Heisenberg Ferromagnetic Spin Chain Research Articles

Spin dynamic soliton in ferromagnetic materials over the (2 + 1)-dimensional beta fractional HFSC model

Ferromagnetic materials have important exploitation practice in permanent information in electromagnets, electric motors, generators, recording in thin film etc. This research explores spin dynamic soliton in Ferromagnetic materials via the (2 + 1)-D Heisenberg ferro-magnetic Spin Chains (HFSC) model. The Extended (I,R) and Extended Simple schemes treatment are applied to integrate the model. Through the technique, various novel dynamical wave solutions afford as optical dark and bright soliton envelope, spin wave envelope Black soliton, optical bell-shock interaction, optical bell-anti-shock wave, optical Dark-bright bell soliton and optical bright periodic waves from modulus plots, besides these real and imaginary profiles exhibits bright periodic wave with dark bell wave, periodically increasing–decreasing carrier wave, periodic carrier wave increase its amplitude by shock, periodic carrier wave suddenly decrease its amplitude by shock waves. The effect of fractional derivative, neighboring interaction as well as uniaxial crystal field anisotropy parameters is explored on the envelope soliton and amplitude of carrier waves. The changing value of neighboring interaction parameters are exhibited as increases wave height with the increases of parametric values, but while increasing values of the uni-axial crystal arena anisotropy factor causes the reduction of wave heights.

Exact solutions, symmetry groups and conservation laws for some (2+1)-dimensional nonlinear physical models

In this paper, the Bernoulli sub-equation function method is used to construct new exact travelling wave solutions for two important physical models: (2+1)-dimensional hyperbolic nonlinear Schrödinger (HNLS) equation and (2+1)-dimensional Heisenberg ferromagnetic spin chain (HFSC) equation. These solutions provide valuable insights into the behavior of these models, described in terms of exponential and hyperbolic tangent (tanh) functions. The study also involves an exploration of the infinitesimal generators and symmetry groups through the Lie symmetry method. In addition, by using multiplier approach, the conservation laws are established for these models. Graphical simulation of some solutions in the form of two-dimensional and three-dimensional are plotted to understanding of the underlying physical phenomena and mathematical properties of the (2+1)-dimensional HNLS and HFSC equations. The solutions and graphing are performed using Maple software.

Stability analysis and soliton solutions of truncated M-fractional Heisenberg ferromagnetic spin chain model via two analytical methods

Stability analysis and soliton solutions of truncated M-fractional Heisenberg ferromagnetic spin chain model via two analytical methods

Analytical study of nonlinear models using a modified Schrödinger’s equation and logarithmic transformation

Optical solitons are special waves that maintain their shape while traveling. Hence, solitary optical waves have great significance when it comes to representing pulse propagation through nonlinear partial differential equations. In our research, we have uncovered unique solutions for the formation of solitary wave patterns in the equation of the Heisenberg ferromagnetic spin chain (HFSC). This equation aptly describes the behavior of electromagnetic waves in contemporary magnetism. By employing innovative techniques based on logarithmic transformations and analytical methods, we have obtained various solution forms expressed in a concise manner using elementary functions. We have tested the correctness of these solutions by substituting them directly into the main equation. These recent discoveries provide novel perspectives on the complex realm of solitons as depicted by this model. Moreover, since the model finds applications in fiber optic communications, fluid dynamics, and other fields, the implications of these discoveries are broad. The utilized methods stand out for being simple, reliable, and capable of creating fresh solutions for nonlinear partial differential equations in the realm of mathematical physics. The research findings presented here showcase the effectiveness of the applied methods in reliably studying nonlinear phenomena in the HFSC equation and other nonlinear problems in mathematical physics. By utilizing these tools, scholars have the opportunity to expand and enhance their understanding of the complex mathematical frameworks underlying real-world problems.

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.

Exploring lump soliton solutions and wave interactions using new Inverse $$(G'/G)$$-expansion approach: applications to the (2+1)-dimensional nonlinear Heisenberg ferromagnetic spin chain equation

Exploring lump soliton solutions and wave interactions using new Inverse $$(G'/G)$$-expansion approach: applications to the (2+1)-dimensional nonlinear Heisenberg ferromagnetic spin chain equation

Magnetocaloric and hydrogen storage multi-functional properties of Eu4Ga8Ge16 compounds

We investigated the anisotropic magnetic, electrical transport, and heat capacity of Eu4Ga8Ge16 single crystals. Magnetization measurements with temperature and magnetic field revealed a complex behavior. Specifically, we observed anisotropic metamagnetic transitions at low magnetic field, and inverse hysteresis at high magnetic fields. These phenomena can be attributed to a Heisenberg ferromagnetic spin chain aligned along the a-axis. Additionally, this ferromagnetic behavior is interspersed with antiferromagnetic interactions between adjacent Heisenberg spin chains. We also noticed an anomalous increase in electrical resistivity at low temperature under magnetic fields, as well as different temperature-exponents of ρ(T) depending on crystal directions, which are attributed to the anisotropic scattering of carriers due to anisotropic magnetic interactions. We also evaluated the magnetocaloric effect and found a substantial magnetic entropy change than those of type-I Eu-based clathrates. The high entropy change (-ΔSM = 13.5 J kg−1 K−1) and adiabatic temperature difference (ΔTad = 7.8 K) near Néel temperature TN = 7.9 K reveal that the Heisenberg spin chain system might be advantageous for inducing a larger magnetic entropy change. Furthermore, we measured the hydrogen storage capacity of Eu4Ga8Ge16 as a multifunctional property because the zeolite-like cage structure can be a good candidate for hydrogen storage applications. Although the hydrogen storage capacity is considerably lower than that of the leading-edge materials, the hydrogen storage capacity can be improved further when we control the Eu-deficiency to place the hydrogen molecule at the cage site, because the hydrogen molecules reside at the (Ga,Ge) framework not in the cage site for fully occupied Eu atomic chain compounds. Hence, Eu4Ga8Ge16 emerges as a versatile substrate for engineering multifunctional energy materials, excelling in both low-temperature magnetocaloric effects and hydrogen storage potential.

Optical and rogue type soliton solutions of the (2+1) dimensional nonlinear Heisenberg ferromagnetic spin chains equation

In this study, the uses of unified method for finding solutions of a nonlinear Schrödinger equation that describes the nonlinear spin dynamics of (2+1) dimensional Heisenberg ferromagnetic spin chains equation. We successfully construct solutions to these equations. For each of the derived solutions, we provide the parametric requirements for the existence of a valid soliton. In order to visualize some of the discovered solutions, we plot the 2D and 3D graphics. The results of this investigation, which have been presented, might be useful in elucidating the model's physical significance. These are a highly useful tool for studying how electrical solitons, which travel as voltage waves in nonlinear dispersive media, spread out, as well as for doing various physical calculations. The study’s findings, which have been disclosed, might be useful in illuminating the models under consideration's physical significance and electrical field.

The new structure of stochastic solutions for the Heisenberg ferromagnetic spin chain equation

The new structure of stochastic solutions for the Heisenberg ferromagnetic spin chain equation

Rogue wave solutions on different periodic backgrounds for the (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation

In this paper, we will present exact rogue wave solutions on different periodic backgrounds for the (2+1)-dimensional Heisenberg ferromagnetic spin chain equation, which can govern nonlinear spin dynamics of the (2+1)-dimensional Heisenberg ferromagnetic spin chains with bilinear and anisotropic interactions in the semiclassical limit. We will derive different spectral parameters and corresponding periodic eigenfunctions of Lax pair according to the nonlinearization of spectral problem. Via Darboux transformation method, first- and second-order rogue wave solutions will be derived under two different periodic seed solutions, which can be expressed by the Jacobian elliptic functions dn and cn. Meanwhile, dynamic features of these various solutions with different parameters on two kinds periodic backgrounds taking different elliptic modulus will be analytically and graphically analyzed.

Whitham modulation theory and periodic solutions for the fifth-order nonlinear Schrödinger equation in the Heisenberg ferromagnetic spin chain

In this paper, we investigate the periodic solutions and Whitham modulation theory for the fifth-order nonlinear Schrödinger equation, which can describe the one-dimensional anisotropic Heisenberg ferromagnetic spin chain. First, we introduce the principle of the finite-gap integration method. Then, we discuss the single-phase periodic solutions and their degenerate forms in two limit cases. In addition, we analyze the influence of higher-order term parameters on the propagation of periodic solutions and solitons. Further, we derive the single-phase Whitham modulation equation for the fifth-order nonlinear Schrödinger equation. Moreover, we systematically derive the two-phase periodic solutions and the corresponding Whitham modulation equations.

New and more solitary wave patterns of the Heisenberg ferromagnetic spin chain model in fiber optics

The primary focus of this paper is the determination of novel soliton solutions for the [Formula: see text]-dimensional Heisenberg ferromagnetic spin chain (HFSC) problem. The suggested model may be thought of as a special case of the nonlinear Schrödinger equation. Exact solutions to the proposed equation have been found using efficient analytical approaches such as the singular manifold method and the [Formula: see text]-expansion method. These proposed methods are significant mathematical tools to obtain the exact traveling wave solutions of nonlinear complex partial differential equations (PDEs). After decomposing the governing problem into its real and imaginary components, we analyze both the real and imaginary components separately. Soliton solutions are obtained using computational tools like Maple. Trigonometric function solutions, rational solutions and hyperbolic function solutions are found for Heisenberg ferromagnetic model by the application of the proposed techniques. Furthermore, the physical properties of the solutions, such as hyperbolic functions, are important. The hyperbolic tangent is used in the computation of magnetic moment and velocity in special relativity. As a result, we hypothesize that the obtained results have physically comparable meanings to those stated by these collocations. By selecting suitable values of arbitrary parameters, it has been observed graphically that the amplitude of obtained solutions can be changed. Graphical representations of few of the reported solutions are presented in both two and three dimensions by choosing appropriate values of parameters. The suggested approaches are very efficient and reliable for finding exact solutions of wide range of nonlinear PDEs in a complex medium. The advantage of these techniques is evident since they are not limited in their ability to locate such wave patterns. Back substitution in the original equation using Maple 18 validated all solutions found, and the physical significance of these results has been underlined. The constraint conditions for the existence of constructed solutions are also provided in this paper.

Characteristics of Solitary Stochastic Structures for Heisenberg Ferromagnetic Spin Chain Equation

The impact of Stratonovich integrals on the solutions of the Heisenberg ferromagnetic spin chain equation using the unified solver approach is examined in this study. In particular, using arbitrary parameters, the traveling wave arrangements of rational, trigonometric, and hyperbolic functions are developed. The detailed arrangements are exceptionally critical for clarifying diverse complex wonders in plasma material science, optical fiber, quantum mechanics, super liquids and so on. Here, the Itô stochastic calculus and the Stratonovich stochastic calculus are considered. To describe the dynamic behaviour of random solutions, some graphical representations for these solutions are described with appropriate parameters.

Various Solitons and Other Wave Solutions to the (2+1)-Dimensional Heisenberg Ferromagnetic Spin Chain Dynamical Model

This paper outlines a study into the exact solutions of the (2+1)-dimensional Heisenberg ferromagnetic spin chain equation that is used to illustrate the ferromagnetic materials of magnetic ordering by applying two recent techniques, namely, the Sardar-subequation method and extended rational sine–cosine and sinh–cosh methods. Abundant exact solutions such as the bright soliton, dark soliton, combined bright–dark soliton, singular soliton and other periodic wave solutions expressed by the generalized trigonometric, generalized hyperbolic, trigonometric and hyperbolic functions are obtained. The numerical results are illustrated in the form of 3D plots, 2D contours and 2D curves by choosing proper parametric values to interpret the physical behavior of the model. The obtained results in this work are expected to provide a rich platform for constructing the soliton solutions of PDEs in physics.

Exact wave solutions and obliqueness of truncated M-fractional Heisenberg ferromagnetic spin chain model through two analytical techniques

This research is concerned to some modernistic wave solutions of truncated M-fractional Heisenberg ferromagnetic spin chains model. The collected solutions can be executed in exposing of this model in prominent form. The obtained results include the trigonometric, hyperbolic trigonometric and exponential functions. The verification of the results is also done by using Mathematica tool. Two techniques named as modified simplest equation (MSE) and Sardar sub-equation (SSE) techniques are employed to protect the results. The achieved results are also illustrated by 2-D, 3-D and contour plots for different values truncated M-fractional parameters as well as obliqueness. The gained results can also be fruitful for the development of model in the future.

Abundant Soliton Structures to the ( 2 + 1 )-Dimensional Heisenberg Ferromagnetic Spin Chain Dynamical Model

In this paper, we aim to investigate the ( 2 + 1 )-dimensional Heisenberg ferromagnetic spin chain equation that is used to describe the nonlinear dynamics of magnets. Two recent effective technologies, namely, the variational method and subequation method, are employed to construct the abundant soliton solutions. By these two methods, diverse solutions such as the bright soliton, dark soliton, bright-dark soliton, perfect periodic soliton, and singular periodic soliton are successfully extracted. The numerical results are illustrated in the form of 3-D plots and 2-D curves by choosing proper parametric values to interpret the dynamics of wave profiles. Finally, the physical interpretation of the acquired results is elaborated in detail. The results obtained in this study are helpful to explain some physical meanings of some nonlinear physical models in electromagnetic waves.

WAVE PROPAGATION AND MAGNETIC ORDERING IN FERROMAGNETIC MATERIALS

The soliton wave solutions to the (2+1)-dimensional Heisenberg ferromagnetic spin chain [Formula: see text] problem are explored in this paper. The (2+1)-dimensional [Formula: see text] equation describes the nonlinear spin dynamics of Heisenberg ferromagnetic spin chains in the semiclassical limit. This formula is based on the spin-chain of the Heisenberg field. The bilinear and anisotropic interactions are accounted for in this equation. Even ferromagnetism may be explained by this paradigm, since it describes the propagation of waves inside a substance (the magnetic ordering in ferromagnetic materials). To construct a new soliton wave solution and validate its correctness, modern analytical and approximative schemes are utilized such as the Khater II and Adomian decomposition methods. Numerous interpretations for solitary waves are shown by various plots such as polar plots, contour plots, two-dimensional plots, and three-dimensional plots. The study’s novelty may be appreciated by contrasting our findings with those presented in previously published research publications. Most of the many computational simulations used are performed with the aid of a program called Mathematica 13.1.

Abundant Exact Soliton Solutions of the (2+1)-Dimensional Heisenberg Ferromagnetic Spin Chain Equation Based on the Jacobi Elliptic Function Ideas

The Heisenberg ferromagnetic spin chain equation (HFSCE) is very important in modern magnetism theory. HFSCE expounded the nonlinear long-range ferromagnetic ordering magnetism. Also, it depicts the characteristic of magnetism to many insulating crystals as well as interaction spins. Moreover, the ferromagnetism plays a fundamental role in modern technology and industry and it is principal for many electrical and electromechanical devices such as generators, electric motors, and electromagnets. In this article, the exact solutions of the nonlinear (2+1)-dimensional HFSCE are successfully examined by an extended modified version of the Jacobi elliptic expansion method (EMVJEEM). Consequently, much more new Jacobi elliptic traveling wave solutions are found. These new solutions have not yet been reported in the studied models. For the study models, the new solutions are singular solitons not yet observed. Additionally, certain interesting 3D and 2D figures are performed on the obtained solutions. The geometrical representation of the HFSCE provides the dynamical information to explain the physical phenomena. The results will be significant to understand and study the (2+1)-dimensional HFSCE. Therefore, further studying EMVJEEM may help researchers to seek for more soliton solutions to other nonlinear differential equations.

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.

Analytical and hybrid numerical simulations for the (2+1)-dimensional Heisenberg ferromagnetic spin chain

In this study, we investigate the solitary wave solutions for the (2+1)-dimensional Heisenberg ferromagnetic spin chain (HFSC). New solitary wave solutions are generated and checked using the Bernoulli sub-equation (BSE), a novel Kudryashov (NKud), and He’s homotopy perturbation (He’s HP). One may learn about solitary waves by looking at polar, contour, two-dimensional, or three-dimensional charts. Our research is original because it contrasts with what has already been done. Mathematica software 13.1 is utilized for checking the computational techniques solutions’ accuracy by putting them back into the original model.