On the Concurrent Bipartite Entanglement of a Spin-1 Heisenberg Diamond Cluster Developed for Tetranuclear Nickel Complexes

Abstract

The bipartite entanglement of a quantum spin-1 Heisenberg diamond cluster in the presence of the external magnetic field is quantified through the negativity, which is calculated for spin pairs from a diagonal and a side of the diamond spin cluster taking into consideration two different coupling constants. The magnetic field may cause a few crossings of energy levels of the spin-1 Heisenberg diamond cluster, which is responsible at low enough temperatures for a stepwise dependence of the negativity on the magnetic field accompanied with a drop of the negativity at respective magnetic-field-driven transitions due to emergence of mixed states. It is shown that the bipartite entanglement between spin pairs on a diagonal and a side of the diamond spin cluster is concurrent although they may eventually become both nonzero albeit not fully saturated. It is predicted that the tetranuclear nickel complex [Ni4(μ-CO3)2(aetpy)8](ClO4)4 (aetpy = 2-aminoethyl-pyridine), which represents an experimental realization of the spin-1 Heisenberg diamond cluster with two different antiferromagnetic coupling constants, exhibits a substantial bipartite entanglement between two spin-1 Ni2+ magnetic ions from a shorter diagonal of the diamond spin cluster up to temperatures approximately about 50 K and up to magnetic fields about 70 T.

Keywords

• spin-1 Heisenberg diamond cluster
• bipartite entanglement
• tetranuclear nickel complex