The effect of parametrically excited spin waves on the dispersion and damping of magnetostatic surface waves in ferrite films

This paper describes an experimental study of variations of the dispersion and damping of magnetostatic surface waves in ferrite films, caused by three-and four-magnon interactions with parametric spin waves excited by an auxiliary surface magnetostatic pump wave with frequency f _p. The variations in the dispersion and damping were identified, respectively, with variations Δk″ in the real part and Δk′ in the imaginary part of the wave number of the surface magnetostatic wave. The Δk″ and Δk′ values were determined from the ratio of the changes of the phase increment Δφ and the amplitude increment ΔA of the surface magnetostatic wave to the length L of the nonequilibrium section of the film, where the parametric spin waves exist. It is found that, when three-magnon decay processes are allowed for the pump wave and the surface magnetostatic probe wave, the probe wave can substantially alter the distribution of the parametric spin waves in the film. Zh. éksp. Teor. Fiz. 115, 318–332 (January 1999)     

Theory of ferromagnetic resonance in metallic and insulator films

Simple intuitive explanations of the frequencies and intensitiesI of magnetostatic modes (with negligible exchange energy) and exchange modes (negligible microwave-field demagnetization energy) are given. The effects of explicit boundary conditions on the transverse, time-varying componentm of the magnetization (i.e., the amount of pinning) and the effects of inhomogeneities in the internal fieldH _i and saturation magnetizationM _s are discussed. A bulk inhomogeneity inM _s changes the effective exchange constant, while a bulk inhomogeneity inH _i lowers the fields for resonance of all high-order exchange modes by the same amount. The pinning conditions affect the values of andI of the exchange modes and the mixed exchange-magnetostatic modes, but have little effect on the magnetostatic modes. A surface-imperfection source of pinning and of the inhomogeneities inH _i andM _s is discussed.Part of this work was performed while the author was atNorth American Rockwell Science Center, Thousand Oaks, California.     

Second-order optical susceptibility in doped III-V piezoelectric semiconductors in the presence of a magnetostatic field

A detailed analytical investigation of second-order optical susceptibility has been made in moderately doped III-V weakly piezoelectric semiconductor crystal, viz. n-InSb, in the absence and presence of an external magnetostatic field, using the coupled mode theory. The second-order optical susceptibility arises from the nonlinear interaction of a pump beam with internally generated density and acoustic perturbations. The effect of doping concentration, magnetostatic field and pump intensity on second-order optical susceptibility of III-V semiconductors has been studied in detail. The numerical estimates are made for n-type InSb crystals duly shined by pulsed 10.6 μm CO₂ laser and efforts are made towards optimising the doping level, applied magnetostatic field and pump intensity to achieve a large value of second-order optical susceptibility and change of its sign. The enhancement in magnitude and change of sign of second-order optical susceptibility, in weakly piezoelectric III-V semiconductor under proper selection of doping concentration and externally applied magnetostatic field, confirms the chosen nonlinear medium as a potential candidate material for the fabrication of nonlinear optical devices. In particular, at B ₀ = 14.1 T, the second-order susceptibility was found to be 3.4 × 10^-7 (SI unit) near the resonance condition.     

A lower bound for the volume-averaged mean-square magnetostatic stray field

Based on a micromagnetics model, we develop a method through which quantitative information on the volume-averaged mean-square magnetostatic stray field 〈|H ^b _d|²〉 _v due to non-zero divergences of the magnetization M within the bulk of a ferromagnetic body can be obtained by analysis of magnetic-field-dependent small-angle neutron scattering data. In the limit of high applied magnetic field H _a, when the direction of M deviates only sligthly from H _a, we have estimated a lower bound for 〈|H ^b _d|²〉 _v as a function of the external field, and we have applied the method to bulk samples of nanocrystalline electrodeposited Ni and Co and coarse-grained polycrystalline cold-worked Ni. The root-mean-square magnetostatic stray field, which is inherent to a particular magnetic microstructure, shows a pronounced field dependence, with values ranging from about 5 to 50mT. Even at applied fields as large as 1.7T, the quantity μ〈|H ^b _d|²〉^1/2 _v of nanocrystalline Co is still 24mT, which suggests that contributions to the total magnetostatic field originating from the bulk are significant in nanocrystalline ferromagnets; therefore, 〈|H ^b _d|²〉 _v cannot be ignored in the interpretation of e.g. measurements of magnetization or spin-wave resonance. A comparison of 〈|H ^b _d|²〉 _v with the volume-averaged mean-square anisotropy field reveals that both quantities are of comparable magnitude. Received 25 April 2002 Published online 31 October 2002 RID="a" ID="a"e-mail: anmi@nano.uni.saarland.de     

Parametric interaction of magnetostatic waves with a nonstationary local pump

A solution is obtained for the general problem of the nonstationary interaction of backward volume magnetostatic waves in films of yttrium-iron garnet with local parametric pumping. In the case of a large pump region, l≫λ, where λ is the wavelength of the backward volume magnetostatic waves, the problem reduces to a system of truncated equations for two packets of counter propagating waves. In the opposite case, l<λ, the exact problem of parametric interactions of the eigenmodes of a ferrite film (both counterpropagating and in the same direction) is solved numerically. Both cases are studied experimentally and good qualitative and quantitative agreement is obtained with the theory. For the first time, the reversal of a wave front and the time reversal of the shape of backward volume magnetostatic wave pulses are observed and a change in the propagation time for the peak of the signal pulse and a reduction in its width owing to pumping are recorded. Two operating regimes are identified for a nonstationary parametric backward volume magnetostatic wave amplifier with local pumping, which differ in the ratio of the duration of the pump pulse to the transit time for the wave through the local pump region, and the effect of the parametric excitation of two-dimensional spin waves on the interaction of backward volume magnetostatic waves with a local nonstationary parametric pump is determined. Zh. éksp. Teor. Fiz. 116, 2192–2211 (December 1999)     

Spectrum and losses of surface magnetostatic waves in a 1D magnon crystal

The spectrum and propagation losses of a surface magnetostatic wave in a 1D ferrite magnon crystal are experimentally studied as a function of angle φ between the wavevectors of the surface magnetostatic wave and periodic crystal lattice. Variation in the positions of Bragg forbidden bands with angle φ is described. A wide transmission band is discovered near long-wave frequency boundary f ₀ of the surface magnetostatic wave in a narrow interval of angles around φ ≈ 57°. In the interval 70° < φ < 90° and at frequencies below f ₀, there exists a magnetostatic wave with a wavevector that is normal to the bias field.     

The propagation of magnetostatic surface waves in ferrite/superconductor structures

An electrodynamic model that describes the dispersion of magnetostatic surface waves in ferrite/superconductor structures is suggested. On its basis, a new approach to determining the microwave sheet resistance R _S of superconducting films in a magnetic field is elaborated. The values calculated (R _S =0.20–0.96 mΩ) agree with results obtained by the Tauber method. For YIG/YBCO structures, the controllable phase shift is about 1.5π when the depth of magnetostatic wave penetration into the YBCO film varies from 2.0 to 0.8 μm.     

Propagation of magnetostatic waves in a ferrite plus high-T c superconductor structure in the presence of transport current in the superconductor

A thin-film structure consisting of a ferrite and a high-T _c superconductor was used to investigate the effct of the transport current in the superconductor on the amplitude-frequency characteristic and dispersion of surface magnetostatic waves (MSWs) in a ferrite film. It was found that the nature of energy transfer between the MSWs and the superconducting film undergoes a significant change as the transport current is varied. In particular, in one of the current ranges, energy can be transferred both from the MSWs to the superconductor and back again, whereas in another range it can only be efficently transferred to the superconductor. Fiz. Tverd. Tela (St. Petersburg) 39, 2195–2202 (December 1997)     

Self-consistent problem of the excitation of beams of magnetostatic waves

An analytical solution is obtained for the self-consistent problem of the excitation of beams of magnetostatic waves by a converter of arbitrary type. Radiation patterns are calculated numerically for stripline converters at the frequencies where magnetostatic surface waves exist. Zh. Tekh. Fiz. 68, 95–101 (August 1998)     

Investigation of the photothermally modulated ferromagnetic resonance signal from magnetostatic modes in yttrium iron garnet films

The conventional and photothermally modulated (PM) ferromagnetic resonance (FMR) of magnetostatic modes (MSM) in yttrium iron garnet (YIG) films have been investigated as a function of temperature. Approaching the ferrimagnetic transition at T _c=560 K a strong enhancement of the PM-FMR signal amplitude is observed which is accompanied by a change of the signal shape. The observations are discussed in the framework of a model that takes into account the temperature derivatives of those quantities that contribute to the high-frequency susceptibility. At temperatures still below T _c a paramagnetic line emerges. The MSM disappear in a state of finite magnetization which is explained on the basis of damping of the MSM being important in the vicinity of the magnetic phase transition. Additionally, frequency and power dependent measurements are presented and the imaging ability of PM-FMR is demonstrated.     

Chaotic electron trajectories in electromagnetic wiggler free-electron laser with a guide magnetic field

Summary The Hamiltonian for an electron travelling through a large-amplitude backward electromagnetic wave, an axial guide magnetic field and radiation field is formulated. Poincaré surface-of-section plots show that this Hamiltonian is non-integrable, and leads to chaotic trajectories. Equilibrium conditions are derived in the limit where the radiation field approaches zero. Compared to conventional FEL, the total energy of the system at pondermotive resonanceE _c is large, while the electron's critical energy γ_c is low for electromagnetic wiggler FEL. Moreover, the threshold wave amplitude (A _r=A _c) of beam chaoticity is found at lower values of the radiation field amplitude compared to magnetostatic wiggler FEL. Previous features confirmed that electromagnetic wiggler FEL can operate more coherently and more efficiently at moderated particle's energy compared to magnetostatic wiggler FEL.     

Simplified components of the spin-other-orbit interaction near the middle of the atomic f shell

To honour the memory of Brian Garner Wybourne, an analysis is presented of three components of the spin-other-orbit interaction for f electrons using the kind of Lie groups he would have been familiar with. The components have been named z ₆, z ₈ and z ₁₀. They all belong to the irreducible representation (IR) (30) of Racah’s group G₂. Near the middle of the f shell it is often found that fewer independent blocks of numbers are needed to express their matrix elements than the Wigner–Eckart theorem, generalized to the IRs U of G₂, would indicate. Each block corresponds to a given U and U?′, and possesses rows and columns labelled by the angular momenta L and L′. The number of independent blocks would be expected to be given by Racah’s multiplicity function c(UU?′ (30)); but near the middle of the shell the number c(UU?′ (20)) (or less) often suffices. For this to occur, z ₈ and z ₁₀ have to be replaced by linear combinations corresponding to IRs of the types (20)×(10) and (21)×(10) of the direct product group G_2A×G_2B, where A and B refer to electrons with their spins up (A) and spins down (B). A detailed example is provided by the IR (31) of G₂, which occurs in the configurations f ⁵ through f ⁹. In addition, two antiHermitian operators (z _a6 and z _a7) that also belong to the IR (30) of G₂ are discussed.     

Nonlinear response of uniaxial ferromagnets and applications to surface magnetostatic waves

The nonlinear susceptibilities of uniaxially anisotropic ferromagnets are obtained analytically. The expressions show that the anisotropy effect on the first- and second-order components means just an increased H_1a (the first-order anisotropy field) of the dc field H₀ along the anisotropy axis, but the third-order components are complicated and new terms appear. Applying the above results to surface magnetostatic waves in the films, we find new magnetostatic modes from the joint effect of the anisotropy and nonlinearity since higher powers of frequency are introduced in the dispersion equation by the nonlinearity and anisotropy. Very obvious non-reciprocity is seen from the dispersion curves.     

Hysteresis of the characteristics of magnetostatic waves in ferrite films with stripe domains whose magnetization vectors are oriented close to the plane of the film

The propagation of zero-exchange spin waves (magnetostatic waves) is investigated in yttrium iron garnet films having a regular stripe domain structure with almost in-plane orientation of the domain magnetization vectors. The characteristics of the waves are studied for magnetizations of the film parallel and perpendicular to projections of the [111] crystallographic axes onto the plane of the film. It is established, in contrast with films having the domain magnetization vectors oriented close to the normal to the plane of the film, that both the propagation of magnetostatic waves and the variation of the parameters of the domain structure exhibit a distinctly pronounced hysteretic character as the magnetizing field is varied. The hysteresis of the amplitude-frequency response, equiphase, and dispersion curves of the magnetostatic waves is investigated. The authors examine how the hysteresis of these parameters is related to the hysteresis of the domain structure. The spectrum of magnetostatic waves is found to have an interval of wavelengths (wave numbers) that are not excited in the unsaturated film when the applied field is close to the saturation value, and this phenomenon as well exhibits hysteresis. Zh. éksp. Teor. Fiz. 114, 1430–1450 (October 1998)     

In search of photon’s elementary axial magnetostatic field

 Experimental investigations of the photon’s B ⁽³⁾-field (third longitudinal polarization) are reported. The existence of an “axial magnetostatic field of photon” has been predicted in B _π or B ⁽³⁾-theory as the fundamental property of the circularly polarized light, and reported in numerous papers and monographs. High-sensitivity detection has been employed in photomagnetic induction, Faraday, and inverse Faraday effects (IFE) originating from such a field. The results of all three experiments clearly disprove the claims of B _π-theory. Putting together these results and theoretical calculations in perspective, it is concluded that such fields are non-existent. Received: 25 January 1996 / Revised version: 24 May 1996     

Implications of time-reversal symmetry for the band structure of single-wall carbon nanotubes

When electron states in carbon nanotubes are characterized by two-dimensional wave vectors with the components K ₁ and K ₂ along the nanotube circumference and cylindrical axis, respectively, then two such vectors symmetric about a M-point in the reciprocal space of graphene are shown to be related by the time-reversal operation. To each carbon nanotube there correspond five relevant M-points with the following coordinates: K ₁⁽¹⁾ = N/2R, K ₂⁽¹⁾= 0; K ₁⁽²⁾ = M/2R, K ₂⁽²⁾= −π/T; K ₁⁽³⁾= (2N −M)/2R, K ₂⁽³⁾= π/T; K ₁⁽⁴⁾= (M + N)/2R, K ₂⁽⁴⁾= -π/T, and K ₁⁽⁵⁾= (N − M)/2R, K ₂⁽⁵⁾= π/T, where M and N are the integers relating the chiral, C _h , symmetry, R, and translational, T, vectors of the nanotube by N R = C _h + M T, T = |T|, and R is the nanotube radius. The states at the edges of the one-dimensional Brillouin zone, which are symmetric about the M-points with K ₂ = ±π/T, are shown to be degenerate due to the time-reversal symmetry.     

Synthesis and magnetic properties of Fe100-xMox alloy nanowire arrays

The Fe100-xMox(13≤x≤25) alloy nanowire arrays are synthesized by electrodeposition of Fe 2+ and Mo 2+ with different ionic ratios into the anodic aluminum oxide templates.The crystals of Fe100-xMox alloy nanowires gradually change from polycrystalline phase to amorphous phase with the increase of the Mo content and the nanowires are of amorphous structure when the Mo content reaches 25 at%,which are revealed by the X-ray diffraction and the selected area electron diffraction patterns.As the Mo content increases,the magnetic hysteresis loops of Fe100-xMox alloy nanowires in parallel to the nanowire axis are not rectangular and the slopes of magnetic hysteresis loops increase.Those results indicate that the magnetostatic interactions between nanowires and the magnetocrystalline anisotropy both have significant influences on the magnetization reversal process of the nanowire arrays.     

EPR investigation of the spin-spin interactions in a Cu(II)-Gd(III)-Fe(III) heterospin system

The spin-spin interactions in a system that contains three different spin carriers, [{LCu}Gd(H₂O)₃×{Fe(CN)₆}] _n ·4nH₂O (1) [L²⁻, N,N-propylenedi(3-methoxysalicylideneiminato)], were investigated by electron paramagnetic resonance spectroscopy. Additional information was obtained by analyzing the discrete heterobinuclear system [LCu(OH₂)Gd(O₂NO)₃] (2), which contains the Cu(II)-Gd(III) pair also existing in the structure of 1, and the compounds [{LCu}Gd(H₂O)₃{Co(CN)₆}] _n ·3.5nH₂O and [{LCu}La(H₂O)₃×{Fe(CN)₆}] _n ·4nH₂O, which are isostructural with 1 and in which the paramagnetic low-spin Fe(III) and Gd(III) ions were replaced by diamagnetic low-spin Co(III) and La(III), respectively. The investigations were carried out in the temperature range of 293–4 K in both X- and Q-bands and also using a dual-mode X-band. The experimental spectra of the Cu(II)-Gd(III) pairs in 2 were interpreted as the sum of spectra of the ground spin state with total S = 4 and the excited state with S = 3 appearing due to the ferromagnetic exchange interaction between Cu(II) and Gd(III) ions. By fitting the experimental and simulated spectra, the zero-field splitting parameters of the Gd(III) ion are estimated and it is shown that no influence of the anisotropic interaction is detected. The magnetic properties of 1 are discussed from the perspective of the interaction of the Cu(II)-Gd(III) binuclear fragments with the Fe(III) ions.     

Magnetostatic properties of K2Co x Fe1−x F4, a system with competing anisotropies

The magnetostatic properties of K₂Co _x Fe_1–x F₄ have been investigated by susceptibility and Mössbauer measurements at different concentrations and temperatures. Three magnetically ordered phases are found: a planar phase, an OAF phase, and an uniaxial phase. The experimental results are compared to a molecular-field calculation. At certain concentrations and temperatures it is not possible to obtain a good least squares fit of the Mössbauer spectra, which is tentatively assigned to relaxation effects due to fast spin fluctuations at the OAF phase transition.     

ESR in quasi 2-d ferromagnets: The coexistence of paramagnetic excitations and magnetostatic spin waves and new interference effects

The quasi 2-dimensional layer structures (C_nH_2n+1NH₃)₂CuCl₄ with n = 1,2 have been investigated by electron spin resonance. New phenomena arise for samples with well defined natural surfaces: (i) well resolved magnetostatic volume and surface spin wave modes at 4.2 K comparable in quality with spectra of YIG, (ii) a magnetostatic spin wave spectrum which is coincident with the paramagnetic resonance over a wide temperature range, (iii) interference effects between these two types of resonances.