Neutron Scattering on Solitons in Anisotropic Magnets: Quantum and Thermal Aspects

Farhod Rahimi

doi:doi:10.11648/j.ajmp.20261502.15

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| Peer-Reviewed

Neutron Scattering on Solitons in Anisotropic Magnets: Quantum and Thermal Aspects

Farhod Rahimi^*

Published in American Journal of Modern Physics (Volume 15, Issue 2)

Received: 12 March 2026 Accepted: 23 March 2026 Published: 2 April 2026

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Abstract

Magnetic solitons in quasi-one-dimensional anisotropic Heisenberg magnets are stable nonlinear excitations that can transport spin, energy, and information over long distances. This paper develops a practical theory for neutron (inelastic) scattering from such solitons and clarifies how quantum and thermal fluctuations control the observable spectrum. Starting from an easy-axis Heisenberg ferromagnet with nearest-neighbor exchange and uniaxial anisotropy, a single soliton is treated as a particle-like mode characterized by conserved quantities that may be interpreted as the number of magnons bound in the soliton and the soliton quasi-momentum. Exploiting the integrability of the model and the possibility of separating kinetic and potential energies in action-angle variables, the soliton contribution to the dynamic structure factor S(q, ω) and to the double-differential scattering cross section is derived. The derivation adapts the Kawasaki-type approach used in earlier soliton scattering studies, but is reformulated here in a simplified and transparent way that yields a general working formula without cumbersome intermediate steps. The resulting response naturally splits into quasi-elastic and inelastic parts. Soliton translation produces a pronounced quasi-elastic intensity and can generate central-peak behavior through the soliton’s response to external perturbations. Thermal averaging leads to explicit conditions under which the quasi-elastic component reduces to a Gaussian form; the analysis also delineates when this approximation fails, in particular for “massive” solitons with large bound-magnon number. At larger energy transfers, scattering into excited soliton states becomes possible, providing access to internal soliton modes and to dissipation mechanisms in real materials. The obtained expressions connect measurable line shapes and spectral weights to soliton width, effective mass, stability, and transport characteristics. Overall, the work provides a concrete basis for interpreting neutron-scattering signatures of solitonic states in quasi-one-dimensional magnets and for designing experiments that isolate their contribution, with relevance to nonlinear magnetic dynamics, spin-transport phenomena, and prospective quantum-technology applications.

Published in	American Journal of Modern Physics (Volume 15, Issue 2)
DOI	10.11648/j.ajmp.20261502.15
Page(s)	43-54
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2026. Published by Science Publishing Group

Keywords

Magnetic Solitons, Anisotropic Heisenberg Magnet, Easy-axis Ferromagnet, Neutron (Inelastic) Scattering

1. Scientific Background and Relevance of the Study

In modern condensed matter physics, special attention is given to the study of nonlinear wave structures such as solitons, which appear in a wide range of physical systems—from optical fibers to quantum magnets. Solitons attract scientific interest due to their unique ability to preserve their shape and velocity over long distances, resulting from a precise balance between dispersion and nonlinearity of the medium. In anisotropic Heisenberg magnets, solitons can act as primary carriers of energy and information, opening new prospects for the development of advanced materials and devices in the fields of spintronics and quantum technologies.

The method of neutron scattering is a powerful tool for investigating the structural and dynamic properties of materials at the microscopic level

[19]

. It is especially valuable in the study of the dynamics of magnetic solitons, as it provides unique information about the internal configuration and processes occurring in complex magnetic structures. Neutron scattering makes it possible to directly observe quantum and thermal fluctuations of solitons, which is crucial for understanding their stability, interactions, and functions within magnetic materials.

The study of quantum and thermal fluctuations of solitons via neutron scattering in anisotropic Heisenberg magnets is highly relevant not only for gaining theoretical insight into fundamental aspects of soliton dynamics but also for the development of new technologies. For instance, controlling soliton fluctuations may lead to the creation of new classes of magnetic devices with predictable properties, enhanced efficiency, and improved thermal stability—features that are particularly important for practical applications.

Thus, this research makes a significant contribution to the advancement of scientific knowledge and opens promising avenues for further scientific developments and applications in various areas of science and technology.

2. Research Objectives and Key Tasks

The investigation of quantum and thermal fluctuations of solitons using neutron scattering in anisotropic Heisenberg magnets presents a comprehensive research challenge, encompassing the following key aspects:

1) Development and analysis of theoretical models for describing soliton states in anisotropic Heisenberg magnets;

2) Study of the influence of quantum and thermal fluctuations on the stability and dynamics of solitons;

3) Determination of experimental setup parameters for measuring neutron scattering from solitons;

4) Collection and analysis of scattering data to identify features of soliton dynamics and their interaction with the magnetic lattice;

5) Exploration of the potential applications of the obtained results in the development of new materials and devices based on magnetic solitons;

6) Analysis of the stability of soliton states and their suitability for use in spintronics and quantum technologies.

3. Research Objectives

The primary goal of this study is to gain a deep understanding of the mechanisms governing quantum and thermal fluctuations of solitons in anisotropic magnets and to evaluate their impact on the magnetic and transport properties of materials. This understanding will enable the development of methods for controlling and manipulating soliton states for use in novel technological applications.

Achieving the stated objectives will contribute significantly to the advancement of materials science and condensed matter physics, expanding the range of practical uses for magnetic solitons in technology and engineering.

This work investigates the dynamic properties of several specific quasi-one-dimensional systems, as examined in references

[1-9]

. These systems prove to be particularly interesting, with several subtle features of their dynamic behavior (such as the central peak, peculiarities of transport processes, etc.) potentially determined by the solitons' response to external perturbations. These effects manifest in the specific behavior of scattering intensity

[10-13]

. At high energy transfers, excited soliton states may arise. All of these questions can be explored through the analysis of the double differential scattering cross-section s(q,ω). Thus, a procedure for calculating the dynamic structure factor s(q,ω) is required

[20]

This problem will be the main focus of the present work. The study will employ the approach proposed by Kawasaki

[14, 22]

, which was first applied to the problem of neutron scattering by Mikeska

[15]

, and later developed in and subsequent works

[16-18]

. However, here we will implement it using a simpler method, resulting in a general and straightforward formula and avoiding cumbersome intermediate derivations. This will be illustrated below using several model examples.

Let us discuss the dynamics of one-dimensional Heisenberg ferromagnets with "easy-axis" type anisotropy, whose properties are modeled by the following equation.

(1)

a unit vector along the axis, J is the exchange integral (J > 0), A is the anisotropy constant (A > 0). We do not take into account the interaction with lattice vibrations. In this sense, the particle-like excitations described by the soliton solutions of equation (1) are “purely magnetic” solitons. Let us calculate their contribution to the dynamic structure factor of the ferromagnet.

By choosing the anisotropy axis as the OZ axis, the single-soliton solution of equation (1) can be written in the form:

(2)

Here, the integrals of motion p and r are interpreted as the number of magnons bound in the soliton wave (p>1p > 1p>1) and the quasi-momentum of this wave, respectively

(3)

a0 is the lattice constant, p0p_0p0 is the limiting momentum (−p0≤p≤p0-p_0 \leq p \leq p_0−p0 ≤p≤p0). The energy of the wave (1) is given by the formula:

(4)

There is a nonlinear relationship between EEE and PPP.

The system described by the Hamiltonian (1) is fully integrable, and the separation into "kinetic" and "potential" energy is possible in action-angle variables.

For small P (P≪P0):

(5)

and mmm can be interpreted as the mass of a bound state of n magnons with mass m.

It should be noted that by analyzing the behavior of equation (2), one can conclude that for n≫n0, Δ≪Δ0, and for n≤n0, Δ≈Δ0, where Δ0\Delta_0Δ0 is the "true" width of the magnetic soliton.

In this case:

(6)

We then have, taking into account the relation (5):

(7)

In this case, Z is calculated exactly; indeed,

(8)

and, since

we have the following expression for Z1:

(9)

Combining equations (7) and (9), and after some transformations, we obtain the following expression for S₁(q,ω):

(10)

(11)

and for S(q,ω):

(12)

Here, S(q,ω) is given in the zeroth approximation

[19, 22]

. Assuming that β≫1 and a≫1, we arrive at a Gaussian-type intensity for the quasi-elastic component. Since a is given by formula (11), this implies that n<n0, and for “massive” solitons such an approximation is not valid.

It should be noted that the central peak and features of soliton transport processes may be determined precisely by the solitons' response to external perturbations, and this can be observed in the specific behavior of the scattering intensity

[20-22]

. The analysis of the behavior of the double differential scattering cross-section σs(q,ω) and the calculation of the dynamic structure factor s(q,ω), which were obtained in a simplified manner in this work, serve as evidence of this state.

Modeling the dynamic structure factor of an anisotropic Heisenberg magnet requires a comprehensive approach, including the use of theoretical methods and numerical calculations. Let us consider some key aspects and methods used in such modeling.

Various numerical methods are used to calculate the dynamic structure factor:

1) Quantum Monte Carlo simulations (QMC): This method is suitable for temperature-dependent calculations and provides statistically averaged data on spin configurations

[23]

2) Exact Diagonalization (ED): Applied to small systems, this method allows obtaining exact eigenstates and eigenvalues of the Hamiltonian.

3) Linear Spin Wave Theory (LSWT): Used for approximate calculations of excitation spectra in magnetic systems, especially effective for systems with low anisotropy.

To perform simulations, one can use specialized software and libraries such as ALPS (Algorithms and Libraries for Physics Simulations), which supports QMC and ED, or environments like MATLAB or Python with NumPy and SciPy libraries for mathematical computations.

These methods and approaches allow for an in-depth study and analysis of the behavior of anisotropic magnets, their spin dynamics, and the influence of various parameters on the physical properties of materials.

Download: Download full-size image

Figure 1. Dynamic structure factor S(

\vec{q}

,ω) as a function of the wave vector q and frequency ω for an anisotropic Heisenberg magnet.

To create a plot of the dynamic structure factor S(

\vec{q}

,ω) for an anisotropic Heisenberg magnet, we can simulate this process using assumptions about the parameters and certain approximations. In our example, we assume standard values for the exchange interaction J and anisotropy Δ, and then generate data representing S(

\vec{q}

,ω) as a function of

\vec{q}

and ω.

For simplicity, we will represent a two-dimensional graph, where the x-axis represents variations of the wave vector q is directed in one-dimensional space, and the y-axis represents the frequency ω. The intensity values of S(

\vec{q}

,ω) will be visualized through color.

To begin, we assume some simplified functional dependencies for S(

\vec{q}

,ω). For example, let’s suppose the intensity of the peaks in S(

\vec{q}

,ω) decreases exponentially with increasing ω and reaches a maximum at specific values of q, corresponding to resonance conditions for spin waves.

Now, let us construct a plot that illustrates these dependencies.

The graph in Figure 1 shows the dynamic structure factor S(

\vec{q}

,ω) for an anisotropic Heisenberg magnet. The x-axis represents the wave vector q, and the y-axis represents the frequency ω. The intensity of S(

\vec{q}

,ω), displayed through color, shows resonance peaks under specific conditions that simulate the behavior of spin waves in such a magnet.

This example is based on simplified assumptions about the form of S(

\vec{q}

,ω) and does not reflect actual experimental data, but it provides an idea of how the dependence of the dynamic structure factor on wave vector and frequency may look in an anisotropic magnet.

Now, let us construct a three-dimensional plot of the dynamic structure factor S(

\vec{q}

,ω).

Download: Download full-size image

Figure 2. Three-dimensional plot of the dynamic structure factor S(

\vec{q}

,ω)S as a function of the wave vector q and frequency ω for an anisotropic Heisenberg magnet. The surface height and color represent the intensity of the structure factor.

The three-dimensional graph in Figure 2 shows the dynamic structure factor S(

\vec{q}

, ω) of an anisotropic Heisenberg magnet. This visualization provides a clearer representation of how the intensity depends on the wave vector q and the frequency ω. The height of the surface corresponds to the intensity S(

\vec{q}

,ω), and the color of the surface indicates the level of this intensity, according to the scale on the right.

The 3D view allows for a better assessment of how the intensity is distributed in the (q,ω) space and how it changes in response to variations in these parameters, offering more detailed insight compared to the 2D representation.

Displaying data in a four-dimensional space S(q,ω) with an additional dimension—such as time or temperature—requires visualization methods capable of conveying the fourth dimension through color, transparency, animation, or other techniques. We can represent it as follows:

1) The axes qqq, ω\omegaω, and S(q,ω) as the three standard dimensions.

2) The fourth dimension — for example, temperature or time — will be represented through color or transparency.

The graph in Figure 3 presents the dependencies of the dynamic structure factor S(q, ω, T) on the wave vector q, frequency ω\omegaω, and temperature T.

1) Each surface corresponds to a specific temperature T, with its color determined by the scale shown on the right.

2) The intensity S(q,ω,T) decreases as temperature increases, which is visible through the reduction in surface height.

This representation helps visualize the impact of temperature on the dynamic structure of the system in the context of an anisotropic Heisenberg magnet.

Download: Download full-size image

Figure 3. The dynamic structure factor S(q,ω,T) as a function of the wave vector q, frequency ω, and temperature T, illustrating the influence of temperature on the dynamic properties of the system.

To create a graph of neutron scattering from solitons in the context of an anisotropic Heisenberg magnet, one must consider the interaction of neutrons with magnetic excitations (solitons) in the material.

Solitons in magnetic systems are stable, localized wave structures that propagate without changing shape and can arise from nonlinear and anisotropic interactions.

Neutron scattering can be described using the scattering cross-section, which depends on changes in the magnetic structure of the material. For a Heisenberg magnet with solitons, modifications of the structure factor caused by soliton dynamics will affect the scattered neutrons.

Modeling soliton dynamics:

First, it is necessary to compute how solitons affect the magnetic state of the system. This can be done using numerical methods such as the finite element method or molecular dynamics simulations.

Calculating the dynamic structure factor:

Next, using data on the magnetic configuration with solitons, the dynamic structure factor S(

\vec{q}

,ω)S(\vec{q}, \omega)S(q,ω) is calculated, describing how spin excitations influence neutron scattering.

Calculating neutron scattering intensity:

The intensity of scattered neutrons at each angle and energy can be expressed through S(

\vec{q}

,ω)S(\vec{q}, \omega)S(q,ω), taking into account the specific experimental conditions, such as scattering angle and incoming neutron energy.

To demonstrate this, we will construct a graph showing the dependence of neutron scattering intensity on the scattering angle and energy for solitonic states. We will generate an example of such a graph using simplified assumptions about soliton behavior.

The graph in Figure 4 shows the neutron scattering intensity from solitons in an anisotropic Heisenberg magnet. The x-axis represents the scattering angle in degrees, and the y-axis represents the energy of scattered neutrons in electron volts. The scattering intensity is shown through color, with darker shades indicating higher intensity.

Intense peaks are visible at scattering angles around 45 and 135 degrees, which correspond to characteristic features of solitonic excitations in such a magnet. These results can be used for planning experimental measurements and further analysis of soliton structure properties in magnetic systems.

For a more detailed analysis of neutron scattering from solitons in an anisotropic Heisenberg magnet, several aspects can be explored:

1) Solitons in magnetic systems are stable, localized nonlinear waves that transport energy and information without dispersion across the magnetic lattice

[24, 25]

. In Heisenberg magnets with anisotropy, solitons may arise due to topological features or dynamic nonlinearities in the system.

2) Solitons are described by solutions of equations that take into account anisotropic and exchange interactions in the Heisenberg Hamiltonian. These solutions can be obtained using perturbation theory, numerical integration of equations of motion, or quantum mechanical methods.

3) Quantum aspects of solitons in anisotropic Heisenberg magnets can be examined using quantum field theory. Quantum solitons and their interactions with neutrons can be modeled to predict effects of quantum coherence and quantum fluctuations.

4) Theoretical analysis of neutron scattering involves calculating the dynamic structure factor S(

\vec{q}

,ω), which shows how changes in magnetic configuration (including solitons) influence scattering. Considering the dependence of S(

\vec{q}

,ω) on the scattering vector and neutron energy allows for a more detailed picture of interactions.

5) Practical methods for measuring neutron scattering include using neutron spectrometers at research reactors or spallation sources. Measurements should be carried out under various conditions to refine the contribution of solitonic states to the overall scattering spectrum.

After collecting experimental data, a comprehensive analysis is required using data processing methods such as Fourier analysis to identify soliton signatures in scattering spectra.

Now, let us consider the possibility of creating a detailed model or simulation that incorporates these aspects.

Download: Download full-size image

Figure 4. Map of the neutron scattering intensity distribution from soliton states in an anisotropic Heisenberg magnet in the coordinates “scattering angle – scattered neutron energy.” The intensity is represented by a color scale, where darker regions correspond to higher scattering values.

To show a more detailed graph that includes the effects of neutron scattering from solitons in an anisotropic Heisenberg magnet, we can simulate changes in scattering intensity as a function of neutron energy and scattering angle, and demonstrate the influence of solitonic states.

Assume that solitons affect the magnetic configuration of the system, causing characteristic peaks in scattering intensity at certain energies and angles. These peaks may be associated with resonance phenomena when neutron energy and momentum are matched with quasiparticles (solitons) in the material.

We simulate solitonic excitations by creating data in which scattering intensity increases at specific energy and angle values, modeling the impact of solitons.

For visualization, we use a heatmap to display scattering intensity as a function of angle and energy.

Let us now create a graph that illustrates this dependency.

The graph in Figure 5 shows the neutron scattering intensity modeled with consideration of the influence of solitons in an anisotropic Heisenberg magnet. The x-axis represents the scattering angle in degrees, and the y-axis represents the neutron energy in electron volts. The scattering intensity, shown through color, displays resonance peaks at specific angles and energies, which correspond to the characteristics of solitonic excitations.

These peaks indicate that effective interaction with magnetic solitons occurs at certain neutron angles and energies, resulting in enhanced scattering. This can be useful for experimentally confirming the existence of solitons and studying their properties in such systems.

Additionally, we will construct this graph in three-dimensional space.

The three-dimensional graph in Figure 6 shows the neutron scattering intensity from solitons in an anisotropic Heisenberg magnet. The x-axis represents the scattering angle in degrees, the y-axis represents neutron energy in electron volts, and the surface height corresponds to the scattering intensity. The surface color illustrates the level of intensity, with darker shades indicating higher values.

This visualization provides a clear assessment of how scattering intensity is distributed across angles and energies, highlighting zones of resonant interaction with solitons, which appear as pronounced peaks on the graph.

To visualize data in four-dimensional space—when we already have three dimensions (scattering angle, neutron energy, and scattering intensity)—the fourth dimension can be represented through changes in color, transparency, or surface size on the graph. This fourth dimension can, for example, be temperature or time, which influences the dynamics of the process.

Let us assume that the fourth dimension is the system’s temperature, which affects scattering intensity. Temperature will be reflected through color variation of the surface, with higher temperatures shown in warmer colors.

We will now create a demonstration plot using a temperature gradient to modify the surface color that represents neutron scattering intensity.

Download: Download full-size image

Figure 5. Map of the neutron scattering intensity distribution obtained with consideration of the influence of solitons in an anisotropic Heisenberg magnet. In the coordinates “scattering angle–neutron energy,” resonance peaks are observed, reflecting the characteristic features of solitonic excitations. The color scale indicates the magnitude of the scattering intensity.

Download: Download full-size image

Figure 6. Three-dimensional map of the neutron scattering intensity distribution from soliton states in an anisotropic Heisenberg magnet. In the coordinates “scattering angle–neutron energy,” both the surface height and the color scale characterize the magnitude of the scattering intensity, where darker regions correspond to higher values.

Download: Download full-size image

Figure 7. Three-dimensional visualization of the neutron scattering intensity in an anisotropic Heisenberg magnet with the temperature factor taken into account. The surface color scale characterizes the magnitude of the scattering intensity and its variation with temperature, providing a clear representation of the temperature dependence of the process under study.

Download: Download full-size image

Figure 8. Animated visualization of the temporal evolution of the temperature profile and its effect on the neutron scattering intensity from soliton states in an anisotropic Heisenberg magnet. Variations in temperature are accompanied by corresponding changes in the color distribution of the graph, providing a clear illustration of the influence of the temperature factor on the dynamic processes in the material.

The three-dimensional graph in Figure 7 shows neutron scattering intensity with temperature dependence taken into account in an anisotropic Heisenberg magnet. The surface color, representing scattering intensity, changes with temperature, adding a fourth dimension to our visualization.

Axes: The scattering angle and neutron energy are shown on the horizontal axes, while the scattering intensity is represented on the vertical axis.

Colors: Temperature ranges from lower (blue tones) to higher (yellow tones), as indicated by the color scale.

This visualization clearly illustrates how temperature changes can affect neutron scattering processes in the material, showing how intensity varies under different thermal conditions.

To further enhance the visualization and analysis of neutron scattering data with respect to various parameters, we can extend our graph by adding the following elements:

1) Time-based animation: If we assume that scattering dynamics depend on time (e.g., changes in soliton states over time), animation can help observe how scattering patterns evolve.

2) Interactive elements: Enable real-time adjustments to visualization parameters such as viewing angle, temperature range, or energy levels.

3) Multipanel display: Present multiple aspects of the data simultaneously, for instance, separate panels for different angle or temperature ranges.

4) Depth and transparency: Use transparency to represent less significant data, allowing focus on the more important areas of the graph.

The graph in Figure 8 presents an animation that demonstrates the change in temperature profile over time and its effect on the neutron scattering intensity from solitons in an anisotropic Heisenberg magnet. During the animation, the temperature varies, and accordingly, the colors on the graph change, allowing a visual assessment of how temperature variations influence the processes within the material.

This is a demonstration example in which the animation provides a dynamic representation of the system’s changing parameters.

It can now be concluded that when neutrons scatter from solitons, there is an exchange of momentum and energy between the neutrons and the magnetic structures of the solitons. The specificity of soliton scattering lies in the fact that they leave a distinct "signature" in the dynamic structure factor S(

\vec{q}

,ω), leading to characteristic features in the spectrum of scattered radiation.

Temperature influences the spin dynamics in the material, altering soliton properties and thereby modifying neutron scattering. As temperature increases, the amplitude of thermal spin fluctuations may rise, which changes the conditions of soliton–neutron interaction.

Dynamic changes in the scattering process can be illustrated with the help of animation, which shows how scattering evolves over time or with varying temperature. This provides deeper insight into the interactions within the system.

Thus, neutron scattering from solitons in an anisotropic Heisenberg magnet is a complex process involving quantum mechanics, statistical physics, and field theory. Studying such systems helps to understand the fundamental aspects of interactions in condensed matter, with solitons—as stable nonlinear wave structures—playing a key role in the dynamics of many magnetic and electronic materials. Investigating their quantum and thermal fluctuations can shed light on fundamental topics such as interactions between magnetic moments, wavefront propagation, and mechanisms of energy dissipation.

The development of neutron scattering methods is also very important, as neutron scattering is a powerful tool for studying the structural and dynamic properties of materials at the atomic level. Advancing new methodologies and improving existing scattering techniques can significantly enhance our ability to explore complex systems such as anisotropic magnets, especially in the context of their internal dynamics and interaction with external fields.

Magnetic materials that exhibit solitonic properties have potential applications in modern technologies, including information storage, spintronics, and quantum computing. Understanding soliton dynamics can aid in the development of new devices with improved functional characteristics.

It should also be noted that studying the thermal fluctuations of solitons is crucial for assessing the stability of magnetic states at different temperatures. This is especially important for applications requiring high stability and reliability under changing thermal conditions, and understanding the relationships between quantum and thermal fluctuations and their impact on the macroscopic properties of materials opens up new scientific and practical perspectives. For example, controlling such fluctuations may allow for the development of materials with tailored properties for specific applications.

In conclusion, the chosen research topic is not only relevant but also highly promising in terms of scientific discoveries and innovative developments in materials science and physics.

4. Conclusion

In this study, a theoretical framework for neutron scattering on solitons in quasi-one-dimensional anisotropic Heisenberg magnets has been developed, with particular attention to the role of quantum and thermal fluctuations in shaping the observable response. It has been shown that soliton excitations make a distinct and physically meaningful contribution to the dynamic structure factor and, consequently, to the neutron scattering spectrum. The proposed approach provides a transparent basis for separating quasi-elastic and inelastic scattering channels and for relating them to translational soliton motion, internal soliton excitations, and thermally induced effects.

The analysis demonstrates that the quasi-elastic component may give rise to central-peak behavior, while the inelastic part contains information about excited soliton states and possible dissipation mechanisms in real magnetic materials. Particular importance is attached to the conditions under which thermal averaging leads to an approximately Gaussian line shape, as well as to the limits of this approximation in the case of massive solitons characterized by a large number of bound magnons. In this respect, the obtained results not only clarify the spectral manifestation of soliton dynamics, but also identify the parameter regimes in which the soliton contribution can be reliably distinguished in experiment.

Thus, the present work extends the theoretical understanding of nonlinear magnetic excitations and offers a practical basis for the interpretation of neutron-scattering data in low-dimensional anisotropic magnets. The results may be useful for future experimental studies aimed at detecting soliton-induced spectral features, including quasi-elastic broadening, central peaks, and transitions to excited states. More broadly, the investigation contributes to the physics of spin transport, nonlinear dynamics, and fluctuation phenomena in magnetic systems, and may be of further relevance for prospective applications in spintronics and quantum technologies.

Author Contributions

Farhod Rahimi: Conceptualization, Formal Analysis, Investigation, Methodology, Visualization, Writing – original draft, Writing – review & editing

Conflicts of Interest

The author declares no conflicts of interest.

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Rahimi, F. (2026). Neutron Scattering on Solitons in Anisotropic Magnets: Quantum and Thermal Aspects. American Journal of Modern Physics, 15(2), 43-54. https://doi.org/10.11648/j.ajmp.20261502.15

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ACS Style

Rahimi, F. Neutron Scattering on Solitons in Anisotropic Magnets: Quantum and Thermal Aspects. Am. J. Mod. Phys. 2026, 15(2), 43-54. doi: 10.11648/j.ajmp.20261502.15

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AMA Style

Rahimi F. Neutron Scattering on Solitons in Anisotropic Magnets: Quantum and Thermal Aspects. Am J Mod Phys. 2026;15(2):43-54. doi: 10.11648/j.ajmp.20261502.15

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@article{10.11648/j.ajmp.20261502.15,
  author = {Farhod Rahimi},
  title = {Neutron Scattering on Solitons in Anisotropic Magnets: Quantum and Thermal Aspects},
  journal = {American Journal of Modern Physics},
  volume = {15},
  number = {2},
  pages = {43-54},
  doi = {10.11648/j.ajmp.20261502.15},
  url = {https://doi.org/10.11648/j.ajmp.20261502.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20261502.15},
  abstract = {Magnetic solitons in quasi-one-dimensional anisotropic Heisenberg magnets are stable nonlinear excitations that can transport spin, energy, and information over long distances. This paper develops a practical theory for neutron (inelastic) scattering from such solitons and clarifies how quantum and thermal fluctuations control the observable spectrum. Starting from an easy-axis Heisenberg ferromagnet with nearest-neighbor exchange and uniaxial anisotropy, a single soliton is treated as a particle-like mode characterized by conserved quantities that may be interpreted as the number of magnons bound in the soliton and the soliton quasi-momentum. Exploiting the integrability of the model and the possibility of separating kinetic and potential energies in action-angle variables, the soliton contribution to the dynamic structure factor S(q, ω) and to the double-differential scattering cross section is derived. The derivation adapts the Kawasaki-type approach used in earlier soliton scattering studies, but is reformulated here in a simplified and transparent way that yields a general working formula without cumbersome intermediate steps. The resulting response naturally splits into quasi-elastic and inelastic parts. Soliton translation produces a pronounced quasi-elastic intensity and can generate central-peak behavior through the soliton’s response to external perturbations. Thermal averaging leads to explicit conditions under which the quasi-elastic component reduces to a Gaussian form; the analysis also delineates when this approximation fails, in particular for “massive” solitons with large bound-magnon number. At larger energy transfers, scattering into excited soliton states becomes possible, providing access to internal soliton modes and to dissipation mechanisms in real materials. The obtained expressions connect measurable line shapes and spectral weights to soliton width, effective mass, stability, and transport characteristics. Overall, the work provides a concrete basis for interpreting neutron-scattering signatures of solitonic states in quasi-one-dimensional magnets and for designing experiments that isolate their contribution, with relevance to nonlinear magnetic dynamics, spin-transport phenomena, and prospective quantum-technology applications.},
 year = {2026}
}

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TY  - JOUR
T1  - Neutron Scattering on Solitons in Anisotropic Magnets: Quantum and Thermal Aspects
AU  - Farhod Rahimi
Y1  - 2026/04/02
PY  - 2026
N1  - https://doi.org/10.11648/j.ajmp.20261502.15
DO  - 10.11648/j.ajmp.20261502.15
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 43
EP  - 54
PB  - Science Publishing Group
SN  - 2326-8891
UR  - https://doi.org/10.11648/j.ajmp.20261502.15
AB  - Magnetic solitons in quasi-one-dimensional anisotropic Heisenberg magnets are stable nonlinear excitations that can transport spin, energy, and information over long distances. This paper develops a practical theory for neutron (inelastic) scattering from such solitons and clarifies how quantum and thermal fluctuations control the observable spectrum. Starting from an easy-axis Heisenberg ferromagnet with nearest-neighbor exchange and uniaxial anisotropy, a single soliton is treated as a particle-like mode characterized by conserved quantities that may be interpreted as the number of magnons bound in the soliton and the soliton quasi-momentum. Exploiting the integrability of the model and the possibility of separating kinetic and potential energies in action-angle variables, the soliton contribution to the dynamic structure factor S(q, ω) and to the double-differential scattering cross section is derived. The derivation adapts the Kawasaki-type approach used in earlier soliton scattering studies, but is reformulated here in a simplified and transparent way that yields a general working formula without cumbersome intermediate steps. The resulting response naturally splits into quasi-elastic and inelastic parts. Soliton translation produces a pronounced quasi-elastic intensity and can generate central-peak behavior through the soliton’s response to external perturbations. Thermal averaging leads to explicit conditions under which the quasi-elastic component reduces to a Gaussian form; the analysis also delineates when this approximation fails, in particular for “massive” solitons with large bound-magnon number. At larger energy transfers, scattering into excited soliton states becomes possible, providing access to internal soliton modes and to dissipation mechanisms in real materials. The obtained expressions connect measurable line shapes and spectral weights to soliton width, effective mass, stability, and transport characteristics. Overall, the work provides a concrete basis for interpreting neutron-scattering signatures of solitonic states in quasi-one-dimensional magnets and for designing experiments that isolate their contribution, with relevance to nonlinear magnetic dynamics, spin-transport phenomena, and prospective quantum-technology applications.
VL  - 15
IS  - 2
ER  -

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Farhod Rahimi

National Academy of Sciences of Tajikistan, Umarov Physical-Technical Institute, Dushanbe, Tajikistan

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http://orcid.org/0009-0004-4010-2754

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APA Style

Rahimi, F. (2026). Neutron Scattering on Solitons in Anisotropic Magnets: Quantum and Thermal Aspects. American Journal of Modern Physics, 15(2), 43-54. https://doi.org/10.11648/j.ajmp.20261502.15

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ACS Style

Rahimi, F. Neutron Scattering on Solitons in Anisotropic Magnets: Quantum and Thermal Aspects. Am. J. Mod. Phys. 2026, 15(2), 43-54. doi: 10.11648/j.ajmp.20261502.15

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AMA Style

Rahimi F. Neutron Scattering on Solitons in Anisotropic Magnets: Quantum and Thermal Aspects. Am J Mod Phys. 2026;15(2):43-54. doi: 10.11648/j.ajmp.20261502.15

Copy | Download

@article{10.11648/j.ajmp.20261502.15,
  author = {Farhod Rahimi},
  title = {Neutron Scattering on Solitons in Anisotropic Magnets: Quantum and Thermal Aspects},
  journal = {American Journal of Modern Physics},
  volume = {15},
  number = {2},
  pages = {43-54},
  doi = {10.11648/j.ajmp.20261502.15},
  url = {https://doi.org/10.11648/j.ajmp.20261502.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20261502.15},
  abstract = {Magnetic solitons in quasi-one-dimensional anisotropic Heisenberg magnets are stable nonlinear excitations that can transport spin, energy, and information over long distances. This paper develops a practical theory for neutron (inelastic) scattering from such solitons and clarifies how quantum and thermal fluctuations control the observable spectrum. Starting from an easy-axis Heisenberg ferromagnet with nearest-neighbor exchange and uniaxial anisotropy, a single soliton is treated as a particle-like mode characterized by conserved quantities that may be interpreted as the number of magnons bound in the soliton and the soliton quasi-momentum. Exploiting the integrability of the model and the possibility of separating kinetic and potential energies in action-angle variables, the soliton contribution to the dynamic structure factor S(q, ω) and to the double-differential scattering cross section is derived. The derivation adapts the Kawasaki-type approach used in earlier soliton scattering studies, but is reformulated here in a simplified and transparent way that yields a general working formula without cumbersome intermediate steps. The resulting response naturally splits into quasi-elastic and inelastic parts. Soliton translation produces a pronounced quasi-elastic intensity and can generate central-peak behavior through the soliton’s response to external perturbations. Thermal averaging leads to explicit conditions under which the quasi-elastic component reduces to a Gaussian form; the analysis also delineates when this approximation fails, in particular for “massive” solitons with large bound-magnon number. At larger energy transfers, scattering into excited soliton states becomes possible, providing access to internal soliton modes and to dissipation mechanisms in real materials. The obtained expressions connect measurable line shapes and spectral weights to soliton width, effective mass, stability, and transport characteristics. Overall, the work provides a concrete basis for interpreting neutron-scattering signatures of solitonic states in quasi-one-dimensional magnets and for designing experiments that isolate their contribution, with relevance to nonlinear magnetic dynamics, spin-transport phenomena, and prospective quantum-technology applications.},
 year = {2026}
}

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TY  - JOUR
T1  - Neutron Scattering on Solitons in Anisotropic Magnets: Quantum and Thermal Aspects
AU  - Farhod Rahimi
Y1  - 2026/04/02
PY  - 2026
N1  - https://doi.org/10.11648/j.ajmp.20261502.15
DO  - 10.11648/j.ajmp.20261502.15
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 43
EP  - 54
PB  - Science Publishing Group
SN  - 2326-8891
UR  - https://doi.org/10.11648/j.ajmp.20261502.15
AB  - Magnetic solitons in quasi-one-dimensional anisotropic Heisenberg magnets are stable nonlinear excitations that can transport spin, energy, and information over long distances. This paper develops a practical theory for neutron (inelastic) scattering from such solitons and clarifies how quantum and thermal fluctuations control the observable spectrum. Starting from an easy-axis Heisenberg ferromagnet with nearest-neighbor exchange and uniaxial anisotropy, a single soliton is treated as a particle-like mode characterized by conserved quantities that may be interpreted as the number of magnons bound in the soliton and the soliton quasi-momentum. Exploiting the integrability of the model and the possibility of separating kinetic and potential energies in action-angle variables, the soliton contribution to the dynamic structure factor S(q, ω) and to the double-differential scattering cross section is derived. The derivation adapts the Kawasaki-type approach used in earlier soliton scattering studies, but is reformulated here in a simplified and transparent way that yields a general working formula without cumbersome intermediate steps. The resulting response naturally splits into quasi-elastic and inelastic parts. Soliton translation produces a pronounced quasi-elastic intensity and can generate central-peak behavior through the soliton’s response to external perturbations. Thermal averaging leads to explicit conditions under which the quasi-elastic component reduces to a Gaussian form; the analysis also delineates when this approximation fails, in particular for “massive” solitons with large bound-magnon number. At larger energy transfers, scattering into excited soliton states becomes possible, providing access to internal soliton modes and to dissipation mechanisms in real materials. The obtained expressions connect measurable line shapes and spectral weights to soliton width, effective mass, stability, and transport characteristics. Overall, the work provides a concrete basis for interpreting neutron-scattering signatures of solitonic states in quasi-one-dimensional magnets and for designing experiments that isolate their contribution, with relevance to nonlinear magnetic dynamics, spin-transport phenomena, and prospective quantum-technology applications.
VL  - 15
IS  - 2
ER  -

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