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

TL;DR

This study theoretically investigates the ground-state spin configurations and bipartite entanglement in a heterometallic coordination polymer using a symmetric spin-1/2 Ising-Heisenberg model, revealing five distinct quantum phases and their magnetization signatures.

Contribution

It introduces a detailed theoretical analysis of quantum entanglement and spin arrangements in a complex polymer, identifying multiple ground states and their magnetic properties.

Findings

Identification of five ground states with varying entanglement levels.

Discovery of specific magnetization plateaus corresponding to different phases.

Observation of temperature-dependent entanglement dynamics.

Abstract

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 $16.26\mu_{\rm B}$ and at the saturation value $20.82\mu_{\rm B}$, 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 $9.27\mu_{\rm B}$ per unit cell, while the latter ones as zero magnetization plateau and intermediate plateau at the magnetization $18.54\mu_{\rm B}$. 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.