Quantum entanglement generation in heterometallic Ni24+Gd34+ complexes

We investigate various types of quantum entanglement in the octanuclear heterometallic 3d/4 f complexes de-noted as Ni2+4 Gd3+4 under an external magnetic field, using the exact diagonalization approach. These molecular magnets, which can be effectively described by Heisenberg spin models, consist of two identical {Ni2+2 Gd3+2 } cubane subunits bridged by acetate and hydroxide ligands. Our analysis reveals that their magnetization exhibits intermediate plateaus at low temperatures, indicating distinct ground states characteristic of Ni-containing compounds. Using negativity as a measure of quantum entanglement, we examine the influence of single-ion anisotropy and magnetic field on tetrapartite, bipartite, 1–3 tangle, and 2–2 tangle entanglements in two families of Ni2+ 4 Gd3+ 4 complexes: (1) without anisotropy and (2) with anisotropy. Complex (1) exhibits strong bipartite entanglement between Ni ions, which persists up to T ≈ 3.0 K and B ≈ 4.0 T, but shows significantly weaker tetrapartite entanglement and vanishing bipartite entanglement between Gd ··· Gd and Ni ··· Gd pairs. In contrast, complex (2) displays nonzero and sizable values for all types of entanglement considered. These findings emphasis the crucial role of single-ion anisotropy in generating and shaping the entanglement landscape of heterometallic Ni2+
4 Gd3+ 4 complexes. Notably, we find that the 1–3 tangle entanglement between a Ni ion and the remaining sites in a cubane unit serves as a reliable indicator of ground-state phase transitions, exhibiting distinct changes across phase boundaries irrespective of the presence of single-ion anisotropy.