Modes of natural vibration for magnetic domains

We analyze wall-vibration modes for the case of plane parallel stripe domains in a uniaxial film whose easy axis is normal to the film plane, using Landau-Lifshitz equations carried to the limit of vanishing wall thickness. We take into account long-range dipole interactions and wall-moment twist due to stray fields from magnetic charges on the film surfaces. The small-amplitude wall displacement q(k, z) depends on the position coordinate z normal to the film plane, and on a two dimensional wave vector k parallel to the film plane. Numerically computed natural frequencies v_n(k) depend on the number of nodes n(=0, 1, 2 …) in the dependence of q on z. Surface and bulk modes are distinguished by the z-dependence of computed eigenmodes q_n(k, z). The spectrum of computed natural frequencies compares favorably with available experimental data.     

Ferrimagnetic resonance spectra of magnetic bubble films at low microwave frequencies

Magnetic bubble films exhibit a number of ferrimagnetic resonance modes due to the spatial variation of the anisotropy. The resonance frequencies have been measured as a function of the applied bias fieldH ₀. In the lower field range the magnetization of the transient layer, which has negative anisotropy, is not yet parallel toH ₀. In this range the resonance frequencies are shifted to higher values due to pinning effects. In films grown by the vertical dipping method an additional layer on top of the transient layer is observed within which the magnetization rotates from the direction in the transient layer to that of the bulk of the film. In films grown by horizontal dipping no such layer could be detected. Each ferrimagnetic resonance mode excites transverse elastic waves in the film due to the magnetoelastic interaction and thus gives rise to elastic resonances of the whole crystal, film and substrate. These elastic resonances lead to a fine-structure of the ferrimagnetic resonances. The observed fine-structure vanishes periodically with frequency and from this behaviour the thickness of the magnetic film and of the transient layer has been determined.     

Inhomogeneous magnetostriction states in uniaxial ferromagnetic films

Surface magnetoelastic Love waves and nonuniform distributions of the magnetization and elastic strains are investigated in a uniaxial ferromagnetic film on a massive nonmagnetic substrate in a tangential external magnetic field. A new inhomogeneous phase is predicted having spatial modulation of the order parameter, arising from magnetostrictive coupling of the magnetization with lattice strains near the interface of the magnetoelastic and elastic media. It is shown that, at some critical magnetic field H _c, different from the orientational transition field in an isolated sample, a magnetoelastic Love wave propagating parallel to the magnetization vector in the film plane becomes unstable. The frequency and group velocity of the wave vanish at wave number k=k _c≠0 and the wave freezes, forming a domain structure localized in the film and adjoining substrate. Fiz. Tverd. Tela (St. Petersburg) 41, 665–671 (April 1999)     

Surface wave modes in PEMC backed chiral slab

The characteristics of surface wave modes in a PEMC backed chiral slab are studied theoretically. First, the analytical solution of electromagnetic fields and dispersion relations are carried out. Then, the fractional field solutions are found using the fractional curl operator. The numerical results are given by assuming that wave numbers k and k_± are either real or imaginary. These results are also evaluated at real and imaginary values of fractional parameter describing the order of curl operator. The discussion contains fractional dispersion curves at various cut-off frequencies and the fractional surface waves in chiral-PEMC and achiral-PMC slabs respectively. For numerical analysis it is assumed that the fractional order of the curl operator is related to chiral admittance, thickness of the slab, and PEMC admittance. For the values of the fractional order equal to 0, 1, and 2 geometry corresponds to PMC backed ordinary dielectric slab, PEMC backed chiral slab, and PEC backed chiral slab respectively. Consequently TE, HE (even), and HE (odd) modes are produced in the respective geometries.     

High-Frequency Backward Waves in Longitudinally Magnetized Gyrotropic Waveguides

Backward waves in waveguides completely filled with magnetoactive plasma (gaseous or semiconductor plasma) have been investigated numerically. It is shown that two types of backward waves exist in such waveguides: cyclotron backward waves and waveguide HE-modes. While the cyclotron modes are backward waves at arbitrary system parameters (plasma density, magnetic field and waveguide radius), the waveguide backward waves appear only at certain values of there parameters. In addition the cyclotron backward waves can propagate at arbitrary wave-number k_z and at arbitrary phase velocity. The backward waveguide modes exist only at limited values of k_z and of phase velocities.     

Temperature-dependent Brillouin scattering studies of surface acoustic modes in Nd0.5Sr0.5MnO3

Brillouin scattering experiments are carried out to study the surface acoustic waves in Nd_0.5Sr_0.5MnO₃ as a function of temperature in the range of 40-300 K covering the metal-insulator and charge-ordering phase transitions. The surface modes include surface Rayleigh wave, pseudo-surface acoustic wave (PSAW) and high velocity PSAW. The observed softening of the sound velocities for the surface modes below paramagnetic to ferromagnetic transition, T_c is related to the softening of the C₄₄ elastic constant. The subsequent hardening of the sound velocity below the charge ordering transition temperature T_co is attributed to the coupling of the acoustic phonon to the charge ordered state via long range ordering of the strong Jahn-Teller (JT) distortion.     

Polar oscillation and dispersion properties of quasi-confined optical phonon modes in a wurtzite GaN/AlxGa1−xN nanowire

Under the dielectric continuum model and Loudon’s uniaxial crystal model, the properties of the quasi-confined (QC) optical phonon dispersions and the electron-QC phonons coupling functions in a cylindrical wurtzite nanowire are deduced via the method of electrostatic potential expanding. Numerical computations on a GaN/Al_0.15Ga_0.85N wurtzite nanowire are performed. Results reveal that, for a definite axial wave number k_z and a certain azimuthal quantum number m, there are infinite branches of QC modes. The frequencies of these QC modes fall into two regions, i.e. a high frequency region and a low frequency region. The dispersion of the QC modes are quite apparant only when k_z and m are small. The lower-order QC modes in the higher frequency region play more important role in the electron-QC phonon interactions. Moreover, for the higher-order QC modes in the high frequency region, the electrostatic potentials “escaping” out of the well-layer material nearly could be ignored.     

Impact of anisotropy on polar optical vibration in a wurtzite cylindrical nanowire with ring geometry

The quasi-confined (QC) phonon modes, surface optical (SO) phonon modes and corresponding Fröhlich-like Hamiltonian in a wurtzite cylindrical nanowire with ring geometry are investigated in the framework of the dielectric continuum model and Loudon’s uniaxial crystal model. Numerical calculations are focused on the dispersion relations of the SO phonons and the electron–SO phonon coupling strength. Results show that there are only two branches of SO phonon modes. The dispersions of the two branches of SO phonon modes are obvious when the phonon wave-number k_z or the azimuthal quantum number m is small. Typical degenerating behavior of the SO modes is evidenced due to the anisotropic effect of wurtzite crystal. Moreover, when k_z or m are large enough, the frequencies of the two branches of SO modes converge to a definite limiting frequency in single planar heterostructure. The calculations of the electron–SO phonon coupling strength reveal that the high-frequency SO modes (SO₊) play a more important role in the coupling strength than the low-frequency ones (SO₋). Furthermore, the long-wavelength SO phonons with small m are the main factor contributing to the electron–phonon interaction.     

Magnetization process in twisted uniaxial polycrystals

A single model has been developed to obtain the general features of the Matteucci, ME, and the inverse Wiedemann, IWE, effects. The model will be confined to polycrystalline tubes and thin wires whose uniaxial crystals are arbitrarily oriented. The domain arrangement is expressed as a function of applied twist in order to determine the remanent magnetization of the M_z-M_ø and M_ø-H_z hysteresis loops. Theory shows that, for certain values of the applied magnetic field, the ME and IWE decrease and vanish with torsion. The relation between the symmetry properties of the ME and IWE and the symmetry of the initial domain structure of the sample is discussed.     

Electronic structure of paramagnetic In<Subscript>1-x</Subscript>Mn<Subscript>x</Subscript> As nanowires

The electronic structure, spin splitting energies, and g factors of paramagnetic In_1-xMn_xAs nanowires under magnetic and electric fields are investigated theoretically including the sp-d exchange interaction between the carriers and the magnetic ion. We find that the effective g factor changes dramatically with the magnetic field. The spin splitting due to the sp-d exchange interaction counteracts the Zeeman spin splitting. The effective g factor can be tuned to zero by the external magnetic field. There is also spin splitting under an electric field due to the Rashba spin-orbit coupling which is a relativistic effect. The spin-degenerated bands split at nonzero k_z (k_z is the wave vector in the wire direction), and the spin-splitting bands cross at k_z = 0, whose k_z-positive part and negative part are symmetrical. A proper magnetic field makes the k_z-positive part and negative part of the bands asymmetrical, and the bands cross at nonzero k_z. In the absence of magnetic field, the electron Rashba coefficient increases almost linearly with the electric field, while the hole Rashba coefficient increases at first and then decreases as the electric field increases. The hole Rashba coefficient can be tuned to zero by the electric field.     

A Brillouin study of the temperature-dependence of the acoustic modes across the insulator-metal transitions in V2O3 and Cr-doped V2O3

Brillouin scattering studies have been carried out on high-quality single crystals of undoped and 0.9% Cr-doped V₂O₃. The observed modes in both the samples at ∼12 and ∼60 GHz are associated with the surface Rayleigh wave (SRW) and bulk acoustic wave (BAW), respectively. In the undoped sample, the mode frequencies of the SRW and BAW modes decrease as the temperature is lowered from room temperature to the insulator-metal transition temperature (T_IM=T_N=∼130 K). Below the transition, the modes show hardening. In the doped sample, the SRW mode shows a similar temperature-dependence as the undoped one, but the BAW mode shows hardening from room temperature down to the lowest temperature (50 K). This is the first measurement of the sound velocity below T_IM in the V₂O₃ system. The softening of the SRW frequency from 330 K to T_IM can be qualitatively understood on the basis of the temperature-dependence of C₄₄, which, in turn, is related to the orbital fluctuations in the paramagnetic metallic phase. The hardening of the mode frequencies below T_IM suggests that C₄₄ must increase in the antiferromagnetic insulating phase, possibly due to the orbital ordering.     

Observation of indirect parallel pumping of magneto-elastic modes in layered YIG/GGG structures

In this work we report new experimental results on nonlinear excitation of magnetoelastic (ME) modes in layered YIG/GGG waveguide structures at GHz frequencies, obtained by a guided-wave light scattering technique. It is shown that the fundamental spin-dipole wave (SDW) mode induces a secondary microwave field at double frequency that can efficiently excite shear elastic modes of the structure. The distinctive feature of a mechanism for ME coupling proposed is that it is free from the selection rules and provides continuous excitation of elastic modes within a wide frequency range by means of the standard microstripe line excitation system.     

Influence of the slow wave on the relation between the angular resonances and the leaky guided modes properties for a poroelastic plate embedded in water

A numerical study of the guided modes in a water-saturated poroelastic plate that obeys the Biot theory is presented. In the first part, we study the leaky guided modes and the angular resonances when the slow wave does not propagate. Two types of guided modes exist. The first ones occur from coupling of the fast longitudinal wave with the shear wave; most of them propagate whatever the frequency is, provided that it is not close to their cut-off frequencies. The leaky guided modes of the second type occur from coupling of the two longitudinal waves and the shear wave. These modes do not propagate (they are highly damped) as long as the slow wave remains diffusive. We show that the characteristics of the angular resonances can be linked to the leaky guided waves of the first type in the same way as for an elastic plate. The guided modes of the second type may not be associated to angular resonances. In the second part, we consider a thinner plate in a higher frequency range so that the slow wave can propagate. Once again its influence is studied both on the leaky guided modes and on the angular resonances.     

Multidimensional elastic waves excited by oscillating domain walls

Magnetoelastic excitations with a fine structure in the 50kHz range have been observed in the study of the domain wall resonance (DWR) in magnetic garnet thin films. DWR excites standing transverse elastic waves which have a resonance frequency given by $\text{f=}\text{nv}\text{2d}$, where f is the frequency, n is an integer, v=3.5×10⁵ cm/sec is the transversal velocity of the elastic wave, and d=0.05 cm is thickness of the film/substrate system. A fine structure associated with each of these modes has been identified as due to two dimensional bulk elastic waves by using a set of parallel microstrip lines. The dispersion relation of these elastic waves is ω²=v²(k²₁+k²₂), where ω is the radial frequency, k₁ and k₂ are the wave vectors in the orientation perpendicular and parallel to the sample surface respectively. In the case of k₁?k₂, $\text{f=}\text{f}{}_0\text{+v}{}^2\text{k}{}^2{}_2\text{f}{}_0$, where f₀ is the resonance when k₂=0. The experimental results are in excellent agreement with this model. A linear dispersion, observed when using a shorted slot-line structure, is understood as the excitation of three dimensional modes due to the complex structure of the slot-line and the sample geometry.     

Anisotropy and dynamic properties of Co2MnGe Heusler thin films

Co₂MnGe films of 30 and 50 nm in thickness were grown by RF-sputtering. Their magnetic anisotropies, dynamic properties and the different excited spin wave modes have been studied using conventional ferromagnetic resonance (FMR) and Microstrip line FMR (MS-FMR). From the in-plane and the out-of-plane resonance field values, the effective magnetization (4πM_eff) and the g-factor are deduced. These values are then used to fit the in-plane angular-dependence of the uniform precession mode and the field-dependence of the resonance frequency of the uniform mode and the first perpendicular standing spin wave to determine the in-plane uniaxial, the four-fold anisotropy fields, the exchange stiffness constant and the magnetization at saturation. The samples exhibit a clear predominant four-fold magnetic anisotropy besides a smaller uniaxial anisotropy. This uniaxial anisotropy is most probably induced by the growth conditions.     

Wide-band magnetoelectric characterization of a ferrite-piezoelectric multilayer using a pulsed magnetic field

The use of a pulsed magnetic field for studies on frequency characteristics of the magnetoelectric (ME) effect in multilayer composite structures is described. The method is based on the excitation of a ferrite-lead zirconate titanate multilayer with short magnetic field pulses, followed by the measurement and Fourier analysis of the ME response signal. It is shown that the ME voltage coefficient α_E generally decreases as the frequency increases from 1 kHz to 1 MHz except (i) at some discrete frequencies where the coefficient increases by an order of magnitude due to electromechanical resonance in the structure and (ii) a local maximum at 2-4 kHz in α_E vs. frequency due to relaxation processes caused by the conductivity of individual layers.     

Propagation and conversion of non-axisymmetric modes in non-uniform helicon-sustained plasma

An effect of the radial plasma density gradient on the oblique wave propagation in the helicon-frequency range is investigated. It is shown that the dispersion features of electrostatic and electromagnetic modes are essentially changed in strongly non-uniform helicon plasma. In particular, the transition between helicon eigenmode frequency scales ω ～ k _z and ω ～ k _z ² is demonstrated. The process of total conversion of long-wavelength helicon mode into short-wavelength electrostatic wave in near-axis region of a plasma column is analysed. Due to modification of the wave dispersion relations, the densities at which the mode conversion occurs are considerably reduced if the density gradient is steep enough. The estimation of collisionless axial damping rate of helicon mode connected with linear mode conversion is presented. This damping is compared with the usual collision damping.     

Magneto-electric coupling in piezoelectric-piezomagnetic superlattices

A piezoelectric-piezomagnetic superlattice (PPS) is proposed to present the magneto-electric (ME) coupling wherein electric polarization induces magnetization or vice versa through the layer's coherent strain. We reveal that in PPS, the interaction of electromagnetic waves with the correspondent alternative piezoelectric and piezomagnetic superlattices through their vibrations excites the piezoelectric and the piezomagnetic phonon polaritons simultaneously. The polaritons couple with each other to give rise to a stop band, in which double negative permittivity and permeability can be realized, however negative refraction could not occur. The coupling also results in the huge dynamic ME effect which attributes to the large ME voltage coefficient in a BaTiO₃-CoFe₂O₄ superlattice as large as 14.9 V cm⁻¹ Oe⁻¹.     

Magnetostriction domain structure in a periodic system of magnetoelastic and elastic nonmagnetic layers

The spectrum of magnetoelastic waves in a periodic structure of alternating ferromagnetic and nonmagnetic layers was studied. In the case of ferromagnetic layers with easy magnetization axes parallel to the layer surfaces, an orientational phase transition induced by an external tangential magnetic field H_e was considered. The formation of an inhomogeneous phase with a spatially modulated order parameter, which is caused by the magnetization being coupled through magnetostriction to lattice strains near the interfaces separating the magnetoelastic from elastic media, is predicted. It is shown that at a certain critical field in excess of the orientational phase transition field in the system without magnetostriction, a magnetoelastic wave propagating in a direction parallel to the in-plane magnetization vector M becomes unstable at finite values of the wave vector and condenses into a magnetostriction domain structure. A phase diagram in the (L, T, H_e) coordinates is constructed, and the regions of existence of thermodynamically equilibrium collinear, canted, and domain phases are established (L and T are the thicknesses of the ferromagnetic and nonmagnetic layers, respectively).     

Collective modes in quasi-two-dimensional conductors under strong spatial dispersion

Propagation of electromagnetic and spin waves in layered conductors with a quasi-two-dimensional dispersion law of charge carriers is investigated theoretically in the presence of an external magnetic field with induction B₀. In layered conductors, the drift velocity v_D of electrons along B₀ is an oscillatory function of the angle between the magnetic field direction and the normal to the layers. For certain orientations of the magnetic field with respect to the layers of the conductor, v_D is close to zero. In these directions, there is no collision-free absorption, and weakly damped waves may propagate even under strong spatial dispersion. In the short-wave-length limit, there may exist collective modes with frequencies in the neighborhood of resonances for arbitrary orientation of the wavevector k relative to B₀. Similar types of excitations in quasi-isotropic metals are possible only when k is perpendicular to the direction of the external magnetic field.