Unconventional strengthening of a bipartite entanglement of a mixed spin-(1/2,1) Heisenberg dimer achieved through Zeeman splitting

TL;DR

This paper investigates how Zeeman splitting unexpectedly enhances bipartite entanglement in a mixed spin-(1/2,1) Heisenberg dimer, revealing conditions for maximal entanglement and potential experimental realization in heterodinuclear complexes.

Contribution

It demonstrates that magnetic fields can reinforce entanglement in mixed spin dimers via Zeeman splitting, a novel insight into quantum control of entanglement.

Findings

Magnetic field increases bipartite entanglement through Zeeman splitting.

Maximal entanglement occurs at low nonzero magnetic fields in a ferrimagnetic phase.

Entanglement persists at high temperatures and magnetic fields in a specific heterodinuclear complex.

Abstract

The bipartite quantum and thermal entanglement is quantified within pure and mixed states of a mixed spin-(1/2,1) Heisenberg dimer with the help of negativity. It is shown that the negativity, which may serve as a measure of the bipartite entanglement at zero as well as nonzero temperatures, strongly depends on intrinsic parameters as for instance exchange and uniaxial single-ion anisotropy in addition to extrinsic parameters such as temperature and magnetic field. It turns out that a rising magnetic field unexpectedly reinforces the bipartite entanglement due to the Zeeman splitting of energy levels, which lifts a two-fold degeneracy of the quantum ferrimagnetic ground state. The maximal bipartite entanglement is thus reached within a quantum ferrimagnetic phase at sufficiently low but nonzero magnetic fields on assumption that the gyromagnetic g-factors of the spin-1/2 and spin-1 magnetic ions are equal and the uniaxial single-ion anisotropy is a half of the exchange constant. It is suggested that the heterodinuclear complex [Ni(dpt)(H$_2$O)Cu(pba)]$\cdot$2H$_2$O (pba=1,3-propylenebis(oxamato) and dpt=bis-(3-aminopropyl)amine), which affords an experimental realization of the mixed spin-(1/2,1) Heisenberg dimer, remains strongly entangled up to relatively high temperatures (about 140~K) and magnetic fields (about 140~T) being comparable with the relevant exchange constant.