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Magnetochemistry

On the Magnetization and Entanglement Plateaus in One-Dimensional Confined Molecular Magnets

J. Leiva, Emilio A. Cortés Estay, Eric Suárez Morell, Juan M. Florez

Published Feb 1, 2024• 3 citations
Publisher

Abstract

One-dimensional (1D) magnetic systems offer rich phenomena in the quantum limit, proving more chemically accessible than zero-dimensional or higher-dimensional frameworks. Single-walled carbon nanotubes (SWCNT) have recently been used to encapsulate trimetric nickel(II) acetylacetonate [Nanoscale, 2019, 11, 10615–10621]. Here, we investigate the magnetization on spin chains based on nickel trimers by Matrix Product State (MPS) simulations. Our findings reveal plateaus in the exchange/magnetic-field phase diagram for three coupling configurations, showcasing effective dimeric and trimeric spin-ordering with similar or staggered entanglement across chains. These ordered states allow the qubit-like tuning of specific local magnetic moments, exhibiting disengagement or uniform coupling in entanglement plateaus. This behavior is consistent with the experimental transition from frustrated (3D) to non-frustrated (1D) molecules, corresponding to large and smaller SWCNT diameters. Our study offers insights into the potential of 1D-confined trimers for quantum computation, extending beyond the confinement of trimetric nickel-based molecules in one dimension.

DOI
10.3390/magnetochemistry10020010

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One-dimensional (1D) magnetic systems offer rich phenomena in the quantum limit, proving more chemically accessible than zero-dimensional or higher-dimensional frameworks. Single-walled carbon nanotubes (SWCNT) have recently been used to encapsulate trimetric nickel(II) acetylacetonate [Nanoscale, 2019, 11, 10615–10621]. Here, we investigate the magnetization on spin chains based on nickel trimers by Matrix Product State (MPS) simulations. Our findings reveal plateaus in the exchange/magnetic-field phase diagram for three coupling configurations, showcasing effective dimeric and trimeric spin-ordering with similar or staggered entanglement across chains. These ordered states allow the qubit-like tuning of specific local magnetic moments, exhibiting disengagement or uniform coupling in entanglement plateaus. This behavior is consistent with the experimental transition from frustrated (3D) to non-frustrated (1D) molecules, corresponding to large and smaller SWCNT diameters. Our study offers insights into the potential of 1D-confined trimers for quantum computation, extending beyond the confinement of trimetric nickel-based molecules in one dimension.
Using density matrix renormalization group (DMRG) and perturbative continuous unitary transformations (PCUTs), we study the magnetization process in a magnetic field for all coupling strengths of a quasi-1D version of the 2D Shastry-Sutherland lattice, a frustrated spin tube made of two orthogonal dimer chains. At small inter-dimer coupling, plateaus in the magnetization appear at 1/6, 1/4, 1/3, 3/8, and 1/2. As in 2D, they correspond to a Wigner crystal of triplons. However, close to the boundary of the product singlet phase, plateaus of a new type appear at 1/5 and 3/4. They are stabilized by the localization of bound states of triplons. Their magnetization profile differs significantly from that of single-triplon plateaus and leads to specific NMR signatures. We address the possibility to stabilize such plateaus in further geometries by analyzing small finite clusters using exact diagonalizations and the PCUTs.
Quantum spin-1/2 antiferromagnetic Heisenberg trimerized chain with strong intradimer and weak monomer-dimer coupling constants is studied using the many-body perturbation expansion developed about the exact solution of the spin-1/2 Ising-Heisenberg diamond chain. The Heisenberg trimerized chain shows the intermediate one-third plateau, which was also observed in the magnetization curve of the polymeric compound Cu3_33​(P2_22​O6_66​OH)2_22​ affording its experimental realization. Within the strong-coupling method we have obtained the effective Hamiltonians for the magnetic-field range from zero to one-third plateau, and from one-third plateau to the saturation magnetization. The second-order perturbation theory shows reliable results even for the moderate ratio between weaker dimer-monomer and stronger intradimer coupling constants. We have also examined thermodynamic properties and recovered the low-temperature peak in the specific heat. The accuracy of the developed method is tested through a comparison with numerical density-matrix renormalization group and quantum Monte Carlo simulations. Using the results for the effective Hamiltonian we suggest straightforward procedure for finding the microscopic parameters of one-dimensional trimerized magnetic compounds with strong intradimer and weak monomer-dimer couplings. We found the refined values for the coupling constants of Cu3_33​(P2_22​O6_66​OH)2_22​ by matching the theoretical results with the available experimental data for the magnetization and magnetic susceptibility in a wide range of temperatures and magnetic fields.
We study the elementary excitations and magnetization of a one-dimensional spin-1/2 XX chain comprising trimer-dimer units (the J1-J1-J2-J3-J2 topology) under a transverse magnetic field h. Using Green's function theory and the Jordan-Wigner transformation, we map the system onto spinless fermions and focus on antiferromagnetic (AFM) interactions. At zero temperature, distinct 1/5 and 3/5 magnetization plateaus emerge, determined by the global periodicity Q=5, with the number of plateaus matching the number of excitation gaps above the Fermi level of the spinless fermions. The magnetic phase diagram in the (h-Js) plane features a Luttinger liquid (LL) state, a gapless AFM state, two magnetization plateau states, and a fully polarized gapped magnetic state. The widths of the LL and gapless AFM phases are found to be proportional to the bandwidths gamma = |E(k=0)-E(k=pi)| of the corresponding elementary excitations, whereas the widths of the magnetization plateau states are governed by the excitation gaps. Our study opens new directions for exploring interacting trimer-dimer spin chains in quantum magnetism using experimental techniques such as neutron scattering, as well as theoretical and numerical approaches including quantum Monte Carlo (QMC) and density-matrix renormalization group (DMRG) methods. Furthermore, we extend the Oshikawa-Yamanaka-Affleck (OYA) condition to generalized cluster chains, demonstrating that the allowed magnetization plateaus are governed by the global periodicity of the chain (e.g., Q=5 for a trimer-dimer chain), rather than by the local periodicity of individual units (Q=3 for a trimer or Q=2 for a dimer).
We investigate frustration-induced instabilities in a trimerized quantum spin chain motivated by recent experimental findings for the compound Na2_22​Cu3_33​Ge4_44​O12_{12}12​. Employing a cluster mean-field approach combined with Lanczos exact diagonalization, we analyze the ground-state and quantum-information properties of a Heisenberg model with competing interactions in a magnetic field. In the weakly frustrated regime, the system exhibits a robust 1/31/31/3 magnetization plateau associated with a collective ferrimagnetic-like trimer state. Increasing the next-nearest-neighbor intratrimer coupling drives a pronounced reorganization of spin correlations, leading to a crossover toward a doublon-like correlation regime and providing a static ground-state picture consistent with the composite excitations observed dynamically in trimerized chains. The resulting low-energy behavior can be interpreted in terms of weakly interacting emergent spins, offering a microscopic explanation for the extended stability of the magnetization plateau. Furthermore, through finite-size scaling analyses of the energy gap, von Neumann entanglement entropy, and fidelity susceptibility, we characterize the zero-field criticality of the model. Ultimately, our results suggest that frustration gives rise to qualitatively distinct quantum states and provide a microscopic framework for understanding the emergence of fractionalized excitations in trimerized quantum spin systems.
One dimensional quantum magnets have always been an active area of research due to their experimental realizability and the rich physics that they offer. By including geometrical frustration and additional interactions, it leads to even more novel and exotic quantum phases. In this thesis, we present the results of our investigations conducted by extending the quantum systems to spin–1. We conducted static, topological and dynamical calculations numerically on the spin–1 Heisenberg chain with Dzyaloshinskii–Moriya interaction in a uniform magnetic field in the form of a spin–1 Heisenberg chain in a helical magnetic field as well as the spin–1 Heisenberg model on the spin diamond and orthogonal dimer lattices. For the spin–1 Heisenberg chain in a helical field, we obtained the phase diagram using the density matrix renormalization group method and showed conclusively that the helical field destroys any topological order. We also obtained the dynamical spin structure factor spectra to study the magnon band structures and the softening of the modes near phase transitions. We then investigated the spin–1 Heisenberg model on the spin diamond and orthogonal dimer lattices using both exact diagonalization and the density matrix renormalization group method. We obtained the phase diagrams for both systems and explicitly calculated the magnetization, static spin structure and topological order of the different phases. Similar to the spin–1 Heisenberg chain in a helical magnetic field, we also obtained the dynamical spin structure factor spectra to study the characteristics of the lowest excitation occurring in both quantum systems.
The spin-1/2 Ising-Heisenberg trimerized chain in a magnetic field is revisited with the aim to explore the quantum entanglement and non-locality within the exactly solved spin system, which exhibits in a low-temperature magnetization curve two intermediate plateaux at zero and one-third of the saturation magnetization.The groundstate phase diagram involves two quantum (antiferromagnetic, ferrimagnetic I) and two classical (ferrimagnetic II, saturated paramagnetic) phases.We have rigorously calculated the concurrence and Bell function in order to quantify the quantum entanglement and non-locality at zero as well as non-zero temperatures.It is demonstrated that the entanglement can be thermally induced also above the classical ground states unlike the quantum nonlocality, which means that the thermal entanglement is indispensable for a violation of the locality principle.