Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2607.03965

Katsura-Nagaosa-Balatsky magnetoelectricity in molecular magnets: Bipartite entanglement transfer by means of rotating electric field

Zhirayr Adamyan, Ani Chobanyan, Vadim Ohanyan, Azadeh Ghannadan, Jozef Strečka, Saeed Haddadi, Hamid Arian Zad

Published Jul 4, 2026• 0 citations
arXivHTMLPDF

Abstract

We investigate quantum entanglement in a spin-1/2 Heisenberg trimer with spin-induced electric polarization described by the Katsura-Nagaosa-Balatsky (KNB) mechanism in the presence of external magnetic and electric fields. The electric field is assumed to lie in the plane of the magnetic ions, allowing its strength and orientation to be tuned independently. We analyze both bipartite and tripartite entanglement and demonstrate that the spin-electric-field coupling provides an efficient mechanism for controlling quantum correlations within the molecular nanomagnet. Depending on the electric-field parameters, the bipartite entanglement can be significantly enhanced or suppressed, while the multipartite entanglement exhibits a rich dependence on the microscopic spin-electric coupling. Most notably, we demonstrate that a rotating in-plane electric field of constant magnitude induces a controllable transfer of bipartite entanglement between different spin pairs. In the symmetric case of homogeneous exchange interactions and uniform KNB coupling, this transfer is found to be nearly ideal, with the bipartite negativity approaching its theoretical maximum for one spin pair while simultaneously vanishing for the remaining pairs. We show that the efficiency of the transfer can be tailored through the exchange interactions, bond geometry, and nonuniform spin-electric coupling. These results establish molecular nanomagnets with KNB spin-electric coupling as a promising platform for the electrical manipulation, steering, and localization of quantum entanglement at the molecular scale.

DOI
10.48550/arxiv.2607.03965

Related papers

Molecular nanomagnet Cu 2 + Ni 2 + Cu 2 + as a resource for bipartite and tripartite quantum entanglement and coherence

Azadeh Ghannadan, Hamid Arian Zad, Saeed Haddadi +3 more

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 ${l}_{1}$-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 ${\text{Cu}}^{2+}$ and ${\text{Ni}}^{2+}$ magnetic ions along with robust tripartite entanglement among all three constituent ${\text{Cu}}^{2+}{\text{Ni}}^{2+}{\text{Cu}}^{2+}$ magnetic ions. The significant bipartite and tripartite entanglement persists even at relatively high temperatures up to $37\phantom{\rule{0.16em}{0ex}}\text{K}$ and magnetic fields up to $46\phantom{\rule{0.16em}{0ex}}\text{T}$, whereby the coherence is maintained even at elevated temperatures. It is evidenced that the aforementioned molecular complex with the magnetic core ${\text{Cu}}^{2+}{\text{Ni}}^{2+}{\text{Cu}}^{2+}$ 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.

arXiv:2407.07037•Physical Review A•Feb 7, 2025•8 citations

Effect of Single-Ion Anisotropy on Stability of Quantum and Thermal Entanglement in a Mixed-Spin Heisenberg Trimer

Hana Vargová, Jozef Strečka

The effect of uniaxial single-ion anisotropy on quantum entanglement is rigorously quantified using negativity in a mixed spin-(1,1/2,1) Heisenberg trimer, accounting for different exchange coupling constants between identical and distinct spins. Bipartite negativities between the single-spin entity and the remaining spin dimer are analyzed alongside the global tripartite negativity (gTN) of the whole trimer under the effect of an external magnetic field and both easy-axis and easy-plane types of single-ion anisotropy. Interestingly, the single-ion anisotropy significantly influences the degree of entanglement by altering the stability regions of energetically preferred ground states and it may also introduce additional phases in the overall ground-state phase diagram. Moreover, even an arbitrarily small single-ion anisotropy is sufficient to generate global tripartite entanglement in a state that remains biseparable in the isotropic limit. Finally, the thermal stability of entanglement is discussed in detail, including the emergence of a peculiar local minimum at finite temperatures. The obtained theoretical results may offer deeper insights into bipartite and tripartite entanglement in trimetallic Ni2+-Cu2+-Ni2+molecular compounds.

arXiv:2509.01451•IEEE Transactions on Magnetics•Jan 12, 2026•0 citations

Magnetism-driven ferroelectricity in spin- 12 XY chains

Oleg Menchyshyn, Vadim Ohanyan, Taras Verkholyak +2 more

We illustrate the magnetoelectric effect conditioned by the Katsura-Nagaosa-Balatsky (KNB) mechanism within the frames of exactly solvable spin-$1/2 XY$ chains. Due to three-spin interactions which are present in our consideration, the magnetization (polarization) is influenced by the electric (magnetic) field even in the absence of the magnetic (electric) field. We also discuss a magnetoelectrocaloric effect examining the entropy changes under the isothermal varying of the magnetic and/or electric field.

arXiv:1507.06457•Physical Review B•Nov 30, 2015•28 citations

Quantum entanglement in a mixed-spin trimer: Effects of a magnetic field and heterogeneous g factors

Zhirayr Adamyan, Vadim Ohanyan

Mixed spin-(1/2,1/2,1) trimer with two different Landé g factors and two different exchange couplings is considered. The main feature of the model is nonconserving magnetization. The Hamiltonian of the system is diagonalized analytically. We presented a detailed analysis of the ground-state properties, revealing several possible ground-state phase diagrams and magnetization profiles. The main focus is on how nonconserving magnetization affects quantum entanglement. We have found that nonconserving magnetization can bring a continuous dependence of the entanglement quantifying parameter (negativity) on the magnetic field within the same eigenstate, while for the case of uniform g factors it is a constant. The main result is an essential enhancement of the entanglement in the case of uniform couplings for one pair of spins caused by an arbitrary small difference in the values of g factors. This enhancement is robust and brings almost a sevenfold increase of the negativity. We have also found a weakening of entanglement for other cases. Thus, nonconserving magnetization offers a broad opportunity to manipulate the entanglement by means of a magnetic field.

arXiv:2405.00178•Physical review. E•Sep 26, 2024•7 citations

Enhanced magnetoelectric effect near a field-driven zero-temperature quantum phase transition of the spin-1/2 Heisenberg-Ising ladder

Jozef Strečka, Lucia Gálisová, Taras Verkholyak

The magnetoelectric effect of a spin-1/2 Heisenberg-Ising ladder in the presence of external electric and magnetic fields is rigorously examined by taking into account the Katsura-Nagaosa-Balatsky mechanism. It is shown that an applied electric field may control the quantum phase transition between a Néel (stripy) ordered phase and a disordered paramagnetic phase. The staggered magnetization vanishes according to a power law with an Ising-type critical exponent 1/8, the electric polarization exhibits a weak singularity, and the dielectric susceptibility shows a logarithmic divergence at this particular quantum phase transition. The external electric field may alternatively invoke a discontinuous phase transition accompanied with abrupt jumps of the dielectric polarization and susceptibility on the assumption that the external magnetic field becomes nonzero.

arXiv:1912.06637•Physical review. E•Jan 3, 2020•8 citations

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

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.

Molecules•Jun 5, 2021•20 citations
We investigate quantum entanglement in a spin-1/2 Heisenberg trimer with spin-induced electric polarization described by the Katsura-Nagaosa-Balatsky (KNB) mechanism in the presence of external magnetic and electric fields. The electric field is assumed to lie in the plane of the magnetic ions, allowing its strength and orientation to be tuned independently. We analyze both bipartite and tripartite entanglement and demonstrate that the spin-electric-field coupling provides an efficient mechanism for controlling quantum correlations within the molecular nanomagnet. Depending on the electric-field parameters, the bipartite entanglement can be significantly enhanced or suppressed, while the multipartite entanglement exhibits a rich dependence on the microscopic spin-electric coupling. Most notably, we demonstrate that a rotating in-plane electric field of constant magnitude induces a controllable transfer of bipartite entanglement between different spin pairs. In the symmetric case of homogeneous exchange interactions and uniform KNB coupling, this transfer is found to be nearly ideal, with the bipartite negativity approaching its theoretical maximum for one spin pair while simultaneously vanishing for the remaining pairs. We show that the efficiency of the transfer can be tailored through the exchange interactions, bond geometry, and nonuniform spin-electric coupling. These results establish molecular nanomagnets with KNB spin-electric coupling as a promising platform for the electrical manipulation, steering, and localization of quantum entanglement at the molecular scale.
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 effect of uniaxial single-ion anisotropy on quantum entanglement is rigorously quantified using negativity in a mixed spin-(1,1/2,1) Heisenberg trimer, accounting for different exchange coupling constants between identical and distinct spins. Bipartite negativities between the single-spin entity and the remaining spin dimer are analyzed alongside the global tripartite negativity (gTN) of the whole trimer under the effect of an external magnetic field and both easy-axis and easy-plane types of single-ion anisotropy. Interestingly, the single-ion anisotropy significantly influences the degree of entanglement by altering the stability regions of energetically preferred ground states and it may also introduce additional phases in the overall ground-state phase diagram. Moreover, even an arbitrarily small single-ion anisotropy is sufficient to generate global tripartite entanglement in a state that remains biseparable in the isotropic limit. Finally, the thermal stability of entanglement is discussed in detail, including the emergence of a peculiar local minimum at finite temperatures. The obtained theoretical results may offer deeper insights into bipartite and tripartite entanglement in trimetallic Ni2+-Cu2+-Ni2+molecular compounds.
We illustrate the magnetoelectric effect conditioned by the Katsura-Nagaosa-Balatsky (KNB) mechanism within the frames of exactly solvable spin-1/2XY1/2 XY1/2XY chains. Due to three-spin interactions which are present in our consideration, the magnetization (polarization) is influenced by the electric (magnetic) field even in the absence of the magnetic (electric) field. We also discuss a magnetoelectrocaloric effect examining the entropy changes under the isothermal varying of the magnetic and/or electric field.
Mixed spin-(1/2,1/2,1) trimer with two different Landé g factors and two different exchange couplings is considered. The main feature of the model is nonconserving magnetization. The Hamiltonian of the system is diagonalized analytically. We presented a detailed analysis of the ground-state properties, revealing several possible ground-state phase diagrams and magnetization profiles. The main focus is on how nonconserving magnetization affects quantum entanglement. We have found that nonconserving magnetization can bring a continuous dependence of the entanglement quantifying parameter (negativity) on the magnetic field within the same eigenstate, while for the case of uniform g factors it is a constant. The main result is an essential enhancement of the entanglement in the case of uniform couplings for one pair of spins caused by an arbitrary small difference in the values of g factors. This enhancement is robust and brings almost a sevenfold increase of the negativity. We have also found a weakening of entanglement for other cases. Thus, nonconserving magnetization offers a broad opportunity to manipulate the entanglement by means of a magnetic field.
The magnetoelectric effect of a spin-1/2 Heisenberg-Ising ladder in the presence of external electric and magnetic fields is rigorously examined by taking into account the Katsura-Nagaosa-Balatsky mechanism. It is shown that an applied electric field may control the quantum phase transition between a Néel (stripy) ordered phase and a disordered paramagnetic phase. The staggered magnetization vanishes according to a power law with an Ising-type critical exponent 1/8, the electric polarization exhibits a weak singularity, and the dielectric susceptibility shows a logarithmic divergence at this particular quantum phase transition. The external electric field may alternatively invoke a discontinuous phase transition accompanied with abrupt jumps of the dielectric polarization and susceptibility on the assumption that the external magnetic field becomes nonzero.
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.