Figure 3

Imaginary part of the self-energy as a function of the Matsubara frequencies at $\beta =30{\mathrm{eV}}^{-1}$ for different values of the Coulomb parameter $U$. The corresponding Green's functions for one impurity are shown in the inset.

Figure 4

Spectral functions obtained using the DFT (top panel) and the $\mathrm{DFT}+\mathrm{DMFT}$ for different values of $U$ at $\beta =30{\mathrm{eV}}^{-1}$. Zero corresponds to Fermi energy.

Figure 5

Green's functions at $U=2$ eV for different values of $\beta$ parameter.

Figure 6

Local spin-spin correlation functions $\langle {\mathbf{S}}_z\left(\tau \right){\mathbf{S}}_z\left(0\right)\rangle$ in the imaginary-time domain obtained using the $\mathrm{DFT}+\mathrm{DMFT}$ method at $\beta =30{\mathrm{eV}}^{-1}$ for different values of the Coulomb parameter $U$.

Figure 7

Temperature dependencies of the uniform magnetic susceptibility $\chi \left(T\right)$ and its inverse (in the inset) for different values of $U$. The experimental data [19] are shown by purple circles.