Electric-field control of spin waves at room temperature in multiferroic BiFeO3

To face the challenges lying beyond present technologies based on complementary metal-oxide-semiconductors, new paradigms for information processing are required. Magnonics proposes to use spin waves to carry and process information, in analogy with photonics that relies on light waves, with several advantageous features such as potential operation in the terahertz range and excellent coupling to spintronics. Several magnonic analog and digital logic devices have been proposed, and some demonstrated. Just as for spintronics, a key issue for magnonics is the large power required to control/write information (conventionally achieved through magnetic fields applied by strip lines, or by spin transfer from large spin-polarized currents). Here we show that in BiFeO(3), a room-temperature magnetoelectric material, the spin-wave frequency (>600 GHz) can be tuned electrically by over 30%, in a non-volatile way and with virtually no power dissipation. Theoretical calculations indicate that this effect originates from a linear magnetoelectric effect related to spin-orbit coupling induced by the applied electric field. We argue that these properties make BiFeO(3) a promising medium for spin-wave generation, conversion and control in future magnonics architectures.     

An Iterative Method for Computing the Surface Resistance of YBCO Thin Films in the Nonlinear Regime of RF Power

A numerical method to find, in the nonlinear regime, the quality factor, the surface resistance, and the resonance frequency of YBCO microstrip line resonator, deposited on both sides of an MgO substrate, is presented. The numerical method is based on an iterative self-consistent technique used to find the RF magnetic field in the nonlinear regime of the dissipation mechanisms. The determination of the RF magnetic field yields to the corresponding surface resistance and resonance frequency. The dependence of the geometrical factor of the film on the RF magnetic field is discussed. This latter is usually used as constant in the literature. However, in our calculation this factor has a maximum at a certain RF input power.     

An Iterative Method for Computing the Surface Resistance of YBCO Thin Films in the Nonlinear Regime of RF Power

A numerical method to find, in the nonlinear regime, the quality factor, the surface resistance, and the resonance frequency of YBCO microstrip line resonator, deposited on both sides of an MgO substrate, is presented. The numerical method is based on an iterative self-consistent technique used to find the RF magnetic field in the nonlinear regime of the dissipation mechanisms. The determination of the RF magnetic field yields to the corresponding surface resistance and resonance frequency. The dependence of the geometrical factor of the film on the RF magnetic field is discussed. This latter is usually used as constant in the literature. However, in our calculation this factor has a maximum at a certain RF input power.     

Spin wave spectrum for an antiferromagnetic superconductor

The Ginzburg-Landau theory has been applied for an antiferromagnetic superconductor in order to calculate the spin-wave spectrum, taking into consideration electromagnetic effects and the long-range spin-spin interaction. It is shown that the superconducting state has a strong influence on the spin-wave spectrum of the antiferromagnetic state.     

Analysis of power magnetic components with nonlinear static hysteresis: finite-element formulation

We present a new systematic methodology to efficiently solve coupled electromagnetic problems with nonlinear hysteresis at low frequency (10 kHz), called static hysteresis, by the finite-element method. The methodology integrates a new domain-wall-motion hysteresis model for power magnetic components (POMACs) into a finite-element potential formulation via an implicit-inverse model calculation. It uses a novel two-level iterative algorithm incorporating the efficient implicit-inverse model calculation to solve the complete Maxwell equations after the finite-element discretization. Our formulation does not require an explicit inversion of the hysteresis model as usually done in previous work. The efficient and accurate full-order model simulations applied to POMAC examples show that the proposed procedure can be applied to other electromagnetic problems with nonlinear static hysteresis.     

Broadband spin-wave delay lines with slot antennas

A planar spin-wave delay line with slot antennas based on an yttrium iron garnet (YIG) film has been experimentally studied. A specific feature of the proposed device is a relatively large (about 1.8 GHz) microwave bandwidth. Within this band, the signal delay time can be smoothly controlled from 4 to 18 ns. The central frequency can be tuned by an external magnetic field within 5–9 GHz. It is demonstrated that, using slot antennas and relatively thick ferromagnetic films, it is possible to achieve a significant increase in the microwave bandwidth of spin-wave devices.     

Spin-wave interference patterns created by spin-torque nano-oscillators for memory and computation

Magnetization dynamics in nanomagnets has attracted broad interest since it was predicted that a dc current flowing through a thin magnetic layer can create spin-wave excitations. These excitations are due to spin momentum transfer, a transfer of spin angular momentum between conduction electrons and the background magnetization, that enables new types of information processing. Here we show how arrays of spin-torque nano-oscillators can create propagating spin-wave interference patterns of use for memory and computation. Memristic transponders distributed on the thin film respond to threshold tunnel magnetoresistance values, thereby allowing spin-wave detection and creating new excitation patterns. We show how groups of transponders create resonant (reverberating) spin-wave interference patterns that may be used for polychronous wave computation and information storage.     

Attenuation of coupled waves in antiferromagnetic elastic conductors in weak magnetic fields

Following along the same line of approach as in a previous paper in which dissipative mechanisms were ignored, the present paper discusses the attenuation of coupled magnetoelastic oscillations in a simple deformable antiferromagnet of which the material symmetry has been broken by a relatively weak bias magnetic field. The linearized equations needed in the analysis are deduced from a fully dynamical nonlinear, rotationally invariant and thermodynamically admissible theory of deformable antiferromagnets. Three types of dissipative mechanisms are taken into account: viscosity, Spin-lattice relaxation and electrical conduction. While all these mechanisms affect to a greater or lesser degree the propagation of essentially transverse elastic modes outside resonance regions, electrical conduction modifies the absorption of spin waves due to spin-lattice relaxation and both viscosity and spin-lattice relaxation are shown to contribute, collaboratively and equally, to the damping of mixed elastic-spin modes in the two magnetoacoustic resonance regions which correspond to the interaction of left-circularly polarized transverse elastic waves and an upper spin-wave branch and right-circularly polarized transverse elastic waves and a lower spin-wave branch, respectively. The analytical discussion of the resulting dispersive and attenuated coupled modes is achieved in terms of characteristically small parameters in a quasi-magnetostatic approximation. The phenomenon of heat conduction, important as it may be, is left out of the analysis.     

Direct observation of a propagating spin wave induced by spin-transfer torque

Spin torque oscillators with nanoscale electrical contacts are able to produce coherent spin waves in extended magnetic films, and offer an attractive combination of electrical and magnetic field control, broadband operation, fast spin-wave frequency modulation, and the possibility of synchronizing multiple spin-wave injection sites. However, many potential applications rely on propagating (as opposed to localized) spin waves, and direct evidence for propagation has been lacking. Here, we directly observe a propagating spin wave launched from a spin torque oscillator with a nanoscale electrical contact into an extended Permalloy (nickel iron) film through the spin transfer torque effect. The data, obtained by wave-vector-resolved micro-focused Brillouin light scattering, show that spin waves with tunable frequencies can propagate for several micrometres. Micromagnetic simulations provide the theoretical support to quantitatively reproduce the results.     

Current-induced domain nucleation in ferromagnet

A key mechanism of the current-induced magnetization dynamics is the spin torque from a spin polarized current (spin current), which couples to spatial gradient of magnetization. Recently, it was pointed out that a large spin current applied to a uniform ferromagnet leads to a spin-wave instability. In this paper, we show that such instability is absent in a state containing a domain wall. This may indicate that nucleation of magnetic domains occurs above a certain critical spin current. This scenario is supported by an explicit energy comparison between the uniformly magnetized state and the domain-wall state under spin current.     

Approximate theory of microwave generation in a current-driven magnetic nanocontact magnetized in an arbitrary direction

We present an approximate nonlinear theory of microwave generation by spin-polarized direct current in a magnetic nanocontact magnetized in an arbitrary direction. We argue that, when the spin-transfer torque caused by spin-polarized current compensates the natural magnetic dissipation in a "free" layer of the nanocontact, a nonlinear quasi-uniform precession of magnetization about the direction of the internal bias magnetic field is excited. With the increase of the current magnitude the angle of precession increases, making precession strongly nonlinear and reducing the projection M/sub z/ of the precessing magnetization vector on the precession axis (z axis). This reduction of M/sub z/ is responsible for the nonlinear limitation of the precession amplitude and for the nonlinear frequency shifts of the generated microwave oscillations. Because of the influence of demagnetizing fields in the "free" layer, the nonlinear frequency shifts have different magnitudes and signs for different orientations of the external bias field H/sub e/. The theory gives a good qualitative, and even partly quantitative, explanation of the main part of microwave magnetization dynamics experimentally observed in magnetic nanocontacts.     

Unsteady MHD forced flow due to a point sink

Summary An analysis is performed to study the unsteady laminar incompressible boundary-layer flow of an electrically conducting fluid in a cone due to a point sink with an applied magnetic field. The unsteadiness in the flow is considered for two types of motion, viz. the motion arising due to the free stream velocity varying continuously with time and the transient motion occurring due to an impulsive change either in the strength of the point sink or in the wall temperature. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. The magnetic field increases the skin friction but reduces heat transfer. The heat transfer and temperature field are strongly influenced by the viscous dissipation and Prandtl number. The velocity field is more affected at the early stage of the transient motion, caused by an impulsive change in the strength of the point sink, as compared to the temperature field. When the transient motion is caused by a sudden change in the wall temperature, both skin friction and heat transfer take more time to reach a new steady state. The transient nature of the flow and heat transfer is active for a short time in the case of suction and for a long time in the case of injection. The viscous dissipation prolongs the transient behavior of the flow.     

Entropy generation on MHD flow and convective heat transfer in a porous medium of exponentially stretching surface saturated by nanofluids

This paper examines the unsteady boundary layer magnetohydrodynamic flow and convective heat transfer of an exponentially stretching surface saturated by nanofluids in the presence of thermal radiation. The combined effect of stratifications (thermal and concentration) in the unsteady boundary layer flow past over a stretching surface embedded in a porous medium is analyzed. The system of coupled nonlinear differential equations are solved numerically by developing finite difference scheme together with the Newton’s linearization technique, which allows us to control nonlinear terms smoothly. The study shows that the thermal boundary layer thickness significantly increases with the increase of Brownian motion, thermophoresis number and magnetic field strength. The unsteadiness behavior of the flow of nanofluid has reducing effect on both momentum and thermal boundary layer thickness. The Brownian motion has controlling effect on nanoparticle migration. The entropy generation by means of Bejan number has strong impact on the applied magnetic field, dissipation of energy, thermal radiation and Biot number.     

Some aspects of chaotic and stochastic dynamics for structural systems

In this paper, the bifurcation behaviour of an externally excited four-dimensional nonlinear system is examined. Throughout this paper, a two-degree-of-freedom shallow arch structure under either a periodic or a stochastic excitation will be considered. For the case when the excitation is periodic, the local and global behaviour is examined in the presence of principalsubharmonic resonance and1:2 internal resonance. The method of averaging is used to obtain the first order approximation of the response of the system under resonant conditions. A standard Melnikov type perturbation method is used to show analytically that the system may exhibit chaotic dynamics in the sense of Smale horseshoe for the 1:2 internal resonance case in the absence of dissipation. In the case of stochastic excitation, the stability of the stationary solution is examined by determining themaximal Lyapunov exponent andmoment Lyapunov exponent in terms of system parameters. An asymptotic method is used to obtain explicit expressions for various exponents in the presence of weak dissipation and noise intensity. These quantities provide almost-sure stability boundaries in parameter space. When the system parameters lie outside these boundaries, it is essential to understand the nonlinear behaviour. The method of stochastic averaging is applied to obtain a set of approximate Itô equations which are then examined to describe the local bifurcation behaviour.     

Calculation and Analysis of the Magnetic Force Acting on a Particle in the Magnetic Field of Separator. Analysis of the Equations Used in the Magnetic Methods of Separation

This paper presents the derivation of equation for calculating the magnetic force acting on a paramagnetic ball situated in a region of a nonuniform magnetic field. We suggest the method of its extrapolation to the case of a nonlinear medium-the case of a ferromagnetic ball found under the influence of the magnetic field which is varying in a certain properly defined range. An experimental setting intended for the measurement of the magnetic force is described as well. For the first time a rigorous proof of the isodynamic magnetic field inexistence, that is a field which generates a magnetic force having the same constant direction and the same constant magnitude at each space point, is given. Moreover, using the method of conformal mappings we derive the analytic expressions for the magnetic field strength calculation in the case of a multipole system. With their help, different important features of the magnetic field behavior in this case are elucidated. The latter is done in a wide region of the geometric parameter space of the magnetic system. The interpretations of different issues discussed in the paper are compared to those that seems to be widely accepted in the magnetic methods of separation branch     

Effect of surface spin pinning on the spin-wave propagation inyttrium iron garnet films

The effect of the surface spin pinning on the spin-wave dispersion and propagation characteristics of yttrium iron garnet (YIG) film was studied both experimentally and theoretically. Modification of the spin-wave amplitude frequency response due to the variations of the pinning conditions on the film surfaces and the bias magnetization direction was studied. Ion bombardment with low-energy H⁺ ions was used to control the surface spins pinning. Strong attenuation notches in the spin-wave amplitude-frequency response of ion processed YIG film was treated in terms of dipole hybridization of dispersion branches and appearance of the dipole “gaps” in spin-wave spectrum. The hybridization of spin-wave spectrum was studied for the case of arbitrary magnetization direction and arbitrary surface spin pinning. It has been found that for noninfinite pinning of surface spins, there are magnetization directions for which the gaps in the spectrum are smaller than relaxation frequency, and spin-wave response is smooth     

TWO SIMPLE FAST INTEGRATION METHODS FOR LARGE-SCALE DYNAMIC PROBLEMS IN ENGINEERING

A new simple explicit two-step method and a new family of predictor–corrector integration algorithms are developed for use in the solution of numerical responses of dynamic problems. The proposed integration methods avoid solving simultaneous linear algebraic equations in each time step, which is valid for arbitrary damping matrix and diagonal mass matrix frequently encountered in practical engineering dynamic systems. Accordingly, computational speeds of the new methods applied to large system analysis can be far higher than those of other popular methods. Accuracy, stability and numerical dissipation are investigated. Linear and nonlinear examples for verification and applications of the new methods to large-scale dynamic problems in railway engineering are given. The proposed methods can be used as fast and economical calculation tools for solving large-scale nonlinear dynamic problems in engineering.     

Passage of two-frequency signals in the Bragg resonance band of a one-dimensional magnon crystal

Passage of a two-frequency signal with high and low power levels through a spin-wave transmission line with a one-dimensional periodic microstructure formed on the surface of a ferromagnetic film is experimentally studied. Experiments are carried out under the condition of three-wave parametric instability of spin waves. It is shown that, near the central frequency of the first Bragg resonance at certain power levels of the large and small signals, the nonlinear spin-wave transmission line can operate as either a power limiter or a signal-to-noise enhancer.     

Microwave nonlinear spin wave directional coupler

A nonlinear spin-wave directional coupler for the microwave range has been designed, constructed, and studied for the first time. Each of the four ports of the device can be used as the input or output for a microwave signal. The role of a control element in the coupler is played by a nonlinear spin wave shifter based on a thin ferromagnetic film. A distinctive feature of the proposed device is that an increase in the input power level leads to the signal switching from one to another output, which is caused by a power-dependent variation in the spin wave phase shift.     

Orientational Dynamics and Energy Dissipation in a Liquid Dispersion of Single-Domain Ferroparticles on Exposure to a Linearly Polarized Field

A theoretical investigation of the nonlinear orientational dynamics and energy dissipation in a suspension of noninteracting single-domain ferroparticles with a magnetic hysteresis on exposure to a linearly polarized magnetic field has been performed. The bifurcation properties of the system have been studied; the amplitude and frequency dependences of the powers of total and viscous dissipation have been obtained.__________Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 78, No. 2, pp. 83–92, March–April, 2005.