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The concept of negativity is adapted in order to explore the quantum andthermal entanglement of the mixed spin-(1/2,$S$) Heisenberg dimers in presenceof an external magnetic field. The mutual interplay between the spin size $S$,XXZ exchange and uniaxial single-ion anisotropy is thoroughly examined with agoal to tune the degree and thermal stability of the pairwise entanglement. Itturns out that the antiferromagnetic spin-(1/2,$S$) Heisenberg dimers exhibithigher degree of entanglement and higher threshold temperature in comparisonwith their ferromagnetic counterparts when assuming the same set of modelparameters. The increasing spin magnitude $S$ accompanied with an easy-planeuniaxial single-ion anisotropy can enhance not only the thermal stability butsimultaneously the degree of entanglement. It is additionally shown that thefurther enhancement of a bipartite entanglement can be achieved in the mixedspin-(1/2,$S$) Heisenberg dimers, involving half-odd-integer spins $S$. Underthis condition the thermal negativity saturates at low-enough temperatures inits maximal value regardless of the magnitude of half-odd-integer spin $S$. Themagnetic field induces consecutive discontinuous phase transitions in the mixedspin-(1/2,$S$) Heisenberg dimers with $S\!>\!1$, which are manifested in asurprising oscillating magnetic-field dependence of the negativity observed atlow enough temperature.

Unconventional thermal and magnetic-field-driven changes of a bipartite  entanglement of a mixed spin-(1/2,$S$) Heisenberg dimer with an uniaxial  single-ion anisotropy