The quantum and thermal entanglement in the mixed spin-(1/2,$S$) Heisenberg dimer with an uniaxial single-ion anisotropy

The concept of negativity is used to study the quantum and thermal entanglement in a generalized spin-(1/2,$S$) Heisenberg dimer under presence of an external magnetic field. The competition effect of interplay between the spin diversity, XXZ exchange as well as uniaxial single-ion anisotropy is additionally analysed with a goal to tune the degree and thermal stability of the pairwise entanglement. Obtained analytical results favour the antiferromagnetic spin-(1/2,$S$) Heisenberg dimer instead of the ferromagnetic one, where the higher degree of entanglement and higher threshold temperature are achieved at the same set of model parameters. It is demonstrated and analytically proven that the increasing magnitude of spin $S$ in dimer with an easy-axis uniaxial single-ion anisotropy can enhance not only the thermal stability but simultaneously the degree of entanglement. It is shown additionally, that the further enhancement of entanglement can be improved in dimer with a half-odd-integer spin $S$ as a consequence of different magnetic ground-states. In such system the low-enough thermal negativity saturates in its maximal value regardless the magnitude of half-odd-integer spin $S$. Because of the influence of the magnetic-field induced consecutive second-order phase transitions in dimer with $S\!>\!1$, the surprising oscillating behaviour of negativity upon the magnetic field is observed at low-enough temperature.