Spin density functional study of magnetism in potassium-loaded zeolite A

In order to clarify the mechanism of spin polarization in potassium-loaded zeolite A, we perform ab initio density functional calculations. We find that (i) the system comprising only nonmagnetic elements (Al, Si, O, and K) can indeed exhibit ferromagnetism, (ii) the host cage makes a confining quantum-well potential in which superatom $s$- and $p$-like states are formed, the latter $p$ states are responsible for the spin polarization, and (iii) the size of the magnetic moment depends sensitively on atomic positions of potassium clusters. We show that the spin polarization can be described systematically in terms of the confining potential and the crystal-field splitting in the superatom $p$ states.

Figure 1

(Color online) Upper left: overall profile of zeolite LTA, where O, Al, and Si atoms are denoted by small red, light blue, and dark blue spheres, respectively. $\alpha$ and $\beta$ cages are marked by (red) solid and (blue) dashed lines, respectively. Upper right: two kinds of $\alpha$ cages (${\alpha }_1$ and ${\alpha }_2$). Lower panel: four kinds of sites occupied by potassiums [(purple) large spheres]. For the definition of the sites I-IV, see the text.

Figure 2

(Color online) Four geometries considered in this Rapid Communication, where dark (blue), light (green), and medium (red) spheres stand for the potassiums occupying the site I, III, and IV, respectively. The difference in each geometry comes from the difference in the configuration of site-III potassiums; “two triangles” and “small triangle” (geometry I), “two triangles” and “large triangle” (geometry II), “hexagon” and “small triangle” (geometry III), and “hexagon” and “large triangle” (geometry IV) are accommodated in the ${\alpha }_1$ and ${\alpha }_2$ cages. We note that four site-I potassium in the ${\alpha }_1$ cage are overlapped with the remaining four site-I potassium in this view.

Figure 3

(Color online) Calculated GGA band dispersions along symmetry lines [$W=\frac{2\pi }{a}\left(1,0,\frac{1}{2}\right)$, $X=\frac{2\pi }{a}\left(1,0,0\right)$, $\Gamma =\frac{2\pi }{a}\left(0,0,0\right)$, $L=\frac{2\pi }{a}\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)$, and $K=\frac{2\pi }{a}\left(0,\frac{3}{4},\frac{3}{4}\right)$] (upper) and Bloch wave functions, ${\Psi }_{\text{A}}-{\Psi }_{\text{D}}$, at the $\Gamma$ point (lower) for the geometries I (left) and II (right). In the band dispersion, (red) solid and (blue) dashed lines stand for majority and minority spin states, respectively. The energy zero is set to the Fermi level. In the wave functions, isosurfaces are drawn by the values of $\pm 0.015$ (a.u.). Potassiums occupying the site I, III, and IV are displayed by spheres of the same colors with Fig. 2.

Figure 4

Level diagrams for electronic structures of the four geometries displayed in Fig. 2, where superatom $p$ levels in the ${\alpha }_1$- and ${\alpha }_2$-cage potentials and the resulting spin configurations are drawn schematically. The $p$ states are represented in the local coordinates (for the definition, see the text). The difference between the cage potentials of ${\alpha }_1$ and ${\alpha }_2$ comes from the difference in the configuration of the site-I potassiums (see Fig. 2) and the $p$-level splitting is due to the site-III-potassium configurations.