Ferromagnetic Medium Research Articles

Magnetic Susceptibility Tensor of Anisotropic Ferromagnetic Magnetized Media

Using a method analogous to the Smit–Suhl method, we have calculated the magnetic susceptibility tensor of ferromagnetic media with allowance for the magnetocrystalline anisotropy and the anisotropy of the magnetomechanical ratio. An analysis has been carried out of the obtained formulas in the particular cases of an isotropic medium with anisotropic magnetomechanical ratio, crystals with uniaxial magnetocrystalline anisotropy, and composite materials with randomly distributed ferromagnetic inclusions of ellipsoidal shape.

Reflection of Surface Spin Waves from the Interface of Uniaxial and Biaxial Ferromagnets in a Planar Magnetic Field

The article investigates the process of reflection of surface spin waves passing through the interface of uniaxial and biaxial ferromagnets in a planar external magnetic field directed along the hard axis of ferromagnet. The problem is solved using the spin density formalism and the Landau-Lifshitz equations for the case of the absence of dissipation in the system. Geometrical optics formalism is used to describe the processes of refraction of surface spin waves propagating in the ferromagnetic medium with non uniform distribution of magnetic parameters. Quantum mechanical approach is used for calculation of the amplitudes of reflected and transmitted waves. It is shown that spin wave birefringence phenomenon appears at the interface of two uniform ferromagnetic components. Frequency and field dependencies of reflection coefficients for different branches of spin waves are obtained in the study. It is shown that it is possible to change the “optical” parameters of the system by only changing a magnitude of the external homogeneous magnetic field. It is also shown that reflection amplitude depends heavily on the angle of incidence.

Reflection of Surface Spin Waves from the Interface of Uniaxial and Biaxial Ferromagnets in a Planar Magnetic Field

The article investigates the process of reflection of surface spin waves passing through the interface of uniaxial and biaxial ferromagnets in a planar external magnetic field directed along the hard axis of ferromagnet. The problem is solved using the spin density formalism and the Landau-Lifshitz equations for the case of the absence of dissipation in the system. Geometrical optics formalism is used to describe the processes of refraction of surface spin waves propagating in the ferromagnetic medium with non uniform distribution of magnetic parameters. Quantum mechanical approach is used for calculation of the amplitudes of reflected and transmitted waves. It is shown that spin wave birefringence phenomenon appears at the interface of two uniform ferromagnetic components. Frequency and field dependencies of reflection coefficients for different branches of spin waves are obtained in the study. It is shown that it is possible to change the “optical” parameters of the system by only changing a magnitude of the external homogeneous magnetic field. It is also shown that reflection amplitude depends heavily on the angle of incidence.

FEM Technique for Modeling Eddy-Current Testing of Ferromagnetic Media With Small Skin Depth

The modeling of eddy-current testing problems, by means of finite elements, requires us to carefully consider the skin effect. When the material to inspect has a small skin depth compared with the other dimensions of the problem, which is a typical situation in the case of ferromagnetic media, the classical FEMs can become unsuitable in terms of mesh quality or computation time. In this paper, the overlapping FEM is implemented to efficiently consider the skin effect. 3-D problems are studied and the validity of the proposed approach is shown.

Effect of Varying Dzyaloshinskii—Moriya Interaction on the Bistable Nano-Scale Soliton Switching

The effect of Dzyaloshinskii—Moriya (D-M) interaction on the bistable nano-scale soliton switching offers the possiblity of developing a new innovative approach for data storage technology. The dynamics of Heisenberg ferromagnetic spin system is expressed in terms of generalized inhomogeneous higher order nonlinear Schrödinger (NLS) equation. The bistable soliton switching in the ferromagnetic medium is established by solving the associated coupled evolution equations for amplitude and velocity of the soliton using the fourth order Runge—Kutta method numerically.

Actuation, propagation, and detection of transverse magnetoelastic waves in ferromagnets

We study propagation of ultrasonic waves through a ferromagnetic medium with special attention to the boundary conditions at the interface with an ultrasonic actuator. In analogy to charge and spin transport in conductors, we formulate the energy transport through the system as a scattering problem. We find that the magneto-elastic coupling leads to a non-vanishing magnetic (elastic) energy accompanying the acoustic (spin) waves with a resonantly enhanced effect around the anti-crossing in the dispersion relations. We demonstrate the physics of excitating magnetization dynamics via acoustic waves injected around the ferromagnetic resonance frequency.

The propagation of shape changing soliton in a nonuniform nonlocal media

Magnetization dynamics in uniformly magnetized ferromagnetic media is studied by using Landau—Lifshitz—Gilbert equation. The nonlinear evolution equation is integrable with site-dependent and biquadratic exchange interaction by means of Landau—Lifshitz (LL) equation which is well understood. In the present work, we construct the exact solitary solutions of the nonlinear evolution equation, particularly, we employ the modified extended tangent hyperbolic function method. We show the shape changing property of solitons for the given integrable system in the presence of damping as well as inhomogeneities.

Effective quantities and effective rules in two-dimensional ferromagnetic antidot lattices

In this paper the metamaterial properties of two-dimensional arrays of circular antidots (holes) embedded into a ferromagnetic medium of Permalloy are studied according to both micromagnetic and analytical calculations. The periodicity of the arrays and the diameters of the antidots are in the nanometric range. The collective mode dynamics is described by means of effective physical quantities for the scattering geometry with the external magnetic field applied perpendicularly to the Bloch wave vector in the antidot plane. As an example, the definition of an effective field, incorporating the demagnetizing effects due to the holes, permits to describe the dynamical properties of collective modes in terms of effective properties in the travelling regime. An effective wavelength and a small wave vector are introduced both for extended and localized magnonic modes. By means of these effective quantities it is shown that holes play the role of point defects affecting the spin dynamics in the microwave range. Relations between the effective wavelength and the Bloch wavelength and between the corresponding small wave vector and the Bloch wave vector are found. Some effective rules on the dynamic magnetization, based upon the effective wavelength and the corresponding small wave vector, are derived. An application that exploits the definition of the small wave vector is proposed and an experiment based upon the notion of effective wavelength and small wave vector is suggested.

Magnetization Reversal through a Soliton in a Site-Dependent Weak Ferromagnet

Magnetization reversal or switching is the process by which the magnetization of a specimen is changed from one stable direction into another. Switching the magnetization of a magnetic bit through the flipping of a soliton offers the possibility of developing a new innovative approach for data storage technologies. The spin dynamics of a site-dependent ferromagnet with the antisymmetric Dzyaloshinskii-Moriya interaction is governed by a generalized inhomogeneous higher order nonlinear Schrodinger equation. We demonstrate the magnetization reversal through the flipping of a soliton in the ferromagnetic medium by solving numerically the two coupled evolution equations for the velocity and amplitude of the soliton using the fourth order Runge-Kutta method. We propose a new approach for inducing the flipping behaviour of a soliton in the presence of an inhomogeneity by tuning the parameter associated with the Dzyaloshinskii-Moriya interaction, which causes the soliton to move with constant velocity and amplitude along the spin lattice.

Linear stability of triple-diffusive convection in micropolar ferromagnetic fluid saturating porous medium

The triple-diffusive convection in a micropolar ferromagnetic fluid layer heated and soluted from below is considered in the presence of a transverse uniform magnetic field. An exact solution is obtained for a flat fluid layer contained between two free boundaries. A linear stability analysis and a normal mode analysis method are carried out to study the onset convection. For stationary convection, various parameters such as the medium permeability, the solute gradients, the non-buoyancy magnetization, and the micropolar parameters (i.e., the coupling parameter, the spin diffusion parameter, and the micropolar heat conduction parameter) are analyzed. The critical magnetic thermal Rayleigh number for the onset of instability is determined numerically for a sufficiently large value of the buoyancy magnetization parameter M1. The principle of exchange of stabilities is found to be true for the micropolar fluid heated from below in the absence of the micropolar viscous effect, the microinertia, and the solute gradients. The micropolar viscous effect, the microinertia, and the solute gradient introduce oscillatory modes, which are non-existent in their absence. Sufficient conditions for the non-existence of overstability are also obtained.

Gravitational Instability in a Ferromagnetic Fluid Saturated Porous Medium with Non-Classical Heat Conduction

The problem of Rayleigh-Benard convection in a ferromagnetic fluid saturated porous medium with the Maxwell-Cattaneo law is studied by the method of small perturbation. Modified Darcy-Brinkman model is used to describe the fluid motion. The horizontal porous layer is cooled from the upper boundary, while an isothermal boundary condition is imposed at the lower boundary. The non-classical Maxwell-Cattaneo heat flux law involves a wave type heat transport and does not suffer from the physically unacceptable drawback of infinite heat propagation speed. The resulting eigenvalue problem is solved exactly for simplified boundary conditions and the thresholds for the marginal stability are determined. Some of the known cases are derived as special cases. The influence of porous, magnetic, and non-magnetic parameters on the onset of ferroconvection has been analyzed. It is found that the Benard problem for a Maxwell-Cattaneo ferromagnetic fluid is always less stable than the classical ferroconvection problem. It is shown that the destabilizing influence of the Cattaneo number is not attenuated by that of magnetic forces and vice versa, and that the aspect ratio of the convection cells changes when the parameters involved in the study vary with the porous structure bringing out considerable influence.

Metamaterial properties of ferromagnetic antidot lattices

In this paper the metamaterial properties of two-dimensional arrays of circular antidots (holes) embedded into a ferromagnetic medium of Permalloy are studied according to both micromagnetic and analytical calculations. The periodicity of the arrays and the diameters of the antidots are in the nanometric range. The collective mode dynamics is described by means of effective physical quantities for the scattering geometry with the external magnetic field applied perpendicularly to the Bloch wave vector in the antidot plane. As an example, the definition of an effective field, incorporating the demagnetizing effects due to the holes, permits to describe the dynamical properties of collective modes in terms of effective properties in the travelling regime. An effective wavelength and a small wave vector are introduced both for extended and localized magnonic modes. By means of these effective quantities it is shown that holes play the role of point defects affecting the spin dynamics in the microwave range. Relations between the effective wavelength and the Bloch wavelength and between the corresponding small wave vector and the Bloch wave vector are found. Some effective rules on the dynamic magnetization, based upon the effective wavelength and the corresponding small wave vector, are derived. An application that exploits the definition of the small wave vector is proposed and an experiment based upon the notion of effective wavelength and small wave vector is suggested.

On the Magnetogravitational Instability of a Ferromagnetic Dust Cloud in the Presence of Nonuniform Rotation

The effect of a nonuniform magnetic field on the gravitational instability of a nonuniformly rotating infinitely extending axisymmetric cylinder in a homogenous ferromagnetic medium has been studied. The propagation of the wave is allowed along radial direction. A general dispersion relation, using the normal mode analysis method on the perturbation equations of the problem, is obtained. It is found that Bel and Schatzman criterion determines the gravitational instability of this general problem. Thus, it appears that the effect of non-uniform magnetic field on the gravitational instability as discussed by (Dhiman and Dadwal, 2010) is marginalized by the magnetic polarizability of ferrofluid.

Dynamic Analysis of Magnetoelasticity for Ferromagnetic Plates with Nonlinear Magnetization in Magnetic Fields

Based on a generalized variational principle of magnetoelasticity and Hamilton’s principle, a dynamic theoretical model is developed for magnetoelastic vibration of a soft ferromagnetic plate with nonlinear magnetization being in a stationary magnetic field. The fundamental equations of the magnetic field and the motion of the ferromagnetic plate are derived together with the expression of equivalent magnetic force acting on the ferromagnetic plate as a result of the reciprocity between the magnetizable ferromagnetic plate and the applied field. There involve twofold nonlinearities in which one is from the magnetoelastic coupling and the other arises from the nonlinear magnetization of the ferromagnetic medium. A numerical technique that combines the finite-element method for magnetic-field distribution with the finite-difference and Newmark methods for vibration of the ferromagnetic plate is proposed. Analyses of the dynamic behaviors and stability characteristics of a ferromagnetic cantilevered beam-plate vibrating in an applied stationary magnetic field are implemented numerically, which show that the frequency of magnetoelastic vibration of the ferromagnetic beam-plate increases with the intensity and the incident angle of the applied magnetic field, and that the magnetization nonlinearity obviously influences the magnetoelastic dynamics behavior. Especially for strong magnetic fields and certain geometrical parameters of the ferromagnetic plate, the magnetoelastic dynamic behavior of the ferromagnetic plate, taking into account nonlinear magnetization, exhibits distinctive magnetoelastic characteristics compared with that of the ferromagnetic plate with linear magnetization.

Hysteresis for ferromagnetism: asymptotics of some two-scale Landau–Lifshitz model

We study a two-scale version of the Landau–Lifshitz system of ferromagnetism, introduced by Starynkevitch to modelize hysteresis: the response of the magnetization is fast compared to a slowly varying applied magnetic field. Taking the exchange term into account, in space dimension 3, we prove that, under some natural stability assumption on the equilibria of the system, the strong solutions follow the dynamics of these equilibria. We also give explicit examples of relevant equilibria and exterior magnetic fields, when the ferromagnetic medium occupies some ellipsoidal domain.

Solitonic transport of energy–momentum in a deformed magnetic medium

The energy–momentum transport phenomenon between interacting spins in a deformed ferromagnetic medium is investigated theoretically. The spin dynamics of a one-dimensional (1D) classical continuum Heisenberg ferromagnetic spin system in the presence of varying exchange interactions is considered. The state of the 1D continuum spin system with varying exchange interactions is mapped onto a moving helical space curve in E3. The results are recast in conjunction with the evolution of energy and current densities of the deformed ferromagnetic medium, through a knowledge of the underlying geometry of this system. A set of soliton solutions for energy and current densities is constructed by employing the sine–cosine method coupled with symbolic computation. The evolution and propagation of solitonic energy–momentum transport under the influence of competing linear and nonlinear inhomogeneities have been analyzed briefly.

Influence of external magnetic field on the parameters of a surfaced two-focus spin-wave ferromagnetic lens

Presented are the results of a study of the influence of external magnetic field on the refraction of a surface spin wave propagating through an inhomogeneity in the form of a lens that is a biaxial ferromagnet placed into a uniaxial ferromagnetic medium.

Numerical Analysis of 3D Eddy Current Fields in Laminated Media Under Various Frequencies

A homogenization method for analyzing eddy current fields and resultant loss in laminated ferromagnetic media is presented, where the equivalent conductivity tensor proposed in a previous paper is applied. In order to compute fields at various frequencies, the formulas for the effective skin depths along different directions in the anisotropic solid core are derived, which are accompanied with a new scheme for finite element mesh generation. The proposed method is numerically investigated in a small iron core model over a very wide frequency range. The calculation results are compared with those from the direct method involving the actual description of the laminations and those from the traditional homogenization method. It is shown that the proposed method yields basically the same results as the direct method with much lower computational cost both in linear and nonlinear cases, whereas in some cases the traditional method results in large errors even at low frequencies.

Retarded Modes of Lateral Ferromagnetic/Ferromagnetic Superlattice

In this paper，we calculated the retarded modes of semi-infinite lateral ferromagnetic/ ferromagnetic superlattice with the effective medium theory. Take the Co/Ni system surface modes and bulk modes for the superlattice as the example and found some interesting properties which different from the lateral ferromagnetic/nonmagnetic superlattice. Lateral magnetism/magnetism superlattice have some complex retarded modes which are very common systems，changing the ratio of the superlattice ferromagnetism layer thickness so that two branches of surface modes frequency and bulk modes frequency band can be adjusted consequently. This tailoring effect is related to the two ferromagnetism layers saturation magnetization values. But the two saturation magnetization values are quite different than each other. If the difference between the tow values is large, the tailoring effect of f1 is more obvious. When the saturation magnetization value of the second ferromagnetic medium is approach to zero, this system will become magnetism/non-magnetism superlattice. If in Maxwell equation ε=0, the retarded modes will transite to ferromagnetic/ferromagnetic superlattice magnetostatic modes.

Wet Pre-Concentration of Low-Grade Hematite in High-Pressure Grinding Roller

The wet pre-concentration of comminuted hematite in high-pressure grinding roller was studied, using the cylindrical ferromagnetic medium in a high gradient magnetic separator. The effects of various factors including rod diameter, rod gap and background magnetic field intensity (BMFI) on the performances of pre-concentration in different size feeds are emphatically investigated. The results showed that as the rod diameter increased, the rod gap decreased and the BMFI increased, the tailings grade and the tailings yield reduced, but the concentrates recovery raised. This variation was regardless of the feed size distribution. After the classifying pre-concentration, the overall concentrate grade increases by 9.56 percentage points and the concentrate recovery is up to the 82.67% with a tailing grade of 10.68% and a tailing yield of 40.31%. Compared with the classifying pre-concentration, the full size pre-concentration produced a concentrate with a lower grade only increased by 6.61 percentage points and the higher recovery of 92.32%. The tailings, with a lower yield of only 26.62% and a lower grade of 7.39%, was mainly produced from the fine feed. The coarse feed in the full size pre-concentration was not separated effectively.