Title: Cluster-based Haldane state in edge-shared tetrahedral spin-cluster chain: Fedotovite K$_2$Cu$_3$O(SO$_4$)$_3$,
Abstract: Fedotovite K$_2$Cu$_3$O(SO$_4$)$_3$ is a candidate of new quantum spin
systems, in which the edge-shared tetrahedral (EST) spin-clusters consisting of
Cu$^{2+}$ are connected by weak inter-cluster couplings to from one-dimensional
array. Comprehensive experimental studies by magnetic susceptibility,
magnetization, heat capacity, and inelastic neutron scattering measurements
reveal the presence of an effective $S$ = 1 Haldane state below $T \cong 4$ K.
Rigorous theoretical studies provide an insight into the magnetic state of
K$_2$Cu$_3$O(SO$_4$)$_3$: an EST cluster makes a triplet in the ground state
and one-dimensional chain of the EST induces a cluster-based Haldane state. We
predict that the cluster-based Haldene state emerges whenever the number of
tetrahedra in the EST is $even$.