Ferromagnetic Chain Research Articles

Periodic and rogue waves for Heisenberg models of ferromagnetic spin chains with fractional beta derivative evolution and obliqueness

ABSTRACT The nonlinear Schrodinger equation (NLSE) in (2 + 1) dimensions with beta derivative evolution is considered here to study nonlinear coherent structures for Heisenberg models of ferromagnetic spin chain with magnetic exchanges. Such structures are studied by determining the analytical solutions of NLSE having beta derivative evolution via two different mathematical techniques. The dynamical behaviors of equilibrium points are also studied by deriving the planar dynamical system from the considered equation. Some of obtained analytical solutions are described with graphical representation by varying beta derivative parameter (BDP) and obliqueness. It is revealed that the obliqueness is extensively affected both on the plane wave dynamics as well as equilibrium points of the system, whereas the equilibrium points are independent of BDP.

Dynamics of various waves in nonlinear Schrödinger equation with stimulated Raman scattering and quintic nonlinearity

In this work, we consider a nonlinear Schrodinger equation with stimulated Raman scattering and quintic nonlinearity, which works as a model for the propagation of ultrashort pulse in optical fiber and also corresponds to one-dimensional anisotropic Heisenberg ferromagnetic spin chain. Introducing a Galilean transformation, we transform the model into a fifth-order complex modified KdV equation, the integrability of which has been considered in the AKNS technique framework. The N-fold Darboux transformation for the model is derived in terms of the gauge transformation of the associated $$3 \times 3$$ matrix spectral problem. As applications, abundant intriguing types of nonlinear waves are obtained in zero and nonzero boundary conditions. The dynamical evolution of these nonlinear waves can be well controlled under stimulated Raman scattering and quintic nonlinearity management. Beside that, we also find some novel and interesting conversion phenomena, where a high-order term plays a pivotal role.

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.

Single-Chain Magnet Based on Cobalt(II) Thiocyanate as XXZ Spin Chain.

The cobalt(II) in [Co(NCS)2(4‐methoxypyridine)2]n are linked by pairs of thiocyanate anions into linear chains. In contrast to a previous structure determination, two crystallographically independent cobalt(II) centers have been found to be present. In the antiferromagnetic state, below the critical temperature (T c=3.94 K) and critical field (H c=290 Oe), slow relaxations of the ferromagnetic chains are observed. They originate mainly from defects in the magnetic structure, which has been elucidated by micromagnetic Monte Carlo simulations and ac measurements using pristine and defect samples. The energy barriers of the relaxations are Δτ1=44.9(5) K and Δτ2=26.0(7) K for long and short spin chains, respectively. The spin excitation energy, measured by using frequency‐domain EPR spectroscopy, is 19.1 cm−1 and shifts 0.1 cm−1 due to the magnetic ordering. Ab initio calculations revealed easy‐axis anisotropy for both CoII centers, and also an exchange anisotropy Jxx/Jzz of 0.21. The XXZ anisotropic Heisenberg model (solved by using the density renormalization matrix group technique) was used to reconcile the specific heat, susceptibility, and EPR data.

Nonlinear Dynamics of Rogue Waves in a Fifth-Order Nonlinear Schrödinger Equation

In this paper, nonlinear dynamics of higher-order rogue waves are investigated for a fifth-order nonlinear Schrodinger equation, which can depict the Heisenberg ferromagnetic spin chain. A generalized Darboux transformation is constructed based on the Lax pair. Higher-order rogue waves solutions are given in terms of a recursive formula. Using numerical simulation, the first-order to the third-order rogue waves are displayed on the basis of some free parameters, which play a crucial role in affecting the distribution of rogue waves. The results obtained should be useful in understanding the generation mechanism of rogue waves.

Crystal structure, magneto-structural correlation, thermal and electrical studies of an imidazolium halometallate molten salt: (trimim)[FeCl4

A novel imidazolium halometallate molten salt with formula (trimim)[FeCl4] (trimim: 1,2,3-trimethylimidazolium) was synthetized and studied with structural and physico-chemical characterization. Variable-temperature synchrotron X-ray powder diffraction (SXPD) from 100 to 400 K revealed two structural transitions at 200 and 300 K. Three different crystal structures were determined combining single crystal X-ray diffraction (SCXD), neutron powder diffraction (NPD), and SXPD. From 100 to 200 K, the compound exhibits a monoclinic crystal structure with space group P21/c. At 200 K, the former crystal system and space group are retained, but a disorder in the organic cations is introduced. Above 300 K, the structure transits to the orthorhombic space group Pbcn, retaining the crystallinity up to 400 K. The study of the thermal expansion process in this temperature range showed anisotropically evolving cell parameters with an axial negative thermal expansion. Such an induction occurs immediately after the crystal phase transition due to the translational and reorientational dynamic displacements of the imidazolium cation within the crystal building. Electrochemical impedance spectroscopy (EIS) demonstrated that this motion implies a high and stable solid-state ionic conduction (range from 4 × 10−6 S cm−1 at room temperature to 5.5 × 10−5 S cm−1 at 400 K). In addition, magnetization and heat capacity measurements proved the presence of a three-dimensional antiferromagnetic ordering below 3 K. The magnetic structure, determined by neutron powder diffraction, corresponds to ferromagnetic chains along the a-axis, which are antiferromagnetically coupled to the nearest neighboring chains through an intricate network of superexchange pathways, in agreement with the magnetometry measurements.

Magnetic properties of the finite-length biatomic chains in the framework of the single domain-wall approximation

A simple analytical method for study the magnetic properties of the finite-length biatomic chains in the framework of Heisenberg model with uniaxial magnetic anisotropy is proposed. The method allows to estimate the reversal time of the magnetization of ferromagnetic and antiferromagnetic biatomic chains. Three cases are considered: the spontaneous remagnetization, the remagnetization under the interaction with a scanning tunneling microscope, and the remagnetization in the external magnetic field. The applicability limits of the method are discussed. Within its limits of applicability the method gives results which are in perfect agreement with the results of the kinetic Monte Carlo simulations. As the examples, two physical systems are considered: biatomic Fe chains on Cu2N/Cu(001) surface and biatomic Co chains on Pt(997) surface. The presented method is incomparably less time-consuming than the standard kMC simulations, especially in the cases of low temperatures or long chains.

Wave patterns of (2+1)-dimensional nonlinear Heisenberg ferromagnetic spin chains in the semiclassical limit

A special kind of nonlinear Schrödinger equation (NLSE) with conformable fractional derivative is considered. And via the complete discrimination system for polynomial method, all the single traveling wave solutions are presented, especially the soliton solutions, which are very important in describing the Heisenberg ferromagnetic spin chains. Moreover, to see the fractionalize effects clearly, numerical simulations are conducted and corresponding graphs are also plotted. The results in this paper include all the solutions in the existing literatures, and some solutions, such as elliptic functions solutions, are initially shown. From those results we can see certain wave propagation patterns of the aforementioned model, for example, the soliton and double periodic propagation patterns, which would be helpful for us to understand this model more clearly and could even shed light on the further analysis of the nonlinear properties of magnetic materials.

Solitons and complexitons to the (2 + 1)-dimensional Heisenberg ferromagnetic spin chain model

This paper investigates the ([Formula: see text])-dimensional Heisenberg ferromagnetic spin chain (HMF) model. The model describes the nonlinear spin dynamics of HMF. By adopting the modified [Formula: see text]-Expansion and projective Riccati equation methods, we report the dark, combined dark-bright and envelope optical solitons, complexitons singular solutions of the equation along with the conditions that must be satisfied for solitons to exist. The physical structure of the obtained solutions are shown by graphic illustration in order to give a better understanding on the dynamics of optical solitons.

Tunneling in projective quantum Monte Carlo simulations with guiding wave functions

Quantum tunneling is a valuable resource exploited by quantum annealers to solve complex optimization problems. Tunneling events also occur during projective quantum Monte Carlo (PQMC) simulations, and in a class of problems characterized by a double-well energy landscape their rate was found to scale linearly with the first energy gap, i.e., even more favorably than in physical quantum annealers, where the rate scales with the gap squared. Here we investigate how a guiding wave function --- which is essential to make many-body PQMC simulations computationally feasible --- affects the tunneling rate. The chosen testbeds are a continuous-space double-well problem, the ferromagnetic quantum Ising chain, and the recently introduced shamrock model. As guiding wave function, we consider an approximate Boltzmann-type ansatz, the numerically-exact ground state of the double-well model, and a neural-network wave function based on a Boltzmann machine. Remarkably, for each ansatz we find the same asymptotic linear scaling of the tunneling rate that was previously found in the PQMC simulations performed without a guiding wave function. We also provide a semiclassical theory for the double-well with exact guiding wave function that explains the observed linear scaling. These findings suggest that PQMC simulations guided by an accurate ansatz represent a valuable benchmark for physical quantum annealers and a potentially competitive quantum-inspired optimization technique.

Fractionalized Edge Spins and Boundary Conditions in Frustrated Ferromagnetic Quantum Spin Chains

We examine frustrated ferromagnetic S = 1 spin chains at zero temperature by using the density-matrix renormalization group method. In open boundary conditions, the S = 1 quantum spin chains are known to produce fractionalized free spins on each edge, which causes difficulty in the numerical calculation of the thermodynamic ground states. To overcome this, we propose modified open boundary conditions to suppress the formation of fractionalized edge spins. The comparison of the physical properties of the ground states, which are obtained from the modified and the standard open boundary conditions, reveals that the modified open boundary conditions are more effective in improving the convergence behavior and reducing the computational costs.

Nonlinear Fluctuating Hydrodynamics for the Classical XXZ Spin Chain

Using the framework of nonlinear fluctuating hydrodynamics (NFH), we examine equilibrium spatio-temporal correlations in classical ferromagnetic spin chains with nearest neighbor interactions. In particular, we consider the classical XXZ-Heisenberg spin chain (also known as Lattice Landau Lifshitz or LLL model) evolving deterministically and chaotically via Hamiltonian dynamics, for which energy and $z$-magnetization are the only locally conserved fields. For the easy-plane case, this system has a low-temperature regime in which the difference between neighboring spin's angular orientations in the XY plane is an \textit{almost conserved} field. According to the predictions of NFH, the dynamic correlations in this regime exhibit a heat peak and propagating sound peaks, all with anomalous broadening. We present a detailed molecular dynamics test of these predictions and find a reasonably accurate verification. We find that, in a suitable intermediate temperature regime, the system shows two sound peaks with Kardar-Parisi-Zhang (KPZ) scaling and a heat peak where the expected anomalous broadening is less clear. In high temperature regimes of both easy plane and easy axis case of LLL, our numerics show clear diffusive spin and energy peaks and absence of any sound modes, as one would expect. We also simulate an integrable version of the XXZ-model, for which the ballistic component instead moves with a broad range of speeds rather than being concentrated in narrower peaks around the sound speed.

Optical solitons for modulated compressional dispersive alfven and heisenberg ferromagnetic spin chains

In this paper, we obtain bright and dark solitons for a couple of nonlinear Schrödinger’s equations (NLSEs). First is the nonlinear spin dynamics of Heisenberg ferromagnetic spin chains (HFSC) in (2+1)-dimensions and secondly the dynamics of modulated compressional dispersive Alfven (CDA) envelop in (1+1)-dimensions. We obtain the bright solitons by using sin-cosine method (SCM) and dark soliton with the help of Bernoulli’s equation approach (BEA). At the end, we present some graphical representation of our solutions.

(Cu)tet(Cr2-xSnx)octS4-ySey Spinels: Crystal Structure, Density Functional Theory Calculations, and Magnetic Behavior.

A new series of (Cu)tet[Cr2-xSnx]octS4-ySey compounds was prepared by solid-state reaction at high temperature. Determination of the crystal structures by single-crystal X-ray diffraction revealed that CuCr1.0Sn1.0S2.1Se1.9, CuCr1.2Sn0.8S2.1Se1.9, CuCr1.3Sn0.7S2.2Se1.8, and CuCr1.5Sn0.5S2.2Se1.8 crystallize in a normal spinel-type structure (cubic Fd3m space group). The powder X-ray diffraction patterns and Rietveld refinements of nominal CuCr2-xSnxS2Se2 (x = 0.2, 0.4, 0.6, 0.8, and 1.0) were consistent with single-crystal X-ray diffraction data. Raman scattering analysis revealed that the A1g, Eg, and three F2g vibrational modes were observed in the spectra. The signal at ∼382 cm-1, corresponding to the A1g mode, is attributed to symmetrical stretching of the chalcogen bond with respect to the tetrahedral metal. The samples with x = 0.2 and 0.4 exhibited ferromagnetic behavior, characterized by large positive θ values of +261 and +189 K, respectively. In contrast, antiferromagnetic (AF) behavior was observed for CuCrSnS2Se2 with a Néel temperature (TN) of 18.8 K and a θ value of -36.0 K. Density functional theory (DFT) and effective magnetic moments (μeff/μtheo) experimentally measured showed that the Sn ion is in oxidation state of 4+, i.e., diamagnetic behavior. DFT calculations revealed that the most stable magnetic state of CuCr1.0Sn1.0S2Se2 was AF with exchange constants for first- and second-neighbor interactions of J1 = 56.22 cm-1 and J2 = -33.88 cm-1. Thus, the AF interactions between ferromagnetic chains in CuCr1.0Sn1.0S2Se2 originate from the presence of diamagnetic Sn cations.

Self-learning projective quantum Monte Carlo simulations guided by restricted Boltzmann machines.

The projective quantum Monte Carlo (PQMC) algorithms are among the most powerful computational techniques to simulate the ground-state properties of quantum many-body systems. However, they are efficient only if a sufficiently accurate trial wave function is used to guide the simulation. In the standard approach, this guiding wave function is obtained in a separate simulation that performs a variational minimization. Here we show how to perform PQMC simulations guided by an adaptive wave function based on a restricted Boltzmann machine. This adaptive wave function is optimized along the PQMC simulation via unsupervised machine learning, avoiding the need of a separate variational optimization. As a byproduct, this technique provides an accurate ansatz for the ground-state wave function, which is obtained by minimizing the Kullback-Leibler divergence with respect to the PQMC samples, rather than by minimizing the energy expectation value as in standard variational optimizations. The high accuracy of this self-learning PQMC technique is demonstrated for a paradigmatic sign-problem-free model, namely, the ferromagnetic quantum Ising chain, showing very precise agreement with the predictions of the Jordan-Wigner theory and of loop quantum Monte Carlo simulations performed in the low-temperature limit.

Spin Current Generation in One – Dimension Spin – Chain Model of Insulating Magnetic Interface

In a system of a thin ferromagnetic layer sandwiched by non-magnetic metals, the precession of magnetization of the ferromagnetic layer has been shown to generate spin current in the adjacent non-magnetic metals. The spin current arises from the spin-dependent scattering that is originated by the exchange interaction between the magnetic moment and the spin of adjacent normal metal’s electron. While the theory was originally studied in magnetic multilayer that consists of a thin ferromagnet sandwiched by non-magnetic materials, to be able to describe a more realistic ferromagnetic layer, we need to study how magnetic moments far from the interface can influence the spin current generation. We use a simple model one dimension ferromagnetic spin chain to show the criteria in which the collective movements of the spin moments can enhance the spin current generation.

Arising wave propagation in nonlinear media for the (2+1)-dimensional Heisenberg ferromagnetic spin chain dynamical model

In this study, we study the (2+1)-dimensional nonlinear Schrödinger kind equation which illustrates the non-linear spin dynamics of (2+1)-dimensional Heisenberg ferromagnetic spin chains (HFSCs) through bilinear and anisotropic interactions in the semi-classical limit. This model also illustrates the ferromagnetic materials of magnetic ordering. Two analytical schemes are employed to study the equation namely, improved auxiliary equation and generalized Riccati mapping methods. We construct dark and bright solitons, combined bright–dark solitons, periodic waves, solitary waves and elliptic solutions to this equation. We give graphical presentations of the 2D and 3D of some achieved solutions. The obtained results of this investigation might be useful to explain the physical structure of this model. The achieved results of HFSC show the effectiveness and reliability of the proposed techniques.

Magnetic breathers and chaotic wave fields for a higher-order [formula omitted]-dimensional nonlinear Schrödinger-type equation in a Heisenberg ferromagnetic spin chain

Ferromagnetism, whose physical properties include the Giant-Magneto resistance, spin-transfer torque, spin-Hall effect and so on, attracts researchers’ interest in the search for the spin polarizers in spin electronics. In this paper, we investigate a higher-order (2+1)-dimensional nonlinear Schrödinger-type equation for a Heisenberg ferromagnetic spin chain with the bilinear and biquadratic interaction. Magnetic breathers are derived. Conditions of the transformation from the magnetic breather to the magnetic soliton are obtained. We get the magnetic chaotic wave fields, in which the magnetic breather-like solitons and rogue waves appear. Effects of γ on the magnetic chaotic wave fields are studied: As γ increases, mean amplitude of the magnetic waves in the chaotic wave field increases, and amplitude dispersion degree decreases, where γ represents the lattice parameter.

Highly dispersive magnons with spin-gap-like features in the frustrated ferromagneticS=12chain compoundCa2Y2Cu5O10detected by inelastic neutron scattering

We report inelastic neutron scattering experiments in Ca2Y2Cu5O10 and map out the full one magnon dispersion which extends up to a record value of 53 meV for frustrated ferromagnetic (FM) edge-sharing CuO2 chain (FFESC) cuprates. A homogeneous spin-1/2 chain model with a FM nearest-neighbor (NN), an antiferromagnetic (AFM) next-nearest-neighbor (NNN) inchain, and two diagonal AFM interchain couplings (ICs) analyzed within linear spin-wave theory (LSWT) reproduces well the observed strong dispersion along the chains and a weak one perpendicularly. The ratio R=|J_{a2}/J_{a1}| of the FM NN and the AFM NNN couplings is found as ~0.23, close to the critical point Rc=1/4 which separates ferromagnetically and antiferromagnetically correlated spiral magnetic ground states in single chains, whereas Rc>0.25 for coupled chains is considerably upshifted even for relatively weak IC. Although the measured dispersion can be described by homogeneous LSWT, the scattering intensity appears to be considerably reduced at ~11.5 and ~28 meV. The gap-like feature at 11.5 meV is attributed to magnon-phonon coupling whereas based on DMRG simulations of the dynamical structure factor the gap at 28 meV is considered to stem partly from quantum effects due to the AFM IC. Another contribution is ascribed to the intrinsic superstructure from the distorting incommensurate pattern of CaY cationic chains adjacent to the CuO2 ones. It gives rise to non-equivalent CuO4 units and Cu-O-Cu bond angles Phi and a resulting distribution of all exchange integrals. The J's fitted by homogeneous LSWT are regarded as average values. The record value of the FM NN integral J1=24 meV among FFESC cuprates can be explained by a non-universal Phi (not 90 deg.) and Cu-O bond length dependent anisotropic mean direct FM Cu-O exchange K_{pd}~120 meV. Enhanced K_{pd} values are also needed to compensate a significant AFM J_{dd} > ~6 meV.

Symmetry Reductions, Group‐Invariant Solutions, and Conservation Laws of a (2+1)‐Dimensional Nonlinear Schrödinger Equation in a Heisenberg Ferromagnetic Spin Chain

AbstractNonlinear spin excitations in ferromagnetic spin chains are studied for spintronic and magnetic devices including magnetic‐field sensors and for high‐density data storage. Here, (2+1)‐dimensional nonlinear Schrödinger equation is investigated, which describes the nonlinear spin dynamics for a Heisenberg ferromagnetic spin chain. Lie point symmetry generators and Lie symmetry groups of that equation are derived. Lie symmetry groups are related to the time, space, scale, rotation transformations, and Galilean boosts of that equation. Certain solutions, which are associated with the known solutions, are constructed. Based on the Lie symmetry generators, the reduced systems of such an equation are obtained. Based on the polynomial expansion and through one of the reduced systems, group‐invariant solutions are constructed. Soliton‐type group‐invariant solutions are graphically investigated and effects of the magnetic coupling coefficients, that is, α1, α2, α3, and α4, on the soliton's amplitude, width, and velocity are discussed. It is seen that α1, α2, α3, and α4 have no influence on the soliton's amplitude, but can affect the soliton's velocity and width. Lax pair and conservation laws of such an equation are derived.