Molecular Nanomagnet $\text{Cu}^\text{II}\text{Ni}^\text{II}\text{Cu}^\text{II}$ as Resource for Bipartite and Tripartite Quantum Entanglement and Coherence

Abstract

We investigate key quantum characteristics of the mixed spin-(1/2,1,1/2) Heisenberg trimer under the influence of an external magnetic field. Specifically, we analyze the distributions of bipartite and tripartite entanglement quantified through the respective negativities, and the $l_1$-norm of coherence with the help of rigorous analytical and numerical methods. Our findings suggest that the heterotrinuclear molecular nanomagnet $[\{\text{Cu}^\text{II}\text{L}\}_2\text{Ni}^\text{II}(\text{H}_2\text{O})_2](\text{ClO}_4)_{2} . 3\text{H}_2\text{O}$, which represents an experimental realization of the mixed spin-(1/2,1,1/2) Heisenberg trimer, exhibits a significant bipartite entanglement between $\text{Cu}^\text{II}$ and $\text{Ni}^\text{II}$ magnetic ions along with robust tripartite entanglement among all three constituent $\text{Cu}^\text{II}\text{Ni}^\text{II}\text{Cu}^\text{II}$ magnetic ions. The significant bipartite and tripartite entanglement persists even at relatively high temperatures up to $37\,\text{K}$ and magnetic fields up to $46\,\text{T}$, whereby the coherence is maintained even at elevated temperatures. {It is evidenced that the aforementioned molecular complex with the magnetic core $\text{Cu}^\text{II}\text{Ni}^\text{II}\text{Cu}^\text{II}$ provides an intriguing quantum resource, which exhibits a star-shaped state within the singlet eigenstate at low magnetic fields and W-like state within the triplet eigenstate at moderate magnetic fields.