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Insight into ground-state spin arrangement and bipartite entanglement of the polymeric coordination compound [Dy$_2$Cu$_2$]$_n$ through the symmetric spin-1/2 Ising-Heisenberg orthogonal-dimer chain

The ground-state spin arrangement and the bipartite entanglement within Cu$^{2+}$-Cu$^{2+}$ dimers across the magnetization process of the 4f-3d heterometallic coordination polymer [{Dy(hfac)$_2$(CH$_3$OH)}$_2${Cu(dmg)(Hdmg)}$_2$]$_n$ (H$_2$dmg = dimethylglyoxime, Hhfac = 1,1,1,5,5,5-hexafluoropentane-2,4-dione) are theoretically examined using the symmetric isotropic spin-$1/2$ Ising-Heisenberg orthogonal-dimer chain. The numerical results point to five possible ground states of the compound with three different degrees of the quantum entanglement within Cu$^{2+}$-Cu$^{2+}$. Besides the standard ferrimagnetic and saturated phases without quantum entanglement of Cu$^{2+}$ ions, which are manifested in low-temperature magnetization curve as wide plateaus at the non-saturated magnetization $16.26μ_{\rm B}$ and at the saturation value $20.82μ_{\rm B}$, respectively, one also finds an intriguing singlet-like phase with just partial entanglement within Cu$^{2+}$-Cu$^{2+}$ and two singlet phases with fully entangled Cu$^{2+}$-Cu$^{2+}$ dimers. The former quantum phase can be identified in the low-temperature magnetization process as very narrow intermediate plateau at the magnetization $9.27μ_{\rm B}$ per unit cell, while the latter ones as zero magnetization plateau and intermediate plateau at the magnetization $18.54μ_{\rm B}$. Non-monotonous temperature variations of the concurrence, through which the entanglement within cooper dimers is quantified, point to the possible temporary thermal activation of the entangled states of Cu$^{2+}$-Cu$^{2+}$ also above non-entangled ferrimagnetic and saturated phases.