Effect of Single-Ion Anisotropy on Stability of Quantum and Thermal Entanglement in a Mixed-Spin Heisenberg Trimer

Abstract: The effect of uniaxial single-ion anisotropy on quantum entanglement is rigorously quantified using negativity in a mixed spin-($1$,$1/2$,$1$) Heisenberg trimer, accounting for different exchange coupling constants between identical and distinct spins. Bipartite negativities between the single-spin entity and the remaining spin dimer are analyzed alongside the global tripartite negativity (gTN) of the whole trimer under the effect of an external magnetic field and both easy-axis and easy-plane types of single-ion anisotropy. Interestingly, the single-ion anisotropy significantly influences the degree of entanglement by altering the stability regions of energetically preferred ground states and it may also introduce additional phases in the overall ground-state phase diagram. Moreover, it is demonstrated that within specific ground states, the degree of entanglement primarily depends on the strength of single-ion anisotropy, altering the respective probability amplitudes of the corresponding eigenvectors. Finally, the thermal stability of entanglement is discussed in detail, including the emergence of a peculiar local minimum at finite temperatures. The obtained theoretical results may offer deeper insights into bipartite and tripartite entanglement in trimetallic Ni$^{2+}$-Cu$^{2+}$-Ni$^{2+}$ molecular compounds.