Dimensional Spin Research Articles

Soliton dynamics in (2+1) dimensional Heisenberg spin chain with Dzyaloshinskii–Moriya interaction in nanowire systems

In this study, we delve into the theoretical framework of the (2+1)-dimensional Kadomtsev–Petviashvili equation coupled with Dzyaloshinskii–Moriya (DM) interaction, elucidated from the Landau-Lifshitz equation, a prominent model in the realm of ferromagnetic dynamics. Employing the binary Bell polynomial technique along with the Hirota bilinear form, we construct one- and two-soliton solutions for the considered physical system. Through the manipulation of parameters present in these solutions, we explore the various nonlinear dynamical phenomena characterizing ferromagnetic nano-wires with DM interaction. Our investigations elucidate that solitons can be effectively manipulated in the nanowire system through judicious selection of system parameters. Moreover, our findings illustrate that soliton profiles exhibit compression, amplification, shifting, and changes in orientation during evolution. These insights hold significant implications for experimentalists aiming to analyze the propagation of solitons in ferromagnetic nanowire systems.

Pioneering the plethora of soliton for the (3+1)-dimensional fractional heisenberg ferromagnetic spin chain equation

Abstract In this scholarly article, we investigate the complex structured (3+1)-dimensional Fractional Heisenberg Ferromagnetic Spin Chain equation (FHFSCE) with conformable fractional derivatives. We develop a diverse glut of soliton solutions using an improved version of the G ′ G -expansion method, namely the r + G ′ G -expansion method. The constraints for the existence of these solutions are painstakingly explained. Our findings are clearly communicated through a number of 3D and 2D graphical representations displaying periodic, multiple periodic, kink, and shock soliton solutions. These soliton solutions are expressed in several mathematical function forms, such as hyperbolic, trigonometric, and rational functions. Our findings support the suggested method’s efficacy as a powerful symbolic algorithm for discovering innovative soliton solutions within nonlinear evolution systems.

Magnetic phase transition and critical behavior in (Pr,Sm)[formula omitted]Fe[formula omitted] compounds: A comprehensive study using macroscopic and local experimental approaches

Achieving a comprehensive understanding of the properties and behaviors of magnetic phase transitions and critical behavior is a key objective of this study. A macroscopic approach utilizing magnetization measurement and a local approach utilizing 57Fe Mössbauer spectrometry were employed. The findings indicate that the critical exponents of Pr2Fe17 and (Pr,Sm)2Fe17 closely approximate those of the 3D-Ising model, as confirmed by the scaling analysis of our critical exponents. Moreover, we observed that isotherms collapse into two distinct and independent universal branches above and below the Curie temperature when utilizing the critical exponents we obtained. Our results indicate that the exponents determined using both conventional methods and Mössbauer spectrometry closely match those of the 3D-Ising model for spins coupled in three dimensions (lattice dimensionality d=3, spin dimensionality n=1) with attractive interactions between spins (J(r)) at the boundary of short-range and long-range decay as J(r)∝r−(3+σ).

Dynamical analysis and the soliton solutions of (2+1)-dimensional Heisenberg ferro-magnetic spin chains model with beta fractional derivative

This paper investigates the soliton solutions and dynamical analysis of (2+1)-dimensional Heisenberg ferro-magnetic spin chains model with beta fractional derivative, which is transformed into the ordinary differential equation. By using the second-order complete discriminant system, the soliton solutions are presented. By utilizing the theory of planar dynamical system, the phase portraits of the dynamical system and its disturbance system are drawn. Moreover, three-dimensional, two-dimensional, and contour plots of soliton solutions for (2+1)-dimensional Heisenberg ferro-magnetic spin chains model with beta fractional derivative have also been plotted.

Analytical solutions and soliton behaviors in the space fractional Heisenberg ferromagnetic spin chain equation

This study investigates soliton solutions to the (2 + 1)-dimensional space fractional Heisenberg ferromagnetic spin chain equation incorporating beta fractional derivatives that explain the nonlinear propagation of spin wave in the ferromagnetic material with magnetic interactions including the both classical and semi-classical frameworks. This model has applications in spintronics, plasma physics, magnet theory, and condensed matter physics. Employing the two-potential extended Kudryashov and (G′/G, 1/G)-expansion methods, we derive some original and generic solutions composed of trigonometric functions, hyperbolic functions, and their rational forms. For particular values of the parameters, these solutions offer V-shaped, bell-shaped, kink, periodic, flat kink, and singular periodic solitons. The physical behavior of these solitons is demonstrated through three-dimensional, contour, and two-dimensional plots. The results are important in the study of phase transitions in ferromagnetic materials, lattice vibrations in condensed matter, and the propagation of shock waves in plasma. This study also demonstrates the potential and reliability of the employed strategies.

A continuous-wave and pulsed X-band electron spin resonance spectrometer operating in ultra-high vacuum for the study of low dimensional spin ensembles.

We report the development of a continuous-wave and pulsed X-band electron spin resonance (ESR) spectrometer for the study of spins on ordered surfaces down to cryogenic temperatures. The spectrometer operates in ultra-high vacuum and utilizes a half-wavelength microstrip line resonator realized using epitaxially grown copper films on single crystal Al2O3 substrates. The one-dimensional microstrip line resonator exhibits a quality factor of more than 200 at room temperature, close to the upper limit determined by radiation losses. The surface characterizations of the copper strip of the resonator by atomic force microscopy, low-energy electron diffraction, and scanning tunneling microscopy show that the surface is atomically clean, flat, and single crystalline. Measuring the ESR spectrum at 15K from a few nm thick molecular film of YPc2, we find a continuous-wave ESR sensitivity of 2.6 × 1011spins/G · Hz1/2, indicating that a signal-to-noise ratio of 3.9G · Hz1/2 is expected from a monolayer of YPc2 molecules. Advanced pulsed ESR experimental capabilities, including dynamical decoupling and electron-nuclear double resonance, are demonstrated using free radicals diluted in a glassy matrix.

Anderson localization and quenched induced dynamics of spin orbit coupled Bose–Einstein condensate in a random potential

We consider the localization and dynamical properties of a one dimensional spin orbit coupled Bose–Einstein condensate trapped by a disordered speckle potential. We numerically solve coupled Gross–Pitaevskii equation to obtain ground sate solutions. The effects of spin–orbit coupling and detuning parameter on localization are investigated. It is found that the increase of spin–orbit coupling delocalizes the condensate while the increase of detuning favors localization. After achieving the numerical ground state solutions, we examine the quench induced dynamics of the condensate by the complete cessation of the spin–orbit coupling. We show that at parameters where the ground state is not localized, the dynamics of the system is chaotic.

Soliton solutions in (2 + 1)-dimensional integrable spin systems: an investigation of the Myrzakulov–Lakshmanan equation-II

Soliton solutions in (2 + 1)-dimensional integrable spin systems: an investigation of the Myrzakulov–Lakshmanan equation-II

Magnetization reversal phenomenon of higher-order lump and mixed interaction structures on periodic background in the (2+1)-dimensional Heisenberg ferromagnet spin equation

This paper mainly researches a useful model that can describe the rapid magnetization reversal process, namely the (2+1)-dimensional Heisenberg ferromagnet spin equation. Based on its Lax pair, we construct the iterative generalized (r,N−r)-fold Darboux transformation (DT), and obtain new position-controllable higher-order lump, periodic wave and rich mixed lump–breather interaction structures on periodic background. In particular, with the increase of N in the iterative generalized (r,N−r)-fold DT, we find that the structure of the lump and periodic wave can flip over with respect to the background. Moreover, we also find a bright lump structure with two peaks and two valleys, which does not flip with the increase of N. We study the magnetization trajectory and magnetization on the Bloch sphere, from which we discover that the magnetization is distributed in an incomplete unit sphere for the flipped case, while the magnetization is distributed in a complete unit sphere for the non-flipped case. These magnetization reversal phenomena are expected to have potential applications in understanding the rapid magnetization reversal process.

Remarks on Effects of Projective Phase on Eigenstate Thermalization Hypothesis

Abstract The existence of p-form symmetry in a (d + 1)-dimensional quantum field is known to always lead to the breakdown of the eigenstate thermalization hypothesis for certain (d − p)-dimensional operators other than symmetry operators under some assumptions. The assumptions include the mixing of symmetry sectors within a given energy shell, which is rather challenging to verify because it requires information on the eigenstates in the middle of the spectrum. We reconsider this assumption from the viewpoint of projective representations to avoid this difficulty. In the case of $\mathbb {Z}_N$ symmetries, we can circumvent the difficulty by considering $\mathbb {Z}_N\times \mathbb {Z}_N$-symmetric theories with nontrivial projective phases, and perturbing the Hamiltonian while preserving one of the $\mathbb {Z}_N$ symmetries of our interest. We also perform numerical analyses for (1 + 1)-dimensional spin chains and the (2 + 1)-dimensional $\mathbb {Z}_2$ lattice gauge theory.

Analytical approaches to the (2+1)-dimensional Heisenberg Ferromagnetic Spin Chain equation and their applications for optical devices

Analytical approaches to the (2+1)-dimensional Heisenberg Ferromagnetic Spin Chain equation and their applications for optical devices

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.

The Dabrowski-Sitarz-Zalecki type theorems for six dimensional manifolds with boundary

In this paper, we define the spectral Einstein functionals of spin manifolds with boundary, and we give a complete proof of the Dabrowski-Sitarz-Zalecki type theorem for six dimensional spin manifolds with boundary.

A Chern-Simons transgression formula for supersymmetric path integrals on spin manifolds

Earlier results show that the N=1/2 supersymmetric path integral Jg on a closed even dimensional Riemannian spin manifold (X,g) can be constructed in a mathematically rigorous way via Chen differential forms and techniques from noncommutative geometry, if one considers Jg as a current on the loop space LX, that is, as a linear form on differential forms on LX. This construction admits a Duistermaat-Heckman localization formula. In this note, fixing a topological spin structure on X, we prove that any smooth family g•=(gt)t∈[0,1] of Riemannian metrics on X canonically induces a Chern-Simons current Cg• which fits into a transgression formula for the supersymmetric path integral. In particular, this result entails that the supersymmetric path integral induces a differential topological invariant on X, which essentially stems from the Aˆ-genus of X.

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

Bipartite entanglement via distance between the states in a one dimensional spin 1/2 dimer copper acetate monohydrate

In this paper, we used a theoretical measure known as distance between the states, , to determine the bipartite entanglement of a one dimensional magnetic dimer system. The calculation was compared with the well-known entanglement measure, concurrence, and found to be the same. was, then, expressed in terms of two thermodynamic quantities, namely, magnetic susceptibility and specific heat. Experimental verification of temperature variation of the bipartite entanglement measure in terms of magnetic susceptibility and specific heat was done on single crystals of copper acetate-an excellent one dimensional dimer system. The results showed the existence of bipartite entanglement till temperatures as high as room temperature! Large sized single crystals of copper acetate were grown by a new evaporation technique and characterised by thermogravimetric analysis, IR and Raman spectroscopy measurements. Density functional theory calculations were done to calculate the delocalisation index which showed much lower values of than other bonds, implying that the probability of direct Cu–Cu exchange in copper acetate is very small. Band structure calculations revealed the presence of flat bands at the Fermi level implying very weak intermolecular interactions in copper acetate.

An Algorithm to Compute the Fundamental Classes of Spin Components of Strata of Differentials

Abstract We construct an algorithm for computing the cycle classes of the spin components of a stratum of differentials in the moduli space of stable curves $\overline {\mathcal {M}}_{g,n}$. In addition, we implement it within the Sage package admcycles. Our main strategy is to reconstruct these cycles by their restrictions to the boundary of $\overline {\mathcal {M}}_{g,n}$ via clutching maps. These restrictions can be computed recursively by smaller dimensional spin classes and determine the original class via a certain system of linear equations. To study the spin parities on the boundary of a stratum of differentials of even type, we make use of the moduli space of multi-scale differentials introduced in [4]. As an application of our algorithm, one can verify a conjecture on spin double ramification cycles stated in [18] in many examples, by using the results computed by our algorithm.

Equivariant Bismut Laplacian and spectral Einstein functional

This paper aims to provide an explicit computation of the equivariant noncommutative residue density of which yield the metric and Einstein tensors on even-dimensional Riemannian manifolds. A considerable contribution of this paper is the development of the spectral Einstein functionals by two vector fields and the equivariant Bismut Laplacian over spinor bundles. We prove the equivariant Dabrowski–Sitarz–Zalecki-type theorems for lower dimensional spin manifolds with (or without) boundary.

Magnetic relaxation in a Co(II) based quasi-one dimensional Ising spin system

Single crystal study of Co(NCS)2(aniline)2 reveals that this compound orders at 6.49 K into a canted AF magnetic structure that explains the presence of a hysteresis loop along the b crystal direction. Effective s=1/2 spins of Co(II) ions within the ground state doublet create an Ising spin system that can be described by J1−J2 triangular model. Temperature dependence of specific heat yields exchange interactions J1=31.3(4) K and 2J2=−2.23(7) K. Applying magnetic field ≃6 kOe perpendicular to b compensates for the AF exchange J2 decoupling ferromagnetic spin chains. This restores the one-dimensionality of the system and allows for observation of magnetic relaxation of single chains, similar to previously studied pyridine-based Co(NCS)2L2 compounds. The analysis of the relaxation time is performed taking into account single-ion relaxation mechanisms together with the Glauber relaxation. We also show, using Monte Carlo calculations of specific heat, that for ferromagnetic J1≫|J2|, the triangular Ising model can be approximated by the rectangular Ising model for which the analytical Onsager’s solution is available.