[Paper Review] Quantum correlation and coherence in a mononuclear nickel-based molecular Magnet

S. Bhuvaneswari, R. Muthuganesan+1 more|arXiv (Cornell University)|Feb 23, 2026

Magnetism in coordination complexes0 citations

TL;DR

The paper analyzes entanglement, measurement-induced nonlocality (MIN), and coherence in a mononuclear nickel-based molecular magnet modeled as a mixed spin-1/2,1 Heisenberg dimer, showing entanglement vanishes with temperature and field while MIN and coherence persist in broader regimes.

ABSTRACT

We investigate the behaviors of thermal entanglement, quantum correlation beyond entanglement namely, measurement-induced nonlocality (MIN) and coherence in a nickel radical molecular magnet (Et3NH)[Ni(hfac)2L], whose spin-spin interactions are well described by the Heisenberg model. Using experimentally estimated coupling parameters, we compute the thermal state of the system and analyze the dependence of quantum resources on temperature and magnetic field. The results indicate that the quantum resources of the nickel-radical molecular magnet persist even at room temperature. We show that while negativity (the entanglement measure) rapidly vanishes with increasing temperature and magnetic field, measurement-induced nonlocality and quantum coherence remain comparatively more stable and persist in regions where entanglement is absent. These results highlight the significance of nonclassical correlations beyond entanglement in thermally activated spin systems and suggest that such molecular magnets could serve as viable platforms for quantum information processing in realistic conditions.

Motivation & Objective

• Motivate the search for quantum resources in molecular magnets operable at realistic conditions.
• Model the nickel-radical complex as a mixed spin-(1/2,1) Heisenberg dimer with experimentally estimated parameters.
• Quantify entanglement, MIN, and l1-norm coherence in ground and thermal states across temperature and magnetic field.
• Assess the robustness of quantum resources beyond entanglement for potential quantum-information applications.
• Highlight the practicality of molecular magnets as platforms for room-temperature-like quantum technologies.

Proposed method

• Use an isotropic Heisenberg model for the nickel-radical system with Hamiltonian H = J s·S - g_Rad μ_B B s^z - g_Ni μ_B B S^z.
• Adopt natural units (ħ = k_B = μ_B = 1) and experimental g-factors g_Rad = 2.005 and g_Ni = 2.275.
• Compute the thermal state ρ(T) from ρ(T) = (1/Z) exp(-βH) with partition function Z.
• Diagonalize H to obtain eigenvalues δ1,2, δ3,4, δ5,6 and corresponding eigenvectors, then express ρ(T) in the fixed basis.
• Evaluate negativity from the eigenvalues of the partially transposed density matrix ρ^T_A.
• Compute MIN using the correlation matrix T and the established closed formula for 2x3 systems.
• Measure coherence with the l1 norm defined by the sum of off-diagonal elements of ρ(T).

Figure 1: Schematic representation of the nickel-radical molecular complex $(Et_{3}NH)[Ni(hfac)_{2}L]$ Spinu2021

Experimental results

Research questions

• RQ1 How do entanglement, MIN, and coherence behave in the ground and thermal states of a mixed spin-(1/2,1) Heisenberg dimer representing the nickel-radical complex?
• RQ2 What is the comparative robustness of these quantum resources to temperature and external magnetic field?
• RQ3 Can non-entanglement quantum correlations (MIN and coherence) persist in regimes where entanglement vanishes?
• RQ4 How do the resources respond to experimentally relevant parameter values (J/k_B, g_Rad, g_Ni) for potential quantum-technological applications?

Key findings

• Negativity (entanglement) exists at zero temperature and decreases with temperature and magnetic field, vanishing beyond about 550 K or at high fields.
• MIN remains nonzero beyond the temperature where entanglement vanishes, showing robustness to thermal and magnetic disturbances.
• l1-norm coherence behaves similarly to MIN, persisting over a broad range even when entanglement is absent.
• Ground-state entanglement depends on J, g_Ni, g_Rad, and B, and decreases with increasing B due to Zeeman splitting.
• Density plots show negativity vanishes beyond T ≈ 550 K and B ≈ 370 T, while MIN and coherence persist at higher T and B values.
• The results suggest quantum correlations beyond entanglement as viable resources for quantum information processing in thermally activated solid-state systems.

Figure 2: Variations of quantum resources such as (a) negativity (b) MIN and (c) $l_{1}-$ norm of coherence as a function of temperature at a few selected values of the external magnetic field for the nickel-radical molecular compound described by the Hamiltonian (1) with the parameters set $J/k_{B}