  K clusters arrayed in zeolite A are investigated in detail. K clusters are
generated in regular alpha-cages of zeolite A by the loading of guest K metal
at a loading density of K atoms per alpha-cage, $n$. The value of $n$ was
changed from 0 to 7.2. It is known that this system shows ferromagnetic
properties for $n > 2$, where the Curie temperature increases with $n$, has a
peak of approx,8 K at $n approx 3.6$, and decreases to 0 K at $n = 7.2$. The
negative Weiss temperature is estimated from the Curie-Weiss law for $n > 2$. A
spherical quantum-well (SQW) model for the K cluster with 1$s$, 1$p$, and 1$d$
quantum states has previously been proposed, and the ferromagnetic properties
were explained as being due to $s$-electrons in 1$p$ states. A spin-cant model
of Mott-insulator antiferromagnetism in a K cluster array has been proposed for
the origin of the ferromagnetic properties. However, the SQW model cannot
explain either the $n$-dependence of the Curie temperature or that of the Curie
constant. In the present study, detailed measurements were made of the optical
reflection, magnetic properties, electron spin resonance, and electrical
resistivities. An optical reflection band at 0.7 eV is clearly observed for $2
< n < 6$ at low temperatures, and is assigned to the excitation of the
sigma-bonding state between 1$p$-states in adjoining alpha-cages. The
electrical resistivity indicates an insulating state continuously for $n$. We
propose an advanced SQW model with consideration for sigma-bonding, the orbital
orthogonality of 1$p$-hole states, and also the superlattice structure. We
explain the observed electronic properties using this model based on a
correlated polaron system. We propose an enhancement effect of the
Dzyaloshinsky-Moriya (DM) interaction between adjoining $1p$ orbitals by the
extension of the Rashba mechanism of spin-orbit interaction.
