Magnetic-Field-Orientation Dependent Thermal Entanglement of a Spin-1 Heisenberg Dimer: The Case Study of Dinuclear Nickel Complex with an Uniaxial Single-Ion Anisotropy.

Azadeh Ghannadan,Jozef Strečka

doi:10.3390/molecules26113420

Azadeh Ghannadan, Jozef Strečka

Open Access

https://doi.org/10.3390/molecules26113420

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Abstract

The bipartite entanglement in pure and mixed states of a quantum spin-1 Heisenberg dimer with exchange and uniaxial single-ion anisotropies is quantified through the negativity in a presence of the external magnetic field. At zero temperature the negativity shows a marked stepwise dependence on a magnetic field with two abrupt jumps and plateaus, which can be attributed to the quantum antiferromagnetic and quantum ferrimagnetic ground states. The magnetic-field-driven phase transition between the quantum antiferromagnetic and quantum ferrimagnetic ground states manifests itself at nonzero temperatures by a local minimum of the negativity, which is followed by a peculiar field-induced rise of the negativity observable in a range of moderately strong magnetic fields. The rising temperature generally smears out abrupt jumps and plateaus of the negativity, which cannot be distinguished in the relevant dependencies above a certain temperature. It is shown that the thermal entanglement is most persistent against rising temperature at the magnetic field, for which an energy gap between a ground state and a first excited state is highest. Besides, temperature variations of the negativity of the spin-1 Heisenberg dimer with an easy-axis single-ion anisotropy may exhibit a singular point-kink, at which the negativity has discontinuity in its first derivative. The homodinuclear nickel complex [Ni(Medpt)(-ox)(HO)](ClO)·2HO provides a suitable experimental platform of the antiferromagnetic spin-1 Heisenberg dimer, which allowed us to estimate a strength of the bipartite entanglement between two exchange-coupled Ni magnetic ions on the grounds of the interaction constants reported previously from the fitting procedure of the magnetization data. It is verified that the negativity of this dinuclear compound is highly magnetic-field-orientation dependent due to presence of a relatively strong uniaxial single-ion anisotropy.

Highlights

Entanglement is one of the most peculiar features of quantum mechanics that does not have a classical counterpart and resulted a controversial debate between two prominent groups of physicists [1] in the 1930s
Before proceeding to a detailed investigation of the negativity it is worthwhile to recall that the antiferromagnetic spin-1 Heisenberg dimer has according to reference [51] three different ground states denoted as the quantum antiferromagnetic phase |QAF :
The negativity, which may serve as a measure of bipartite entanglement at zero as well as nonzero temperatures, was rigorously calculated from negative eigenvalues of a partially transposed density matrix according to the definition put forward by Vidal and Werner [34]

Summary

Introduction

Entanglement is one of the most peculiar features of quantum mechanics that does not have a classical counterpart and resulted a controversial debate between two prominent groups of physicists [1] in the 1930s. The bipartite entanglement within pure and mixed states of the Heisenberg spin models can be for instance quantified in terms of von Neumann entropy of the reduced density matrix [30], concurrence [31,32] or negativity [33,34] These entanglement measures can be related to measurable magnetic and thermodynamic quantities [35] and Molecules 2021, 26, 3420 they are amenable to experimental testing [36,37]. We will investigate in detail the quantum and thermal entanglement within pure and mixed states of a spin-1 Heisenberg dimer accounting for the exchange anisotropy, uniaxial single-ion anisotropy and magnetic field. The negativity of the spin-1 Heisenberg dimer can be calculated from the formula: N

Theoretical Results and Discussion

Entanglement in the Dinuclear Nickel Complex NAOC

Conclusions