Realization of Mott-insulating electrides in dimorphic $\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$

Electrides are exotic compounds that confine anionic electrons in periodically distributed subnanometer-sized spaces. Such trapped electrons are free from onsite electron-nuclear interaction and exhibit unconventional properties. Here, we report that α- and $\beta -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$ are inorganic electrides exhibiting Mott-insulating features. Anionic electrons are stabilized in the quasi-one- and -zero-dimensional spaces, and give rise to the corresponding electride bands near their Fermi levels. Despite the partially occupied electronic picture, both of these systems exhibit semiconducting conductivity and Curie-type magnetism with $S=1/2$ moments, demonstrating electron localization. These findings show that anionic electrons can serve as magnetic centers, and inorganic electrides have the potential to act as strongly correlated materials even without the presence of localized atomic orbitals.

Figure 1

The crystal structures of (a) $\alpha -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$ and (b) $\beta -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$. Yb and Sb atoms are depicted using green and blue spheres, respectively. The ${\left(V_{\mathrm{cell}}\right)}^{1/3}$ of (c) $\alpha -L{n}_5\mathrm{S}{\mathrm{b}}_3$ and (d) $\beta -L{n}_5\mathrm{S}{\mathrm{b}}_3$ phases as a function of ionic radius of Ln ions. The black dashed line represents line fitting of $L{n}_5\mathrm{S}{\mathrm{b}}_3$ with trivalent Ln. The $V_{\mathrm{cell}}$ data for α- and $\beta -L{n}_5\mathrm{S}{\mathrm{b}}_3$ were reported in Refs. [20, 21, 22, 23, 24, 25, 26, 27, 28, 29].

Figure 2

The calculated band structures of (a) $\alpha -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3\mathrm{H}$, (b) $\beta -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3\mathrm{H}$, (c) $\alpha -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$, and (d) $\beta -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$. The components of H $1s$ orbitals in (a) and (b), and anionic electrons in (c) and (d) are represented using red color in the band structure.

Figure 3

The total energy of $\alpha -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$ and $\beta -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$ as a function of each magnetic state. Antiferromagnetic configuration is most stable for each system. Black and red circles indicate the data of $\alpha -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$ and $\beta -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$, respectively.

Figure 4

(a), (b) The calculated band structures, (c), (d) density of states, and (e), (f) partial charge densities of (a), (c), (e) $\alpha -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$ and (b), (d), (f) $\beta -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$ using antiferromagnetic configuration. The introduced Hubbard U was 5 eV for $\alpha -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$ and 0 eV for $\beta -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$. The contributions of electrides states are depicted using solid green (spin-up) and dashed green (spin-down) lines in (c) and (d). The isosurface values of partial charge densities in (e) and (f) are 0.002 and $0.003\mathrm{e}/\mathrm{Boh}{\mathrm{r}}^3$, respectively. Yb and Sb atoms are depicted using green and blue spheres, respectively.

Figure 5

Calculated band structures and density of states of (a), (c) $\alpha -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$ and (b), (d) $\beta -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$ using HSE functionals with antiferromagnetic setting. Red and blue dots represent spin-up and spin-down bands.

Figure 6

The spin-density distribution of (a) $\alpha -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$ and (c) $\beta -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$ calculated using HSE functionals. The estimated total magnetic moments of each atomic site was summarized in (b) for α phase and (d) for β phase, respectively. Yb and Sb atoms are depicted using green and blue spheres, respectively.

Figure 7

Electrical resistivity of (a) $\alpha -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$ and $\beta -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$ and (b) corresponding Arrhenius plots. The transport activation energies ($E_{\mathrm{a}}$) were, respectively, estimated to be $E_{\mathrm{a}}\sim 0.07\mathrm{eV}$ for α phase (red) and $E_{\mathrm{a}}\sim 0.10\mathrm{eV}$ for β phase (blue). The black dashed lines represent line fitting.

Figure 8

Magnetic susceptibility of (a) $\alpha -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$ and $\beta -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$. Corresponding ${\chi }^{-1}$ plots are shown in (b). The effective moments (${\mu }_{\mathrm{eff}}$) were, respectively, estimated to be ${\mu }_{\mathrm{eff}}\sim 1.7{\mu }_{\mathrm{B}}$ for α phase (red) and ${\mu }_{\mathrm{eff}}\sim 2.1{\mu }_{\mathrm{B}}$ for β phase (blue). The black dashed lines represent line fitting.

Figure 9

(a) Electrical resistivity, (b) corresponding Arrhenius plots, (c) magnetic susceptibility, and (d) ${\chi }^{-1}$ plot of $\beta -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3{\mathrm{F}}_x$. The data of $\beta -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$ are also shown as blue solid squares for comparisons. The transport activation energy ($E_{\mathrm{a}}$) and effective moment (${\mu }_{\mathrm{eff}}$) of $\beta -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3{\mathrm{F}}_x$ were estimated to be $E_{\mathrm{a}}\sim 0.25\mathrm{eV}$ and ${\mu }_{\mathrm{eff}}\sim 1{\mu }_{\mathrm{B}}$. Transport data were normalized at 390 K for $\beta -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3{\mathrm{F}}_x$ and 300 K for $\beta -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$ in the Arrhenius plots.

Figure 10

Powder XRD diffraction of (a) $\alpha -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$, (b) $\beta -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$, and (c) $\beta -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3{\mathrm{F}}_x$. The reliability parameters are $R_{\mathrm{wp}}=9.456\%$ ($S=1.987$) for $\alpha -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$, $R_{\mathrm{wp}}=9.274\%$ ($S=1.925$) for $\beta -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$, and $R_{\mathrm{wp}}=11.863\%$ ($S=2.577$) for $\beta -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3{\mathrm{F}}_x$.

Figure 11

${\mathrm{H}}_2$-TPD spectrum of sintered $\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$. Clear ${\mathrm{H}}_2$ desorption could not be confirmed below 800 °C.

Figure 12

Calculated DOS of (a) $\alpha -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3\mathrm{H}$ and (b) $\beta -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3\mathrm{H}$ using PBE functionals. The contributions of Yb, Sb, and H orbitals are respectively represented.

Figure 13

Calculated partial electron densities near Fermi levels of (a) $\alpha -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$ and (b) $\beta -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$ using PBE functional. Yb and Sb atoms are depicted using green and blue spheres, respectively. The yellow bubbles represent the electron density in the interstitial sites.

Figure 14

The DFT+U calculations of $\alpha -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$. (a) Calculated band structures of $\alpha -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$ with non-spin-polarized configuration. Calculated band structures of $\alpha -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$ with antiferromagnetic setting and Hubbard U values of (b) 0, (c) 1, and (d) 3 eV.

Figure 15

The DFT+U calculations of $\beta -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$. Calculated band structures of $\beta -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3$ with antiferromagnetic setting and Hubbard U values of (a) 0 and (b) 5 eV.

Figure 16

The band calculations on $\beta -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3{\mathrm{F}}_x$. Calculated band structures of $\beta -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3{\mathrm{F}}_x$ with $x$ values of (a) 1.0, (b) 0.75, (c) 0.50, and (d) 0.25. Conventional DFT calculation was conducted for $x=1.0$, while HSE functionals were employed for $x=0.75$, 0.50, and 0.25.

Figure 17

The band gaps ($E_{\mathrm{g}}$) and magnetic moments (${\mu }_{\mathrm{eff}}$) as a function of F content. (a) The summary of $E_{\mathrm{g}}$ and ${\mu }_{\mathrm{eff}}$ of $\beta -\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3{\mathrm{F}}_x$. (b) Real-space spin-density distribution of $\mathrm{Y}{\mathrm{b}}_5\mathrm{S}{\mathrm{b}}_3{\mathrm{F}}_{0.5}$. Yb, Sb, and F atoms are depicted using green, blue, and gray spheres, respectively.