Ferromagnetic Medium Research Articles

A model to predict the ultrasonic field radiated by magnetostrictive effects induced by EMAT in ferromagnetic parts

An Electro-Magnetic Acoustic Transducer (EMAT) is a non-contact source used in Ultrasonic Testing (UT) which generates three types of dynamic excitations into a ferromagnetic part: Lorentz force, magnetisation force, and magnetostrictive effect. This latter excitation is a strain resulting from a magnetoelastic interaction between the external magnetic field and the mechanical part. Here, a tensor model is developed to transform this effect into an equivalent body force. It assumes weak magnetoelastic coupling and a dynamic magnetic field much smaller than the static one. This approach rigorously formulates the longitudinal Joule’s magnetostriction, and makes it possible to deal with arbitrary material geometries and EMAT configurations. Transduction processes induced by an EMAT in ferromagnetic media are then modelled as equivalent body forces. But many models developed for efficiently predicting ultrasonic field radiation in solids assume source terms given as surface distributions of stress. To use these models, a mathematical method able to accurately transform these body forces into equivalent surface stresses has been developed. By combining these formalisms, the magnetostrictive strain is transformed into equivalent surface stresses, and the ultrasonic field radiated by magnetostrictive effects induced by an EMAT can be both accurately and efficiently predicted. Numerical examples are given for illustration.

Spin transfer torque in the semiconductor/ferromagnetic structure in the presence of Rashba effect

Spin transfer torque in magnetic structure occurs when the transverse component of the spin current that flows from the nonmagnetic medium to ferromagnetic medium is absorbed by the interface. In this paper, considering the Rashba effect on the semiconductor region, we discuss the spin transfer torque in semiconductor/ferromagnetic structure and obtain the components of spin-current density for two models: (i) single electron and (ii) the distribution of electrons. We show that no matter whether the difference in Fermi surface between semiconductor and Fermi spheres for the up and down spins in ferromagnetic increases, the transmission probability decreases. The obtained results for the values used in this article illustrate that Rashba effect increases the difference in Fermi sphere between semiconductor and Fermi sphere for the up and down spins in ferromagnetic. The results also show that the Rashba effect, brings an additional contribution to the components of spin transfer torque, which does not exist in the absence of the Rashba interaction. Moreover, the Rashba term has also different effects on the transverse components of the spin torque transfer.

Soliton switching in a site-dependent ferromagnet

Switching of soliton in a ferromagnetic medium offers the possibility of developing a new innovative approach for information storage technologies. The nonlinear spin dynamics of a site-dependent Heisenberg ferromagnetic spin chain with Gilbert damping under the influence of external magnetic field is expressed in the form of the Landau–Lifshitz–Gilbert equation in the classical continuum limit. The corresponding evolution equation is developed through stereographic projection technique by projecting the unit sphere of spin onto a complex plane. The exact soliton solutions are constructed by solving the associated evolution equation through the modified extended tanh-function method. The impact of damping and external magnetic field on the magnetic soliton under the invariant inhomogeneity is investigated and finally, the magnetization switching in the form of shape changing solitons are demonstrated.

Frequency Characteristics of Reflection and Refraction Coefficients of Bulk Spin Waves in Spin Lens with Non-Ideal Interphaces

Background . This work is devoted to the application of geometrical optics formalism to describe the behavior of spin waves, which is propagating in a ferromagnetic medium with non-uniform distribution of magnetic parameters. Use of this approach allows to describe the process of refraction of spin waves to determine the focal length of spin lenses or mirrors and to operate it by changing the frequency of the spin wave with a given magnetic parameters of a medium. Objective. The objective is to calculate the index of refraction, reflection coefficient and focal length of spin lens as function of frequency of spin waves, the external magnetic field and magnetic parameters of the medium. Methods. In this paper, to find the refractive index and the focal length was used the geometrical optics approach. To describe the dynamics of the magnetization vector the formalism was used of the parameter of order of spin density that also gives an opportunity to use the methods of quantum mechanics to calculate the spin wave reflection coefficient. Results. In the paper the refractive index and focal length of a bulk spin lens have been found. By considering the generalized boundary conditions the expression has been found for the reflection coefficient of spin lens. In addition, results of investigation says that strong dependence exists of transparency of spin lens on the frequency of spin waves that is characterized by corresponding magnetic parameters of structure. Conclusions. It is shown the possibility to change “optical” spin lens parameters in a wide range of values by changing only the frequency of spin waves and keeping constant the values of the external magnetic field and magnetic structure parameters. In addition, the results of studies prove that exists a strong dependence of the spin lens transparency on the quality of its borders, which is characterized by appropriate parameters of interface.

A Modal Approach for the Solution of the Non-Linear Induction Problem in Ferromagnetic Media

The non-linear induction problem in ferromagnetic media is solved using the fixed-point iteration method, where the linearized problem at each iteration is treated by means of a modal approach. The proposed approach does not require meshing of the solution domain, which results in fast computations comparing to conventional mesh-based numerical techniques. Both harmonic and pulse excitations are considered via Fourier and Laplace transform, respectively. An efficient method for the fast computation of the inverse Laplace transform of the magnetic polarization signals is also devised based on the generalized pencil-of-function (GPOF) method. Although being restricted to one dimensional configurations, the present work provide the tools for the treatment of two and three dimensional problems, whose study is under way.

Analysis of Magnetization Properties of the Ferromagnetic Granular Beds

Magnetization properties of the packed beds that are constructed from ferromagnetic balls and metal chips have been examined. The average magnetic permeability and magnetization curves of the non-homogeneous ferromagnetic granulated medium (different size polyballs and chips) have been determined using the channel-by-channel magnetization model. From the magnetic properties of the single chain of the different sized balls as an element of the chain bundle in the polyball medium, application conditions of the model to the polyball medium were estimated. A new correlation for the influence of the packing density factor or the bed porosity change on the average magnetization curve has been evaluated. A new correlation between the packing density factor and the size of the bed elements, and also a relationship between the relative magnetic permeability of the bed elements and the external magnetic field intensity were obtained. The obtained theoretical results were compared with statistical data and an agreement was observed.

A multi-state magnetic memory dependent on the permeability of Metglas

A three-state magnetic memory was developed based on differences in the magnetic permeability of a soft ferromagnetic media, Metglas 2826MB (Fe40Ni38Mo4B18). By heating bits of a 250 nm thick Metglas film with 70–100 mW of laser power, we were able to tune the local microstructure, and hence, the permeability. Ternary memory states were created by using lower laser power to enhance the initial permeability through localized atomic rearrangement and higher power to reduce the permeability through crystallization. The permeability of the bits was read by detecting variations in an external 32 Oe probe field within 10 μm of the media via a magnetic tunnel junction read head. Compared to data based on remanent magnetization, these multi-permeability bits have enhanced insensitivity to unexpected field and temperature changes. We found that data was not corrupted after exposure to fields of 1 T or temperatures of 423 K, indicating the effectiveness of this multi-state approach for safely storing large amounts of data.

Performance Analysis of Ball End Magnetorheological Finishing Process with MR Polishing Fluid

A ball end magnetorheological finishing (BEMRF) process was developed for finishing a flat as well as 3D workpiece surfaces. The BEMRF process has a wide scope in today's advanced manufacturing systems for finishing 3D complex surfaces. Magnetorheological (MR) polishing fluid is used as finishing medium in BEMRF process. The constituent of MR polishing (MRP) fluid includes ferromagnetic carbonyl iron powder, abrasives, and base fluid medium. The workpiece surface is mainly finished by abrasives contained in MRP fluid. Therefore, the different mesh size from 400 to 1200 and volume percent concentration from 5% to 25% of abrasives in MRP fluid were chosen as factors to study their effects on the developed process performance in terms of percent change in roughness values. Silicon carbide abrasives were chosen in the present experimental investigation. Experiments were performed on the ferromagnetic ground surfaces whose initial roughness values (Ra) were measured in the range of 0.428 to 0.767 µm. The experimental results revealed that the MRP fluid with 15 vol % abrasives of mesh number 400 demonstrated better improvements in surface texture of finished surface as compared to other MRP fluid compositions. The finished surface characteristics and textures were studied at microscopic level using scanning electron microscopy and atomic force microscopy.

Spin wave isolator based on frequency displacement nonreciprocity in ferromagnetic bilayer

We demonstrated the spin wave isolator using bilayer ferromagnetic media comprising single crystalline and poly-crystalline yttrium iron garnet films, which can control the propagation frequency of magnetostatic waves by the direction of applied magnetic field. This isolator's property does not depend on their thickness then this can be downsized and integrated for nano-scale magnonic circuits. Calculated dispersion relationship shows good agreement with measured one.

Third-order effect in magnetic small-angle neutron scattering by a spatially inhomogeneous medium

Magnetic small-angle neutron scattering (SANS) is a powerful tool for investigating nonuniform magnetization structures inside magnetic materials. Here, we consider a ferromagnetic medium with weakly inhomogeneous uniaxial magnetic anisotropy, saturation magnetization, and exchange stiffness, and derive, to second order in the amplitudes of the inhomogeneities, the micromagnetic solutions for the equilibrium magnetization textures. Further, we compute the corresponding magnetic SANS cross section up to the third order. For the special case of scattering geometry where the incident neutron beam is perpendicular to the applied magnetic field, twice the cross section along the direction orthogonal to both the field and the neutron beam cancels the cross section along the field direction in the second order. This cancellation does not depend on the defect shape and amplitudes of the exchange inhomogeneities. Hence, such a cross-section difference has only a third-order contribution in the amplitudes of the inhomogeneities. It provides a separate gateway for a deeper analysis of the sample's magnetic structure. We derive and analyze analytical expressions for the dependence of this difference on the scattering-vector magnitude for the case of spherical Gaussian inhomogeneities.

Ferromagnetic/superconducting interface in a hybrid nanoscopic disc

The oscillations exhibited by the magnetization of superconducting nano and mesoscopics structures as a function of the applied magnetic field has attracted attention in the last few years. Nano/Mesoscopic hybrid systems in contact with ferromagnets exhibit interesting transport properties related to the influence of the exchange field on the density of states of clean ferromagnetic structures in contact with superconductor. In this work we study the vortex configurations in a superconducting disk with one central defect inside. The sample is surrounded by a ferromagnetic medium. We calculate the spatial distribution of the Cooper pairs and the phase of the superconducting order parameter and curves of magnetization and vorticity as a function of the magnetic applied field. We found that the first vortex penetration field decrease when a ferromagnetic/superconducting interface is used.

Variable Separation and Exact Solutions for the Kadomtsev-Petviashvili Equation

In the paper, we will discuss the Kadomtsev-Petviashvili Equation which is used to model shallow-water waves with weakly non-linear restoring forces and is also used to model waves in ferromagnetic media by employing the method of variable separation. Abundant exact solutions including global smooth solutions and local blow up solutions are obtained. These solutions would contribute to studying the behavior and blow up properties of the solution of the Kadomtsev-Petviashvili Equation.

Optimizing quantum state transfer in multi-excitation spin chains via information flux

The transfer of quantum states between distant nodes is one of the most fundamental tasks in quantum-information processing. Recent studies show that the antiferromagnetic spin chain initially prepared in a multi-excitation state can provide suitable pathways for quantum state transfer. In this paper, we investigate the quality of state transfer through a uniformly coupled antiferromagnetic spin chain where the initial state of the channel varies with the number of spin excitations. Firstly, by analyzing the dynamics of observables for the output qubit using the information-flux approach, the explicit relation about how the average fidelity of state transfer depends on the initial state of the spin channel is obtained. The results show that the average fidelity of state transfer through a multi-excitation spin channel only relates to the parity of the number of spin excitations in the channel. Then we compare the maximum average fidelity of state transfer through the odd-excitation with those through the even-excitation spin channels, and provide a simple criterion to optimize the quality of state transfer by choosing appropriate channels from the odd-excitation and the even-excitation channels. Compared with the previous studies which initialize the chains into the ground state of the ferromagnetic medium or the Nel state, the maximum average fidelity of state transfer is evidently enhanced by using the optimized channel. Moreover, we analyze the entanglement distribution through the channel having different number of spin excitations via the information-flux approach. It is found that the quality of entanglement distribution not only relates to the number of initial spin excitations present in the channel, but also depends on the initial ordering of these excited spins. The numerical results suggest that the amount of distributed entanglement and duration of distribution in the channel where all spins are down or up are larger than those in other excited channels. Based on these results, we can choose appropriate quantum channels for state transfer and entanglement distribution in practice.

The Regular Pattern of Demagnetizing Factor Behaviour of Various ‘Cores’ of Granule-Ball Chains

We analyze previously not studied issue on the value, nature and manifestation f a demagnetizing factor of effective channels-magnets formed in magnetized granular media by the chains of contacting granules. We provide the factor values for conditionally defined quasi-solid cores of the channels varying in length and diameter, as well as a corresponding consolidating expression which turned out to be exponential with such an argument as the radical of the core relative size. We emphasize full agreement of this expression with the one for a granular medium, i.e. the medium consisting, basically, of the effective channels bundle according to the developed theory of channel-by-channel (selective) magnetization of granular ferro-magnetic media used, e.g. as operating elements in versatile magnetic separators.

A Mean-Field Model for Spin Dynamics in Multilayered Ferromagnetic Media

In this paper, we develop a mean-field model for describing the dynamics of spin-transfer torque in multilayered ferromagnetic media. Specifically, we use the techniques of Wigner transform and moment closure to connect the underlying physics at different scales and reach a macroscopic model for the dynamics of spin coupled with the magnetization within the material. This provides a further understanding of the linear response model proposed by Zhang, Levy, and Fert [Phys. Rev. Lett., 88 (2002), 236601], and in particular we get an extra relaxation term which helps to stabilize the system. We develop efficient numerical methods to overcome the stiffness appearing in this new mean-field model and present several examples to analyze and show its validity.

Phonon-magnon resonant processes with relevance to acoustic spin pumping

The recently described phenomenon of resonant acoustic spin pumping is due to resonant coupling between an incident elastic wave and spin waves in a ferromagnetic medium. A classical one-dimensional discrete model of a ferromagnet with two forms of magnetoelastic coupling is treated to shed light on the conditions for resonance between phonons and magnons. Nonlinear phonon-magnon interactions in the case of a coupling restricted to diagonal terms in the components of the spin degrees of freedom are analyzed within the framework of the multiple timescale perturbation theory. In that case, one-phonon-two-magnon resonances are the dominant mechanism for pumping. The effect of coupling on the dispersion relations depends on the square of the amplitude of the phonon and magnon excitations. A straightforward analysis of a linear phonon-magnon interaction in the case of a magnetoelastic coupling restricted to off-diagonal terms in the components of the spins shows a one-phonon to one-magnon resonance as the pumping mechanism. The resonant dispersion relations are independent of the amplitude of the waves. In both cases, when an elastic wave with a fixed frequency is used to stimulate magnons, application of an external magnetic field can be used to approach resonant conditions. Both resonance conditions exhibit the same type of dependency on the strength of an applied magnetic field.

Magnetothermodynamics of BPS baby skyrmions

The magnetothermodynamics of skyrmion type matter described by the gauged BPS baby Skyrme model at zero temperature is investigated. We prove that the BPS property of the model is preserved also for boundary conditions corresponding to an asymptotically constant magnetic field. The BPS bound and the corresponding BPS equations saturating the bound are found. Further, we show that one may introduce pressure in the gauged model by a redefinition of the superpotential. Interestingly, this is related to non-extremal type solutions in the so-called fake supersymmetry method. Finally, we compute the equation of state of magnetized BSP baby skyrmions inserted into an external constant magnetic field H and under external pressure P , i.e., V = V (P, H), where V is the “volume” (area) occupied by the skyrmions. We show that the BPS baby skyrmions form a ferromagnetic medium.

Leapfrogging vortex rings in the Landau–Lifshitz equation

Vortex rings are ubiquitous in fluids, with smoke rings being a familiar example. The interaction of multiple vortex rings produces complex dynamical behaviour, such as the leapfrogging motion first analysed by Helmholtz more than a century and a half ago. Here we report on numerical investigations of vortex ring dynamics in a different setting from fluids, namely, as solutions of the Landau–Lifshitz equation that models the evolution of the local magnetization in a ferromagnetic medium. We present the results of the first study on the dynamics of interacting magnetic vortex rings and provide a novel link between fluids and magnetism, by showing that a range of phenomena familiar in fluids are reproduced in ferromagnets. This includes the leapfrogging motion of a pair of vortex rings and evidence for the chaotic dynamics of a trio of rings.

Magnetization reversal in a site-dependent anisotropic Heisenberg ferromagnet under electromagnetic wave propagation

Information density and switching of magnetization offers an interesting physical phenomenon which invoke magneto-optical techniques employed on the magnetic medium. In this paper, we explore the soliton assisted magnetization reversal in the nanosecond regime in the theoretical framework of the Landau–Lifshitz–Maxwell (LLM) model. Starting from the Landau–Lifshitz equation, we employ the reductive perturbation method to derive an inhomogeneous nonlinear Schrödinger equation, governing the nonlinear spin excitations of a site-dependent anisotropic ferromagnetic medium under the influence of electromagnetic (EM) field in the classical continuum limit. From the results, it is found that the soliton undergoes a flipping thereby indicating the occurrence of magnetization reversal behavior in the nanoscale regime due to the presence of inhomogeneity in the form of a linear function. Besides, the spin components of magnetization are also evolved as soliton spin excitations.

Spontaneous symmetry breaking in dual-core baby-Skyrmion systems

We introduce a system composed of two (2+1)-dimensional baby-skyrmion models (BSMs) set on parallel planes and linearly coupled by tunneling of fields. This system can be realized in a dual-layer ferromagnetic medium. Unlike dual-core models previously studied\ in nonlinear optics and BEC, here the symmetry-breaking bifurcation (SBB) in solitons (baby skyrmions) occurs with the increase of the inter-core coupling ($\kappa$), rather than with its decrease, due to the fact that even in the uncoupled system neither core may be empty. Prior to the onset of the symmetry breaking between the two components of the solitons, they gradually separate in the lateral direction, due to the increase of $\kappa$, which is explained in an analytical form by means of an effective interaction potential. Such evolution scenario are produced for the originally symmetric states with topological charges in the two cores $\left(B^{(1)},B^{(2)}\right)$, with $% B^{(1)}=B^{(2)}=1,2,3,4$. The evolution of mixed states, of the $\left(1,2\right)$ and $\left(2,4\right)$ types, with the variation of $\kappa$ is studied too.