Magnetization processes and quantum entanglement in a spin-1/2 Ising-Heisenberg chain model of a heterotrimetallic Fe-Mn-Cu coordination polymer

We introduce and exactly solve a spin-1/2 Ising-Heisenberg chain that captures some relevant aspects of the heterotrimetallic coordination compound [CuIIMnII(L1)] [FeIII(bpb)(CN)2] ·ClO4·H2O to be further abbreviated as Fe-Mn-Cu. The magnetic backbone of the coordination polymer Fe-Mn-Cu forms a regular alternation of Fe3+ and Mn2+ ions, whereas Cu2+ ions are laterally attached to Mn2+ ions. The exchange coupling between Fe3+and Mn2+ ions is assumed to be Ising-like, while the exchange coupling between Cu2+and Mn2+ ions is assumed to be an anisotropic XXZ Heisenberg interaction. The gyromagnetic factors of all three metal ions are adjusted so as to obtain proper magnetic moment of individual metal ions when they are treated as spin-1/2 carriers. The ground-state phase diagram exhibits four distinct phases, whereas two of them display a quantum entanglement between spin states of Cu2+and Mn2+ ions. It is shown that the magnetization continuously varies with the magnetic field within two quantum ground states due to the mismatch between the magnetic moments and it also exhibits interesting field-driven phase transitions. The degree of quantum entanglement between the spin states of Cu2+and Mn2+ ions is quantified by the concurrence, which unveils that the entanglement becomes optimal at finite magnetic fields within one of the quantum ground states. The concurrence may exhibit non-monotonous dependences on the magnetic field and temperature.