We investigate various types of quantum entanglement in the octanuclear heterometallic $3d/4f$ complexes denoted as ${\mathrm{Ni}}_4^{2+}{\mathrm{Gd}}_4^{3+}$ 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 {${\mathrm{Ni}}_2^{2+}{\mathrm{Gd}}_2^{3+}$} 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 ${\mathrm{Ni}}_4^{2+}{\mathrm{Gd}}_4^{3+}$ complexes: (1) without anisotropy and (2) with anisotropy. Complex (1) exhibits strong bipartite entanglement between Ni ions, which persists up to $T\approx 3.0\text{K}$ and $B\approx 4.0\text{T}$, but shows significantly weaker tetrapartite entanglement and vanishing bipartite entanglement between $\mathrm{Gd}\cdots \mathrm{Gd}$ and $\mathrm{Ni}\cdots \mathrm{Gd}$ 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 ${\mathrm{Ni}}_4^{2+}{\mathrm{Gd}}_4^{3+}$ 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.

Close

PrevNext

View figure in article

• Magnetic anisotropy
• Magnetic coupling
• Magnetic interactions
• Magnetic phase transitions
• Magnetization dynamics
• Molecular magnetism
• Quantum entanglement
• Specific heat