Phase diagrams for the precession states of the nanoparticle magnetization in a rotating magnetic field

Using the analytical and numerical solutions of the Landau–Lifshitz equation, we calculate the phase diagrams for the precession states of the nanoparticle magnetization in a rotating magnetic field. We show that there are three different scenarios for the magnetization switching. The bias magnetic field applied antiparallel to the nanoparticle magnetization strongly decreases the switching amplitudes and frequencies of the rotating field.     

Electron Paramagnetic Resonance and the Modified Landau–Lifshitz Equation in Strongly Correlated Electronic Systems with Quantum Fluctuations of the Magnetic Moment

Doklady Physics - The Landau–Lifshitz equation modified by quantum fluctuations of the magnetic moment is proposed, on the basis of which several new effects in electron paramagnetic...     

Localized states and non-variational Ising–Bloch transition of a parametrically driven easy-plane ferromagnetic wire

A time-periodic magnetic field applied transversally to the hard axis of an extended easy-plane ferromagnetic sample can produce parametric resonance. For the 2:1 resonance, the prototype order-parameter-equation derived from the Landau–Lifshitz–Gilbert dynamical model for the precessional motion is the parametrically driven damped nonlinear Schrödinger equation. Unfortunately this standard approximation fails to meet the stability feature of the synchronized precession states, and we propose some amendment. Localized solutions supported by the uniform states are characterized and classified into two types: motionless and propagative states, rising through a non-variational Ising–Bloch transition. We propose and investigate a dynamical model ruling this transition.     

A multi-scale model of domain wall velocities based on ab initio parameters

A new approach is presented to evaluate the velocity of field-driven domain walls by means of ab initio parameters. This approach makes intensive use of multi-scaling by means of (a) mapping of domain wall formation energies obtained in terms of a fully relativistic method onto a Landau–Ginzburg-type expression, and (b) applying the Landau–Lifshitz–Gilbert equation to evaluate the time needed to move domain walls. In comparison with the “classical” expression for the domain wall velocity originally proposed by Landau and Lifshitz, according to which the velocity increases with increasing width of the domain wall, three different types of magnetic alloys, namely permalloy (Ni₈₅Fe₁₅), Co _x Ni_1?x and Co _x Pd_1?x , are analyzed. It is shown that the Landau–Lifshitz expression for the velocity seems to be valid whenever the slopes of the exchange and the anisotropy energy with respect to the concentration are either both increasing or both decreasing.     

Domain wall motion in nanowires

We investigated the motion of domain walls in ferromagnetic cylindrical nanowires by solving the Landau–Lifshitz–Gilbert equation numerically for a classical spin model in which energy contributions from exchange, crystalline anisotropy, dipole–dipole interactions, and a driving magnetic field are considered. Depending on the diameter, either transverse domain walls or vortex walls are found. A transverse domain wall is observed for diameters smaller than the exchange length of the given system. In this case, the system effectively behaves one dimensionally and the domain wall velocity agrees with the result of Slonczewski for one-dimensional walls. For larger diameters, a crossover to a vortex wall sets in which enhances the domain wall velocity drastically. For a vortex wall the domain wall velocity is described by the Walker formula.     

Engineering solitons and breathers in a deformed ferromagnet: Effect of localised inhomogeneities

We investigate the soliton dynamics of the electromagnetic wave propagating in an inhomogeneous or deformed ferromagnet. The dynamics of magnetization and the propagation of electromagnetic waves are governed by the Landau–Lifshitz–Maxwell (LLM) equation, a certain coupling between the Landau–Lifshitz and Maxwell's equations. In the framework of multiscale analysis, we obtain the perturbed integral modified KdV (PIMKdV) equation. Since the dynamic is governed by the nonlinear integro-differential equation, we rely on numerical simulations to study the interaction of its mKdV solitons with various types of inhomogeneities. Apart from simple one soliton experiments with periodic or localised inhomogeneities, the numerical simulations revealed an interesting dynamical scenario where the collision of two solitons on a localised inhomogeneity create a bound state which then produces either two separated solitons or a mKdV breather.     

Nonequilibrium dynamics of scalar fields in a thermal bath

We study the approach to equilibrium for a scalar field which is coupled to a large thermal bath. Our analysis of the initial value problem is based on Kadanoff-Baym equations which are shown to be equivalent to a stochastic Langevin equation. The interaction with the thermal bath generates a temperature-dependent spectral density, either through decay and inverse decay processes or via Landau damping. In equilibrium, energy density and pressure are determined by the Bose-Einstein distribution function evaluated at a complex quasi-particle pole. The time evolution of the statistical propagator is compared with solutions of the Boltzmann equations for particles as well as quasi-particles. The dependence on initial conditions and the range of validity of the Boltzmann approximation are determined.     

Reduction in switching current density for current-induced magnetization switching without loss of thermal stability: Effect of perpendicular anisotropy

Solving the Landau–Lifshitz–Gilbert–Slonczewski equation numerically, we show that switching current density for the current-induced magnetization switching decreases by introducing the perpendicular anisotropy smaller than the out-of-plane demagnetization energy in the switched layer as predicted by theories. Interestingly, the introduction of the perpendicular anisotropy does not decrease the thermal stability of magnetization, but rather slightly increases. The reduction in switching current density results from the decrease of demagnetization effect whereas the increase of thermal stability results from the decrease of attempt frequency.     

Critical current density for spin transfer torque switching with composite free layer structure

Critical current density of composite free layer (CFL) in magnetic tunneling junction is investigated. CFL consists of two exchange coupled ferromagnetic layers, where the coupling is parallel or anti-parallel. Instability condition of the CFL under the spin transfer torque, which is related with critical current density, is obtained by analytic spin wave excitation model and confirmed by macro-spin Landau–Lifshitz–Gilbert equation. The critical current densities for the coupled two identical layers are investigated with various coupling strengths, and spin transfer torque efficiencies.     

Ballistic transfer of spin momentum in multiferroic tunnel junction

The field dependence of critical voltages of switching of magnetic states of a synthetic multiferroic structure is studied based on a bifurcation analysis of Landau–Lifshitz–Gilbert equations with the torques caused by a tunneling spin transport, taking into account the voltage dependence of transferred spin momenta at the variations in the magnitude and direction of electric polarization. The voltage dependences of transferred spin momenta are determined based on the free electron model, taking into account exchange splitting of electron energy subbands in magnetic beaches and the effect of changing the tunnel barrier height at the variations in the polarization magnitude and state.     

Dynamical study of remanent magnetization in nanoparticles

For collections of noninteracting nanoparticles, we study the reduced static remanent magnetization, m_R, produced by the removal of a saturating magnetic field. We show that, except for special cases such as easy uniaxial anisotropy, m_R depends on both the ramp-down rate of the field and the energy dissipation rate of the spin dynamics. Using the Landau–Lifshitz equation, we illustrate this result with explicit dynamical calculations of m_R for cubic and for mixed cubic–uniaxial anisotropies.     

Temperature dependence of superparamagnetic resonance of iron oxide nanoparticles

Nanoparticles of maghemite (γ-Fe₂O₃) are formed in a sol–gel silicate glass with a molar ratio Fe/Si of 2% by a treatment at 1000°C for 6 h. Electron paramagnetic resonance spectrum at 300 K shows a relatively narrow sharp line at g_eff≈2. As the temperature lowers to 5 K, the apparent resonance field decreases and the linewidth considerably increases. We develop a theoretical formalism based on a distribution of diameters or volumes of the nanoparticles following a lognormal. The nanoparticles are considered as single magnetic domains with random orientations of magnetic moments and thermal fluctuations of anisotropic axes. The individual line shape function is derived from the damped precession equation of Landau–Lifshitz. An appropriate linewidth expression is put forward, which account for the averaging of the fluctuations of orientations of the magnetic moments with respect to the magnetic field and to the magnetic anisotropy axes. A single set of parameters provides good fits to the spectra recorded at the different temperatures. The low-temperature blocking of the nanoparticle magnetic moments has been clearly evidenced in the resonance absorption intensity and the blocking temperature of the assembly of nanoparticles (averaged over the distribution in the nanoparticle volume) has been evaluated as 90 K.     

High-frequency magnetic permeability of nanocomposite film

The high-frequency magnetic permeability of nanocomposite film consisting of the single-domain spherical ferromagnetic particles in the dielectric matrix is studied. The permeability is assumed to be determined by rotation of the ferromagnetic inclusion magnetic moments around equilibrium direction in AC magnetic field. The composite is modeled by a cubic array of ferromagnetic particles. The magnetic permeability tensor is calculated by solving the Landau–Lifshits–Gilbert equation accounting for the dipole interaction of magnetic particles. The permeability tensor components are found as functions of the frequency, temperature, ferromagnetic inclusions density and magnetic anisotropy. The obtained results show that nanocomposite films could have a rather high value of magnetic permeability in the microwave range.     

Calculation of electric transport close to a Lifshitz transition in a high magnetic field

The effects of the Landau quantization and interactions on a Lifshitz transition are studied. The Landau quantization leads to a quasi-one-dimensional behavior for the direction parallel to the field. The repulsive Coulomb interactions give rise to a gas of strongly correlated carriers. Consequently, in the ground state, an electron pocket is emptied in a discontinuous fashion as a function of the chemical potential or magnetic field. This discontinuity is gradually smeared by temperature, in agreement with experiments for CeIn₃. We further calculate the conductivity and the Hall conductivity in the presence of nonmagnetic impurities, the Landau quantization and interactions.     

Microwave absorption properties of the Ni nanofibers fabricated by electrospinning

Ni nanofibers with an average diameter of about 100 nm were synthesized by a simple and cost-effective electrospinning technology. The nanofibers have a polycrystalline structure and each nanofiber is composed of fine particles. The complex permittivity and permeability properties of Ni nanofibers composite have been measured in the frequency range of 1–15 GHz. The double-resonance behavior of microwave magnetic permeability is observed. Natural resonance peak happens at 4.0 GHz with the contribution of shape anisotropy. The second resonance peak around 12.5 GHz originates from exchange resonance effect. The permeability spectra were fitted with the Landau–Lifshitz–Gibert equation. The minimum reflection loss of the Ni nanofibers composite reaches ?35.4 dB at 1.3 GHz with a matching thickness of 8.4 mm, which shows promising application of the Ni nanofibers composites in microwave absorber.     

Magnetization reversal by a single pulse of magnetic field or spin-polarized current

One of the important requirements for spintronic devices concerns an efficient magnetization reversal, which may eventually lead to ultra-fast non-volatile magnetic memory applications. In particular, it is necessary to achieve stable sub-nanosecond switching times and to reduce magnetization “ringing”, so that the reversal will proceed along the shortest ballistic path connecting the initial and the target magnetization states. This paper is dedicated to the numerical simulations of a mono-domain ferromagnetic particle, described by the Landau–Lifshitz–Gilbert equation. We study the general case of arbitrary orientation of the applied field/current pulses, constructing dynamic diagrams for the reversal time. We have found that even short 50 ps pulses, applied at a proper angle, will induce magnetization reversal with minimal ringing effects.     

Magnetostatic Green's functions for the description of spin waves in finite rectangular magnetic dots and stripes

We present derivation of the magnetostatic Green's functions used in calculations of spin-wave spectra of finite-size non-ellipsoidal (rectangular) magnetic elements. The elements (dots) are assumed to be single domain particles having uniform static magnetization. We consider the case of flat dots, when the in-plane dot size is much larger than the dot height (film thickness), and assume the uniform distribution of the variable magnetization along the dot height. The limiting cases of magnetic waveguides with rectangular cross-section and thin magnetic stripes are also considered. The developed method of tensorial Green's functions is used to solve the Maxwell equations in the magnetostatic limit, and to represent the Landau–Lifshitz equation of motion for the magnetization of a magnetic element in a closed integro-differential form.     

Energy Distributions of the Szekeres Universes in Teleparallel Gravity

In order to evaluate the energy distribution (due to matter and fields including gravitation) associated with a space-time model of Szekeres class I and II metrics, we consider the Einstein, Bergmann–Thomson and Landau–Lifshitz energy definitions in the teleparallel gravity (the tetrad theory of gravitation (TG)). We have found that Einstein and Bergmann–Thomson energy distributions give the same results, Landau–Lifshitz distribution is disagree in TG with these definitions. These results are the same as a previous works of Aygün et al., they investigated the same problem by using Einstein, Bergmann–Thomson, Landau–Lifshitz (LL) and Møller energy-momentum complexes in GR. However, both GR and TG are equivalent theories that is the energy densities are the same using different energy-momentum complexes in both theories. Also, our results are support the Cooperstock’s hypothesis.     

Dynamic susceptibility of thin films with perpendicular magnetic anisotropy

We investigate the spin dynamics related to the Gilbert damping constant in infinite continuous thin films with perpendicular magnetic anisotropy (PMA), based on numerical and analytic approaches. We obtain the dynamic susceptibility of the infinite continuous thin films with various PMA energies by using micromagnetic simulations with periodic boundary conditions. These results are compared with the analytic solution that we derived from the Landau–Lifshitz–Gilbert equation. Based on our numerical and analytic studies, we support the physical analysis for results in the experimental determination of the Gilbert damping constant for PMA materials.