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arXiv:2406.02144 · Inorganics

Room-Temperature Entanglement of the Nickel-Radical Molecular Complex (Et3NH)[Ni(hfac)2L] Reinforced by the Magnetic Field

Jozef Strečka, Elham Shahhosseini Shahrabadi

Published Mar 31, 2024• 5 citations
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Abstract

Bipartite entanglement is comprehensively investigated in the mononuclear molecular complex (Et3NH)[Ni(hfac)2L], where HL denotes 2-(2-hydroxy-3-methoxy-5-nitrophenyl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazol-3-oxide-1-oxyl and hfacH stands for hexafluoroacetylacetone. From the magnetic point of view, the molecular compound (Et3NH)[Ni(hfac)2L] consists of an exchange-coupled spin-1 Ni2+ magnetic ion and a spin-12 nitronyl-nitroxide radical substituted nitrophenol. The nickel-radical molecular complex affords an experimental realization of a mixed spin-(12, 1) Heisenberg dimer with a strong antiferromagnetic exchange coupling, J/kB = 505 K, and two distinct g-factors, gRad = 2.005 and gNi = 2.275. By adopting this set of magnetic parameters, we demonstrate that the Zeeman splitting of a quantum ferrimagnetic ground-state doublet due to a weak magnetic field may substantially reinforce the strength of bipartite entanglement at low temperatures. The molecular compound (Et3NH)[Ni(hfac)2L] maintains sufficiently strong thermal entanglement, even at room temperature, vanishing only above 546 K. Specifically, the thermal entanglement in the nickel-radical molecular complex retains approximately 40% of the maximum value, corresponding to perfectly entangled Bell states at room temperature, which implies that this magnetic compound provides a suitable platform of a molecular qubit with potential implications for room-temperature quantum computation and quantum information processing.

DOI
10.3390/inorganics12040102

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Bipartite entanglement is comprehensively investigated in the mononuclear molecular complex (Et3NH)[Ni(hfac)2L], where HL denotes 2-(2-hydroxy-3-methoxy-5-nitrophenyl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazol-3-oxide-1-oxyl and hfacH stands for hexafluoroacetylacetone. From the magnetic point of view, the molecular compound (Et3NH)[Ni(hfac)2L] consists of an exchange-coupled spin-1 Ni2+ magnetic ion and a spin-12 nitronyl-nitroxide radical substituted nitrophenol. The nickel-radical molecular complex affords an experimental realization of a mixed spin-(12, 1) Heisenberg dimer with a strong antiferromagnetic exchange coupling, J/kB = 505 K, and two distinct g-factors, gRad = 2.005 and gNi = 2.275. By adopting this set of magnetic parameters, we demonstrate that the Zeeman splitting of a quantum ferrimagnetic ground-state doublet due to a weak magnetic field may substantially reinforce the strength of bipartite entanglement at low temperatures. The molecular compound (Et3NH)[Ni(hfac)2L] maintains sufficiently strong thermal entanglement, even at room temperature, vanishing only above 546 K. Specifically, the thermal entanglement in the nickel-radical molecular complex retains approximately 40% of the maximum value, corresponding to perfectly entangled Bell states at room temperature, which implies that this magnetic compound provides a suitable platform of a molecular qubit with potential implications for room-temperature quantum computation and quantum information processing.
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.
Bipartite quantum and thermal entanglement is quantified within pure and mixed states of a mixed spin-(1/2,11/2,11/2,1) 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---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 the twofold 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 under the assumption that the gyromagnetic ggg factors of the spin-1/2 and spin-1 magnetic ions are equal and the uniaxial single-ion anisotropy is half of the exchange constant. It is suggested that the heterodinuclear complex $[\mathrm{Ni}(\mathrm{dpt})({\mathrm{H}}_{2}\mathrm{O})\mathrm{Cu}(\mathrm{pba})]\ifmmode\cdot\else\textperiodcentered\fi{}2{\mathrm{H}}_{2}\mathrm{O}$ [pba = 1,3-propylenebis(oxamato) and dpt = bis-(3-aminopropyl)amine], which affords an experimental realization of the mixed spin-(1/2,11/2,11/2,1) Heisenberg dimer, remains strongly entangled up to relatively high temperatures (about 115 K) and magnetic fields (about 140 T) that are comparable with the relevant exchange constant.
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 [Ni2(Medpt)2(μ-ox)(H2O)2](ClO4)2·2H2O 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 Ni2+ 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.
We investigate key quantum characteristics of the mixed spin-(1/2,1,1/2) Heisenberg trimer under the influence of an external magnetic field. Specifically, we analyze the distributions of bipartite and tripartite entanglement quantified through the respective negativities and the l1{l}_{1}l1​-norm of coherence with the help of rigorous analytical and numerical methods. Our findings suggest that the heterotrinuclear molecular nanomagnet $[{{{\text{Cu}}^{2+}\text{L}}}_{2}{\text{Ni}}^{2+}{({\text{H}}_{2}\text{O})}_{2}]{({\text{ClO}}_{4})}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}3{\text{H}}_{2}\text{O}$, which represents an experimental realization of the mixed spin-(1/2,1,1/2) Heisenberg trimer, exhibits a significant bipartite entanglement between Cu2+{\text{Cu}}^{2+}Cu2+ and Ni2+{\text{Ni}}^{2+}Ni2+ magnetic ions along with robust tripartite entanglement among all three constituent Cu2+Ni2+Cu2+{\text{Cu}}^{2+}{\text{Ni}}^{2+}{\text{Cu}}^{2+}Cu2+Ni2+Cu2+ magnetic ions. The significant bipartite and tripartite entanglement persists even at relatively high temperatures up to 37K37\phantom{\rule{0.16em}{0ex}}\text{K}37K and magnetic fields up to 46T46\phantom{\rule{0.16em}{0ex}}\text{T}46T, whereby the coherence is maintained even at elevated temperatures. It is evidenced that the aforementioned molecular complex with the magnetic core Cu2+Ni2+Cu2+{\text{Cu}}^{2+}{\text{Ni}}^{2+}{\text{Cu}}^{2+}Cu2+Ni2+Cu2+ provides an intriguing quantum resource, which exhibits a star-shaped state within the singlet eigenstate at low magnetic fields and W-like state within the triplet eigenstate at moderate magnetic fields.
The bipartite entanglement of a quantum spin-1 Heisenberg diamond cluster in the presence of the external magnetic field is quantified through the negativity, which is calculated for spin pairs from a diagonal and a side of the diamond spin cluster taking into consideration two different coupling constants. The magnetic field may cause a few crossings of energy levels of the spin-1 Heisenberg diamond cluster, which is responsible at low enough temperatures for a stepwise dependence of the negativity on the magnetic field accompanied with a drop of the negativity at respective magnetic-field-driven transitions due to emergence of mixed states. It is shown that the bipartite entanglement between spin pairs on a diagonal and a side of the diamond spin cluster is concurrent although they may eventually become both nonzero albeit not fully saturated. It is predicted that the tetranuclear nickel complex [Ni4(μ-CO3)2(aetpy)8](ClO4)4 (aetpy = 2-aminoethyl-pyridine), which represents an experimental realization of the spin-1 Heisenberg diamond cluster with two different antiferromagnetic coupling constants, exhibits a substantial bipartite entanglement between two spin-1 Ni2+ magnetic ions from a shorter diagonal of the diamond spin cluster up to temperatures approximately about 50 K and up to magnetic fields about 70 T.
We investigate various types of quantum entanglement in the octanuclear heterometallic 3d/4f3d/4f3d/4f complexes denoted as Ni42+Gd43+{\mathrm{Ni}}_{4}^{2+}{\mathrm{Gd}}_{4}^{3+}Ni42+​Gd43+​ under an external magnetic field, using the exact diagonalization approach. These molecular magnets, which can be effectively described by Heisenberg spin models, consist of two identical {Ni22+Gd23+{\mathrm{Ni}}_{2}^{2+}{\mathrm{Gd}}_{2}^{3+}Ni22+​Gd23+​} cubane subunits bridged by acetate and hydroxide ligands. Our analysis reveals that their magnetization exhibits intermediate plateaus at low temperatures, indicating distinct ground states characteristic of Ni-containing compounds. Using negativity as a measure of quantum entanglement, we examine the influence of single-ion anisotropy and magnetic field on tetrapartite, bipartite, 1--3 tangle, and 2--2 tangle entanglements in two families of Ni42+Gd43+{\mathrm{Ni}}_{4}^{2+}{\mathrm{Gd}}_{4}^{3+}Ni42+​Gd43+​ complexes: (1) without anisotropy and (2) with anisotropy. Complex (1) exhibits strong bipartite entanglement between Ni ions, which persists up to $T\ensuremath{\approx}3.0\phantom{\rule{0.28em}{0ex}}\text{K}$ and $B\ensuremath{\approx}4.0\phantom{\rule{0.28em}{0ex}}\text{T}$, but shows significantly weaker tetrapartite entanglement and vanishing bipartite entanglement between $\mathrm{Gd}\ensuremath{\cdots}\mathrm{Gd}$ and $\mathrm{Ni}\ensuremath{\cdots}\mathrm{Gd}$ pairs. In contrast, complex (2) displays nonzero and sizable values for all types of entanglement considered. These findings emphasis the crucial role of single-ion anisotropy in generating and shaping the entanglement landscape of heterometallic Ni42+Gd43+{\mathrm{Ni}}_{4}^{2+}{\mathrm{Gd}}_{4}^{3+}Ni42+​Gd43+​ complexes. Notably, we find that the 1--3 tangle entanglement between a Ni ion and the remaining sites in a cubane unit serves as a reliable indicator of ground-state phase transitions, exhibiting distinct changes across phase boundaries irrespective of the presence of single-ion anisotropy.