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Szałowski K. Phase Diagram and Quantum Entanglement Properties of a Pentamer S = 1/2 Heisenberg Spin Cluster. Molecules 2023; 28:6418. [PMID: 37687247 PMCID: PMC10489753 DOI: 10.3390/molecules28176418] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2023] [Revised: 08/21/2023] [Accepted: 08/29/2023] [Indexed: 09/10/2023] Open
Abstract
Cluster molecular magnets prove their potential for applications in quantum technologies, encouraging studies of quantum entanglement in spin systems. In the paper we discuss quantum entanglement properties of pentamer cluster composed of spins S=1/2 forming a tetrahedron with additional spin in its center, with geometry reproducing the smallest nonplanar graph. We model the system with isotropic Heisenberg Hamiltonian including external magnetic field and use exact diagonalization approach to explore the ground-state phase diagram and thermodynamic properties within canonical ensemble formalism. We focus the interest on two-spin entanglement quantified by Wootters concurrence. For ground state, we find two states with total cluster spin equal to 3/2 exhibiting entanglement, occurring preferably for antiferromagnetic interactions. For finite temperatures, we predict the presence of magnetic-field-induced entanglement as well as temperature-induced entanglement.
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Affiliation(s)
- Karol Szałowski
- Department of Solid State Physics, Faculty of Physics and Applied Informatics, University of Łódź, ul. Pomorska 149/153, PL90-236 Łódź, Poland
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Panov Y. Residual entropy of the dilute Ising chain in a magnetic field. Phys Rev E 2022; 106:054111. [PMID: 36559516 DOI: 10.1103/physreve.106.054111] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2022] [Accepted: 10/18/2022] [Indexed: 06/17/2023]
Abstract
The properties of the ground state of the simplest frustrated system, the dilute Ising chain in a magnetic field, are rigorously investigated over the entire range of concentrations of charged nonmagnetic impurities. Analytical methods are proposed for calculating the residual entropy of frustrated states, including states at phase boundaries, which are based on the Markov property of the system and involve solving a linear optimization problem for energy and a nonlinear optimization problem for entropy. These methods allow obvious generalizations for one-dimensional pseudospin models with anisotropic interactions. We calculate the composition, entropy, and magnetization for the ground state phases. We prove the absence of pseudotransitions in the dilute Ising chain, since the residual entropy of states at phase boundaries is always higher than the entropy of adjacent phases. The concentration dependencies of magnetization at the phase boundaries are obtained, and unlike linear dependencies for adjacent phases, they have nonlinear behavior. Field-induced transitions between ground states and entropy jumps associated with them are also considered, and in particular, it is shown that the field-induced transition from an antiferromagnetic state to a frustrated one is accompanied by charge ordering.
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Affiliation(s)
- Yury Panov
- Ural Federal University, 19 Mira Street, 620002 Ekaterinburg, Russia
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Monroe JC, Carvajal MA, Landee CP, Deumal M, Turnbull MM, Wikaira JL, Dawe LN. Approaching the isotropic spin-ladder regime: structure and magnetism of all-pyrazine-bridged copper(II)-based antiferromagnetic ladders. Dalton Trans 2022; 51:4653-4667. [PMID: 35212329 DOI: 10.1039/d1dt04219j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The crystal structure and magnetic properties of two all-pyrazine-bridged antiferromagnetic spin ladders are reported. The complexes, catena-(bis(3-X-4-pyridone)(μ-pyrazine)copper(II)(-μ-pyrazine)diperchlorate ([Cu(pz)1.5(L)2](ClO4)2 where L = 3-X-4-pyridone and X = Br (1) or Cl (2)), contain copper(II)-based ladders in which both the rung and rail bridges are pyrazine molecules bonded through the x2-y2 orbital of the copper(II) ions. This structural scaffold is proposed to approach the isotropic spin-ladder regime. 1 and 2 crystallize in the monoclinic space group P21/c. Due to the bulk of the 3-X-4-HOpy ligands, the ladders are well isolated in the a-direction (1, 15.6 Å; 2, 15.5 Å). The ladders, which run in the b-direction, are stacked in the c-direction with the separation (1, 7.87 Å; 2, 7.82 Å) between copper(II) ions caused by the bulk of a semi-coordinate perchlorate ion coordinated in the axial position. Computational evaluation of magnetic JAB couplings between Cu-moieties of 2 supports the experimentally proposed magnetic topology and agrees with an isolated isotropic spin-ladder (Jrail = -4.04 cm-1 (-5.77 K) and Jrung = -3.89 cm-1 (-5.56 K)). These complexes introduce a convenient scaffold for synthesizing isotropic spin-ladders with modest superexchange interactions, the strength of which may be tuned by variations in L. The magnetic susceptibility down to 1.8 K, for both compounds, is well described by the strong-rung ladder model giving nearly isotropic exchange with Jrung ≈ Jrail ≈ -5.5 K (1) and -5.9 K (2) using the Hamiltonian. Theoretical simulations of the magnetic response of 2 using the isotropic ladder model are in excellent agreement with experiment. The measured magnetization to 5 T indicates a quantum-dominated magnetic spectrum. Again, calculated lower and saturation (4.3 and 24 T, respectively) critical fields for 2 are consistent with experimental measurements, and magnetization data at very low temperatures indeed suggest the presence of quantum effects. Further, the computational study of short- and long-range spin ordering indicates that a 2D-to-3D crossover might be feasible at lower temperatures. Analysis of the Boltzmann population corroborates the presence of accessible triplet states above the singlet ground state enabling the aforementioned 2D-to-3D crossover.
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Affiliation(s)
- Jeffrey C Monroe
- Carlson School of Chemistry and Biochemistry, Clark University, 950 Main Street, Worcester, MA 01610, USA.
| | - M Angels Carvajal
- Dept. Ciència de Materials i Química Física, & IQCTUB, Universitat de Barcelona, Martí i Franquès 1, Barcelona, E-08028, Spain
| | - Christopher P Landee
- Department of Physics, Clark University 950 Main Street, Worcester, MA 01610, USA
| | - Mercè Deumal
- Dept. Ciència de Materials i Química Física, & IQCTUB, Universitat de Barcelona, Martí i Franquès 1, Barcelona, E-08028, Spain
| | - Mark M Turnbull
- Carlson School of Chemistry and Biochemistry, Clark University, 950 Main Street, Worcester, MA 01610, USA.
| | - Jan L Wikaira
- Department of Chemistry, University of Canterbury, 20 Kirkwood Ave, Upper Riccarton, Christchurch 8041, New Zealand
| | - Louise N Dawe
- Department of Chemistry and Biochemistry, Wilfrid Laurier University, Waterloo, Ontario, Canada
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