Heisenberg Ferromagnetic Chain Research Articles

Polymeric dichlorido-bridged copper(II) offset stacked dimer coordination compounds and molecular spin stairs

A family of oxygen coordinated dichlorido-bridged n-X-2-pyridone (1, n = 3, X = Cl; 2, n = 3, X = Br; 3, n = 4, X = Cl; 4, n = 4, X = Br; 5, n = 5, X = Cl; 6, n = 5, X = Br) Cu(II) offset stacked dimer compounds, denoted molecular spin stairs, have been prepared and analyzed by single-crystal X-ray diffraction (1–4), powder X-ray diffraction (1–6), and variable temperature magnetic susceptibility measurements (1–6). Ferromagnetism is dominant in all compounds with a weaker antiferromagnetic exchange present in 1–4. The ferromagnetic exchange correlates to increased twist angles which are defined by the extent of the tetrahedral distortion of the copper coordination sphere and the identity of the halogen on the ring. The compounds were qualitatively fit to a ferromagnetic Heisenberg chain model with a Curie-Weiss interchain correction. The general Hamiltonian used is of the form H = − J ∑ S 1 S 2 . The ratio of exchange energies denoted α ( α = J FM | J AFM | ) ranges between 2.6 and 4.7. This family of compounds constitutes possible S = ½ Haldane-like materials.

Semiclassical approach to spin dynamics of a ferromagnetic S = 1 chain

Abstract Motivated by recent experimental progress on the quasi-one-dimensional quantum magnet NiNb2O6, we study the spin dynamics of an S = 1 ferromagnetic Heisenberg chain with single-ion anisotropy by using a semiclassical molecular dynamics approach. This system undergoes a quantum phase transition from a ferromagnetic to a paramagnetic state under a transverse magnetic field, and the magnetic response reflecting this transition is well described by our semiclassical method. We show that at low temperature the transverse component of the dynamical structure factor depicts clearly the magnon dispersion, and the longitudinal component exhibits two continua associated with single- and two-magnon excitations, respectively. These spin excitation spectra show interesting temperature dependence as effects of magnon interactions. Our findings shed light on the experimental detection of spin excitations in a large class of quasi-one-dimensional magnets.

The solitary wave solutions of the stochastic Heisenberg ferromagnetic spin chain equation using two different analytical methods

Here, we consider the stochastic (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation which is forced by the multiplicative Brownian motion in the Stratonovich sense. We utilize the (G′/G)-expansion method and the mapping method to attain the analytical solutions of the stochastic (2 + 1)-dimensional Heisenberg ferromagnetic chain equation. Various types of analytical stochastic solutions, such as the hyperbolic, elliptic, and trigonometric functions, have been obtained. Physicists can utilize these solutions to understand a variety of important physical phenomena because the magnetic soliton has been categorized as one of the interesting groups of nonlinear excitations representing spin dynamics in the semiclassical continuum Heisenberg systems. Moreover, we employ MATLAB tools to plot 3D and 2D graphs for some obtained solutions to address the influence of Brownian motion on these solutions.

2-D exotic soliton in 2-D Heisenberg ferromagnetic chains with Dzyaloshinsky-Moriya interaction

2-D exotic soliton in 2-D Heisenberg ferromagnetic chains with Dzyaloshinsky-Moriya interaction

2-D exotic soliton in 2-D Heisenberg ferromagnetic chains with Dzyaloshinsky-Moriya interaction

The two-dimensional (2D) version of ferromagnet XXZ spin chain with DzyaloshinskyMoriya (DM) interaction, recently introduced by F. Kenmogne and coworkers is reexplored. Firstly by using the Dyson-Maleev transformation, the 2-D discrete nonlinear Schrödinger (DNLS) equation, governing the quantum states behaviors is found. Next using the semidiscrete multiple-scale method, the 2-D DNLS equation is reduced to the 2D extended nonlinear Schrödinger (ENLS) equation which consists of the basic 2-D NLS equation with additional nonlinear dispersive terms. This equation admits the classical 2D pulse quantum states, when additional terms vanish. In addition, this equation admits the 2D compacton and 2D peakon-like boson quantum states. Furthermore, we notice that on the contrary to the classical outcomes where amplitudes of both solutions are free parameters, the amplitudes for two dimensional quantum states are not free parameters since the obtained solutions need to be normalized.

Synthesis, Structural, Magnetic and Computational Studies of a One-Dimensional Ferromagnetic Cu(II) Chain Assembled from a New Schiff Base Ligand

A new asymmetrically substituted ONOO Schiff base ligand N-(2′-hydroxy-1′-naphthylidene)-3-amino-2-naphthoic acid (nancH2) was prepared from the condensation of 2–hydroxy–1–naphthaldehyde and 3–amino–2–naphthoic acid. nancH2 reacts with Cu2(O2CMe)4·2H2O in the presence of Gd(O2CMe)3·6H2O to afford a uniform one-dimensional homometallic chain, [CuII(nanc)]n (1). The structure of 1 was elucidated via single crystal X-ray diffraction studies, which revealed that the Cu(II) ions adopt distorted square planar geometries and are coordinated in a tridentate manner by an [ONO] donor set from one nanc2− ligand and an O− of a bridging carboxylate group from a second ligand. The bridging carboxylato group of the nanc2− ligand adopts a syn, anti-η1:η1:μ conformation linking neighboring Cu(II) ions, forming a 1D chain. The magnetic susceptibility of 1 follows Curie–Weiss law in the range 45–300 K (C = 0.474(1) emu K mol-1, θ = +7.9(3) K), consistent with ferromagnetic interactions between S = ½ Cu(II) ions with g = 2.248. Subsequently, the data fit well to the 1D quantum Heisenberg ferromagnetic (QHFM) chain model with g = 2.271, and J = +12.3 K. DFT calculations, implementing the broken symmetry approach, were also carried out on a model dimeric unit extracted from the polymeric chain structure. The calculated exchange coupling via the carboxylate bridge (J = +13.8 K) is consistent with the observed ferromagnetic exchange between neighbouring Cu(II) centres.

Long-lived solitons and their signatures in the classical Heisenberg chain.

Motivated by the Kardar-Parisi-Zhang (KPZ) scaling recently observed in the classical ferromagnetic Heisenberg chain, we investigate the role of solitonic excitations in this model. We find that the Heisenberg chain, although well known to be nonintegrable, supports a two-parameter family of long-lived solitons. We connect these to the exact soliton solutions of the integrable Ishimori chain with ln(1+S_{i}·S_{j}) interactions. We explicitly construct infinitely long-lived stationary solitons, and provide an adiabatic construction procedure for moving soliton solutions, which shows that Ishimori solitons have a long-lived Heisenberg counterpart when they are not too narrow and not too fast moving. Finally, we demonstrate their presence in thermal states of the Heisenberg chain, even when the typical soliton width is larger than the spin correlation length, and argue that these excitations likely underlie the KPZ scaling.

Mathematical examination for the energy flow in an inhomogeneous Heisenberg ferromagnetic chain

The dynamics of energy transfer through alpha-helical proteins or an inhomogeneous Heisenberg ferromagnetic spin chain can be described by a (2 +1) dimensional variable-coefficient nonlinear Schrödinger equation (NLS). In this paper, we derived Lax pair based on AKNS scheme then we apply the inverse scattering transform (IST) method to explore one-soliton solution and some other novel soliton solutions. Propagation and properties of the solitons are discussed: solitary wave, parabolic and cubic solitons are presented. The obtained one-soliton solution is graphically represented with three dimensions plots and compared with the previous solutions in other contributions.

Possibility to detect the bound state of the Heisenberg ferromagnetic chain at intermediate temperature

Motivated by the lack of direct evidence with inelastic neutron scattering of the well documented bound state of Heisenberg ferromagnets, we use the time-dependent thermal density matrix renormalization group algorithm to study the temperature dependence of the dynamical spin structure factor of Heisenberg ferromagnetic spin chains. For spin 1/2, we show that the bound state appears as a well defined excitation with significant spectral weight in the temperature range $J/12\ensuremath{\lesssim}T\ensuremath{\lesssim}J/3$, pointing to the possibility of detecting it with inelastic neutron scattering near $k=\ensuremath{\pi}$ provided the temperature is neither too low nor too high---at low temperature, the spectral weight only grows as ${T}^{3/2}$ and, at high temperature, the bound state peak merges with the two-magnon continuum. For spin 1, the situation is more subtle because the bound state with two neighboring spin flips competes with an antibound state with two spin flips on the same site. As a consequence, the relative spectral weight of the bound state is smaller than for spin 1/2 and a weak resonance due to the antibound state appears in the continuum. A clearer signature of the bound state (antibound state) can be obtained if a negative (positive) biquadratic interaction is present.

Multimagnon dynamics and thermalization in the S=1 easy-axis ferromagnetic chain

Quasiparticles are physically motivated mathematical constructs for simplifying the seemingly complicated many-body description of solids. A complete understanding of their dynamics and the nature of the effective interactions between them provides rich information on real material properties at the microscopic level. In this work, we explore the dynamics and interactions of magnon quasiparticles in a ferromagnetic spin-1 Heisenberg chain with easy-axis onsite anisotropy, a model relevant for the explanation of recent terahertz optics experiments on NiNb$_2$O$_6$ [P. Chauhan et al., Phys. Rev. Lett. 124, 037203 (2020)],and nonequilibrium dynamics in ultracold atomic settings [W.C. Chung et al., Phys. Rev. Lett. 126, 163203 (2021)]. We build a picture for the properties of clouds of a few magnons with the help of exact diagonalization and density matrix renormalization group calculations supported by physically motivated Jastrow wavefunctions. We show how the binding energy of magnons effectively reduces with their number and explain how this energy scale is of direct relevance for dynamical magnetic susceptibility measurements. This understanding is used to make predictions for ultracold-atomic platforms which are ideally suited to study the thermalization of multimagnon states. We simulate the nonequilibrium dynamics of these chains using the matrix product state based time-evolution block decimation algorithm and explore the dependence of revivals and thermalization on magnon density and easy-axis onsite anisotropy (which controls the strength of effective magnon interactions). We observe behaviors akin to those reported for many-body quantum scars which we explain with an analytic approximation that is accurate in the limit of small anisotropy.

Riemann\u2013Hilbert Problem Associated with the Fourth-Order Dispersive Nonlinear Schr\xf6dinger Equation in Optics and Magnetic Mechanics

In this paper, by using Fokas method, we study the initial-boundary value problems (IBVPs) of the fourth-order dispersive nonlinear Schrödinger (FODNLS) equation on the half-line, which can simulate the nonlinear transmission and interaction of ultrashort pulses in the high-speed optical fiber transmission system, and can also describe the nonlinear spin excitation phenomenon of one-dimensional Heisenberg ferromagnetic chain with eight poles and dipole interaction. By discussing the eigenfunctions of Lax pair of FODNLS equation and analyzing symmetry of the scattering matrix, we get a matrix Riemann–Hilbert (RH) problem from for the IBVPs of FODNLS equation. Moreover, we get the potential function solution u(x, t) of the FODNLS equation by solving this matrix RH problem. In addition, we also obtain that some spectral functions satisfy an important global relation.

Geometric magnetic phase for timelike spherical optical ferromagnetic model

In this paper, we give some constructions for the applications of optical magnetic Heisenberg spherical ferromagnetic chain of T - timelike magnetic particle by spherical de Sitter frame in de Sitter space. This aim may be concluded by well-known de Sitter frame or a new alternative spherical frame with an optical magnetic spherical Heisenberg ferromagnetic chain. Moreover, we achieve total magnetic phases of T - timelike magnetic particle evolutions. Finally, we obtain some numerical modeling of optical magnetic spherical Heisenberg ferromagnetic flows.

Quantum compacton and quantum peakon in Heisenberg ferromagnetic chains with Dzyaloshinsky–Moriya interaction

The one-dimensional ferromagnet XXZ spin chain with Dzyaloshinsky–Moriya (DM) interaction, recently introduced by Djoufack and coworkers is reexplored, with a particular attention carried on their found discrete nonlinear Schrödinger (DNLS) equation, governing the quantum breathers states behaviors. This DNLS equation admits exact bright compacton and peakon-like solutions, where analytical expressions, the existence and stability criteria are found and used to obtain their quantized energy levels. Using the semi-discrete multiple-scale method, the DNLS equation is reduced to the extended nonlinear Schrödinger equation which consists of the basic NLS equation with additional nonlinear dispersive terms Via the bifurcation diagram and Liapunov exponents, we provide a summary of essential dynamics and show that the equation would admit several forms of solutions among which the localized Hartree n compacton and peakon-like boson quantum breathers states. Furthermore, we notice that on the contrary to the classical outcomes where amplitudes of both solutions are free parameters, the amplitudes for quantum states are not free since the obtained solutions need to be normalized. The stationary localization of both compacton and peakon-like states is confirmed by numerical simulations performed on the DNLS equation.

Tunable Magnon Interactions in a Ferromagnetic Spin-1 Chain.

NiNb_{2}O_{6} is an almost ideal realization of a 1D spin-1 ferromagnetic Heisenberg chain compound with weak unidirectional anisotropy. Using time-domain THz spectroscopy, we measure the low-energy electrodynamic response of NiNb_{2}O_{6} as a function of temperature and external magnetic field. At low temperatures, we find a magnonlike spin excitation, which corresponds to the lowest energy excitation at q∼0. At higher temperatures, we unexpectedly observe a temperature-dependent renormalization of the spin-excitation energy, which has a strong dependence on field direction. Using theoretical arguments, exact diagonalizations, and finite temperature dynamical Lanczos calculations, we construct a picture of magnon-magnon interactions that naturally explains the observed renormalization. We show how magnetic field strength and direction may be used to directly tune the sign of the magnon-magnon interaction. This unique scenario is a consequence of the spin-1 nature and has no analog in the more widely studied spin-1/2 systems.

Entanglement structure of the two-component Bose-Hubbard model as a quantum simulator of a Heisenberg chain

We consider a quantum simulator of the Heisenberg chain with ferromagnetic interactions based on the two-component 1D Bose-Hubbard model at filling equal to two in the strong coupling regime. The entanglement properties of the ground state of the two-component Bose-Hubbard model are compared to those of the effective spin model as the interspecies interaction approaches the intraspecies one. A numerical study of the entanglement properties of the two-component Bose-Hubbard model is supplemented with analytical expressions derived from the effective spin Hamiltonian. When the pure ferromagnetic Heisenberg chain is considered, the entanglement properties of the effective Hamiltonian are not properly predicted by the quantum simulator.

Quantum spin transfer torque induced nonclassical magnetization dynamics and electron-magnetization entanglement

The standard spin-transfer torque (STT)---where spin-polarized current drives dynamics of magnetization viewed as a classical vector---requires noncollinearity between electron spins carried by the current and magnetization of a ferromagnetic layer. However, recent experiments [A. Zholud et al., Phys. Rev. Lett. 119, 257201 (2017)] observing magnetization dynamics in spin valves at cryogenic temperatures, even when electron spin is collinear to magnetization, point at overlooked quantum effects in STT which can lead to highly nonclassical magnetization states. Using fully quantum many-body treatment, where an electron injected as spin-polarized wave packet interacts with local spins comprising the anisotropic quantum Heisenberg ferromagnetic chain, we define quantum STT as any time evolution of local spins due to initial many-body state not being an eigenstate of electron+local-spins system. For time evolution caused by injected spin-down electron scattering off local up-spins, entanglement between electron subsystem and local spins subsystem takes place leading to decoherence and, therefore, shrinking of the total magnetization but without rotation from its initial orientation which explains the experiments. Furthermore, the same processes---entanglement and thereby induced decoherence---are present also in standard noncollinear geometry, together with the usual magnetization rotation. This is because STT in quantum many-body picture is caused only by electron spin-down factor state, and the only difference between collinear and noncollinear geometries is in relative size of the contribution of initial many-body state containing such factor state to superpositions of separable many-body quantum states generated during time evolution.

S=12 ferromagnetic Heisenberg chain in a verdazyl-based complex

We present a model compound for the $S$=1/2 ferromagnetic Heisenberg chain composed of the verdazyl-based complex $[$Zn(hfac)$_2]$$[$4-Cl-$o$-Py-V-(4-F)$_2]$. $Ab$ $initio$ MO calculations indicate a predominant ferromagnetic interaction forming an $S$=1/2 ferromagnetic chain. The magnetic susceptibility and specific heat indicate a phase transition to an AF order owing to the finite interchain couplings. We explain the magnetic susceptibility and magnetization curve above the phase transition temperature based on the $S$=1/2 ferromagnetic Heisenberg chain. The magnetization curve in the ordered phase is described by a conventional AF two-sublattice model. Furthermore, the obtained magnetic specific heat reproduces the almost temperature-independent behavior of the $S$=1/2 ferromagnetic Heisenberg chain. In the low-temperature region, the magnetic specific heat exhibits $\sqrt{T}$ dependence, which is attributed to the energy dispersion in the ferromagnetic chain.

From Linear to Nonlinear Responses of Thermal Pure Quantum States

We propose a self-validating scheme to calculate the unbiased responses of quantum many-body systems to external fields of arbitrary strength at any temperature. By switching on a specified field to a thermal pure quantum state of an isolated system, and tracking its time evolution, one can observe an intrinsic thermalization process driven solely by many-body effects. The transient behavior before thermalization contains rich information on excited states, giving the linear and nonlinear response functions at all frequencies. We uncover the necessary conditions to clarify the applicability of this formalism, supported by a proper definition of the nonlinear response function. The accuracy of the protocol is guaranteed by a rigorous upper bound of error exponentially decreasing with system size, and is well implemented in the simple ferromagnetic Heisenberg chain, whose response at high fields exhibits a nonlinear band deformation. We further extract the characteristic features of excitation of the spin-1/2 kagome antiferromagnet; the wave-number-insensitive linear responses from the possible spin liquid ground state, and the significantly broad nonlinear peaks which should be generated from numerous collisions of quasiparticles, that are beyond the perturbative description.

Invariant tori for the Schrödinger equation in the Heisenberg Ferromagnetic chain

In this paper, we consider the nonlinear Heisenberg Ferromagnetic chain equation under Dirichlet boundary conditions. By Taylor formula, the nonlinear Heisenberg Ferromagnetic chain equation can be described by the nonlinear Schrödinger type equation. Using an infinite dimensional KAM theorem for reversible system, we prove the existence of many n-dimensional invariant tori under sufficiently small perturbation and thus many time quasi-periodic solutions for the above equation.

Structures, Thermodynamic Relations, and Magnetism of Stable and Metastable Ni(NCS)2 Coordination Polymers.

Reaction of Ni(NCS)2 with 4-aminopyridine in different solvents leads to the formation of compounds with the compositions Ni(NCS)2(4-aminopyridine)4 (1), Ni(NCS)2(4-aminopyridine)2(H2O)2 (2), [Ni(NCS)2(4-aminopyridine)3(MeCN)]·MeCN (3), and [Ni(NCS)2(4-aminopyridine)2] n (5-LT). Compounds 1, 2, and 3 form discrete complexes, with octahedral metal coordination. In 5-LT the Ni cations are linked by single thiocyanate anions into chains, which are further connected into layers by half of the 4-aminopyridine coligands. Upon heating, 1 transforms into an isomer of 5-LT with a 1D structure (5-HT), that on further heating forms a more condensed chain compound [Ni(NCS)2(4-aminopyridine)] n (6) that shows a very unusual chain topology. If 3 is heated, a further compound with the composition Ni(NCS)2(4-aminopyridine)3 (4) is formed, which presumably is a dimer and which on further heating transforms into 6 via 5-HT as intermediate. Further investigations reveal that 5-LT and 5-HT are related by enantiotropism, with 5-LT being the thermodynamic stable form at room-temperature. Magnetic and specific heat measurements reveal ferromagnetic exchange through thiocyanate bridges and magnetic ordering due to antiferromagnetic interchain interactions at 5.30(5) K and 8.2(2) K for 5-LT and 6, respectively. Consecutive metamagnetic transitions in the spin ladder compound 6 are due to dipolar interchain interactions. A convenient formula for susceptibility of the ferromagnetic Heisenberg chain of isotropic spins S = 1 is proposed, based on numerical DMRG calculations, and used to determine exchange constants.