Cluster-Based Haldane States in Spin Cluster Chains

The S=1 Haldane state has attracted much attention due to its topological characters. This state emerges not only in the S=1 spin chain, but also in an S=1/2 two-leg spin ladder with a ferromagnetic rung interaction. Additionally, our recent study on low-temperature magnetism in a naturally occurring mineral Fedotovite, has shown the Haldane state consisting of cluster-based S=1 spins, in collaboration with experimental groups. In this compound, edge-shared tetrahedral spin clusters which include six spins in a cluster, are linked by a nearest-neighbor antiferromagnetic inter-cluster interaction in one dimension. The low-energy state in a cluster is a triplet and the inter-cluster interaction is perturbative as compared with the intra-cluster excitation energy, so that we can explain the low-temperature physics in an effective S=1 spin model obtained by projection into cluster's triplet states. Furthermore, we extend the cluster-based Haldane state to spin-cluster systems which have odd-number S=1/2 spins in a cluster, and find cluster-based Haldane state with breaking time-reversal symmetry. Thus, we will present several varieties of cluster-based Haldane states obatined in possible spin lattices.