Spatially resolved dynamics of localized spin-wave modes in ferromagnetic wires

We have observed localized spin-wave modes in individual thin-film ferromagnetic wires using time-resolved Kerr microscopy as a micron-scale spectroscopic probe. The localization is due to the internal field profile present when an external field is applied in the plane of the film and perpendicular to the long axis of the wire. Spatially resolved spectra demonstrate the existence of distinct modes at the edges of a rectangular wire. Spectral images clearly show the crossover of the two edge modes into a single mode in low applied fields, in agreement with the results of micromagnetic simulations.     

Andreev reflection in a patterned graphene nanoribbon superconducting heterojunction

In the study, an improved superconducting heterojunction is made up of a zigzag graphene nanoribbon, which is patterned by a triangle and supports localized edge mode. Since all the localized edge modes stem from a pattern operation, the structure features of the pattern exert an enormous function on the coherent quantum transport. Especially, the patterned modes can enhance the Andreev reflection largely both in the ferromagnetic nanoribbon edge and the antiferromagnetic nanoribbon edge. The spin resolved zero bias conductances, in sharp contrast to its counterpart in the infinite width superconducting heterojunction, exhibit the different dependence on the patterned ferromagnetic interaction.     

Band structure of collective modes and effective properties of binary magnonic crystals

In this paper a theoretical study of the band structure of collective modes of binary ferromagnetic systems formed by a submicrometric periodic array of cylindrical cobalt nanodots partially or completely embedded into a permalloy ferromagnetic film is performed. The binary ferromagnetic systems studied are two-dimensional periodic, but they can be regarded as three-dimensional, since the magnetization is non uniform also along the z direction due to the contrast between the saturation magnetizations of the two ferromagnetic materials along the thickness. The dynamical matrix method, a finite-difference micromagnetic approach, formulated for studying the dynamics in one-component periodic ferromagnetic systems is generalized to ferromagnetic systems composed by F ferromagnetic materials. It is then applied to investigate the spin dynamics in four periodic binary ferromagnetic systems differing each other for the volume of cobalt dots and for the relative position of cobalt dots within the primitive cell. The dispersion curves of the most representative frequency modes are calculated for each system for an in-plane applied magnetic field perpendicular to the Bloch wave vector. The dependence of the dispersion curves on the cobalt quantity and position is discussed in terms of distribution of effective “surface magnetic charges” at the interface between the two ferromagnetic materials. The metamaterial properties in the propagative regime are also studied (1) by introducing an effective magnetization and effective “surface magnetic charges” (2) by describing the metamaterial wave dispersion of the most representative mode in each system within an effective medium approximation and in the dipole-exchange regime. It is also shown that the interchange between cobalt and permalloy does not necessarily lead to an interchange of the corresponding mode dispersion. Analogously to the case of electromagnetic waves in two-dimensional photonic crystals, the degree of localization of the localized collective modes is expressed in terms of an energy concentration factor.     

液晶染料填充阶梯型Double-period结构局域模的光学特性

利用传输矩阵法研究了液晶染料填充一维阶梯型Double-period第四代准周期结构局域模的光学特性。计算了增益前局域模与外加电场方向和正入射波方向间夹角θ的变化关系,分析了增益系数与局域模透射率的关系以及局域模在空间位置的光场分布,讨论了增益后的局域模透射率与光场强度的关系。结果表明:随着夹角θ的增大,光子禁带变宽并且只向短波方向拓展;随着夹角θ的增大,增益前的局域模向短波方向移动,透射率逐渐增大,且局域模波长的调控量为23.7nm。随着增益系数的增大,透射率先增大后减小。光场分布呈现局域现象,当夹角θ=43.4°,波长λ=595.0nm时,光强达到6个数量级。增益后的局域模透射率与光场强度呈正比关系。     

应力各向异性下耦合三层薄膜铁磁共振

研究铁磁/铁磁/反铁磁三层薄膜中应力各向异性场对共振场的影响.得到系统存在声学和光学两种模,并且随着应力场的增强,在某些区域声学模和光学模共振场均向高值方向移动.此外发现声学模共振场对两铁磁层厚度的依赖较大,对光学模而言,随着两铁磁层厚度的改变,应力各向异性场对其共振场的影响甚微.     

Localization properties of bulk-dead and comb magnetostatic modes in Brillouin light scattering spectrum

We show that magnetostatic modes with amplitude localized in different regions of the sample along the direction of the magnetic field occur in ferromagnetic stripes: bulk-dead modes, with amplitude localized in two regions and comb modes localized in its central part. We also demonstrate these localization properties can be studied by Brillouin light scattering techniques and applied in practice. Having established that the localization of these modes varies with their frequency, we use this finding as the basis of a trial reinterpretation of experimental results obtained by Demidov et al. [Appl. Phys. Lett. 92 (2008) 232503].     

Micromagnetic dissipation, dispersion, and mode conversion in thin permalloy platelets

Micron-sized ferromagnetic Permalloy disks exhibiting an in-plane ferromagnetic vortex structure are excited by a fast rise time perpendicular magnetic field pulse and their modal structure is analyzed. We find azimuthal and axial modes. By a Fourier filtering technique we can separate and analyze the time dependence of individual modes. Analysis of the experimental data demonstrates that the azimuthal modes damp more quickly than the axial modes. We interpret these results as mode conversion from low-frequency azimuthal modes to the fundamental mode which is higher in frequency, i.e., mode-mode coupling in a system with a single Landau-Lifshitz-Gilbert phenomenological damping constant alpha.     

Intrinsic Localized Spin-Wave Modes in an Anisotropic Ferromagnet with Dzyaloshinsky-Moriya Interaction

The existence and properties of intrinsic localized spin-wave modes in a ferromagnetic XXZ spin chain with Dzyaloshinsky-Moriya interaction are investigated analytically in the semiclassical limit. The model Hamiltonian is quantized by introducing the Dyson-Maleev transformation and the coherent state representation is chosen as the basic representation of the system. By making use of the method of multiple scales combined with a quasidiscreteness approximation, the equation of motion for the coherent-state amplitude is reduced to the nonlinear Schrödinger equation. It is shown that a bright intrinsic localized spin-wave mode whose eigenfrequency lies below the bottom of the magnon frequency band can exist in the ferromagnetic system. We also show that the system can produce a dark intrinsic localized spin-wave mode, i.e., nonpropagating kink, whose eigenfrequency is below the upper of the magnon frequency band. In addition, we find that the introduction of the Dzyaloshinsky-Moriya interaction changes wave numbers in the Brillouin-zone corresponding to the appearance of intrinsic localized spin-wave modes.     

非对称条形纳磁体的铁磁共振频率和自旋波模式

通过建立微波激励下的非对称条形多铁纳磁体的微磁模型,研究了倾斜角和缺陷角对该形纳磁体的铁磁共振谱和自旋波模式的影响.通过对微磁仿真得到的动态磁化数据进行分析发现,非对称条形纳磁体倾斜角度增加,铁磁共振频率随之增加,而这一现象与纳磁体的缺陷角度无关.倾斜角不变,非对称条形纳磁体的铁磁共振频率与缺陷角度呈单调递增关系,并且不同缺陷角度纳磁体的自旋波模式显示出极大的差异.非对称条形纳磁体与矩形纳磁体相比,它的自旋波模式局部化,具体为非对称条形纳磁体的自旋波模式不对称且高进动区域存在于边缘,表现为非对称边缘模式.倾斜角改变导致纳磁体内部退磁场变化,引起纳磁体边缘模式的移动,而中心模式对倾斜角的变化并不敏感.最后,对建立的模型在高频微波磁场激励下的磁损耗进行了分析,验证了模型的可靠性.这些结论说明缺陷角和倾斜角可用于纳磁体自旋波模式和铁磁共振频率的调谐,所得结果为可调纳磁微波器件的设计提供了重要的理论依据和思路.     

Discrete modulational instability and bright localized spin wave modes in easy-axis weak ferromagnetic spin chains involving the next-nearest-neighbor coupling

We report a theoretical work on the properties of modulational instability and bright type nonlinear localized modes in one-dimensional easy-axis weak ferromagnetic spin lattices involving next-nearest-neighbor couplings.With a linear stability analysis, we calculate the growth rates of the modulational instability, and plot the instability regions.When the strength of the next-nearest-neighbor coupling is large enough, two new asymmetric modulational instability regions appear near the boundary of the first Brillouin zone.Furthermore, analytical forms of the bright nonlinear localized modes are constructed by means of a quasi-discreteness approach.The influence of the next-nearest-neighbor coupling on the Brillouin zone center mode and boundary mode are discussed.In particular, we discover a reversal phenomenon of the propagation direction of the Brillouin zone boundary mode.     

立方铁磁体中的自旋波局域模

本文计算了简单立方铁磁体中由于磁性杂质的存在而形成的局域自旋波。其空间对称有s型模、p型模和d_r型模三种。求出了各类局域模的波函数和自旋偏离的相角分布,其相应的能级与参量J′S′/JS的关系均由曲线表出。其次分析了在体心立方和面心立方铁磁体中可能出现的局域模的对称类型。我们指出,s型局域自旋波是最有可能实际观测到的。作为观测局域自旋波的样品的铁磁体,其居里点应随渗杂浓度的增加而上升。按照这一判据,我们举出一些可以试用的实验样品。最后,通过总自旋量子数的分析,一般地断定了辐射场不可能激 关键词：     

Dual Space Analyzing Based on Symmetry Properties for Phonons of Si Quantum Dot

Phonon modes in spherical Si quantum dots (QDs) with up to 7.9 nm in diameter are calculated by using the projection operators of the group theory into valence force field model. The phonons of dot modes in each of five irreducible representations (symmetries) are classified by using a dual space analysis method. It is found that the bulk-like modes with localization radius much smaller than the dot‘s radius have clearly pronounced bulk specific-κdefinite bulk band (one in six modes). In Si dots of all sizes, each specific bulk-like dot mode has specific symmetry.TO dot modes and bulk-like X-derived TA and LA dot modes red-shift in frequency with decreasing dot size. There is almost not LO/TO mixing for bulk-like modes. As for the surface-like modes localized at the periphery of the dot,their eigenmodes have not a dominant bulk specific-κ point parentage or a dominant BZ parentage around some special point. They are a superposition of many bulk bands with κ from all over the bulk BZ. They have much significant mode mixing than the bulk-like phonons. The classification of dot modes based on the symmetry of group theory will bring advantageous to the discussion of Ramam spectrum, electron-phonon interaction and other phonon-assisted effects in QDs.     

Spin orientation and excitation of magnetic nanocluster on metal surface

The spin orientation and excitation of the ferromagnetic nanocluster on the magnetic metal surface are studied numerically. We show that localized magnetic excitation modes are generated by the spin fluctuation of the cluster, when the ferromagnetic interaction J′ between the cluster and the metal surface is small and the spins in the cluster are oriented in the opposite direction with those of the metal surface by the external field. This magnetic structure is similar to the domain wall (DW) structure of a ferromagnetic wire, both sides of which connect with metal surfaces. As the interaction J′ increases, the sign of the thermal average of the spins in the cluster changes, i.e., the spin-flip takes place. In this time, the magnetic fluctuation of the cluster becomes large and the magnetic excitation energies, except for that of one excitation mode, overlap with the excitation spectrum of the spin wave. We also show that, by the overlap, sharp peaks and dips occur in the excitation spectrum of the spin wave.     

Comparison of frequency,field, and time domain ferromagnetic resonance methods

We present vector network analyzer ferromagnetic resonance measurements of epitaxial Fe films having a thickness of 16 monolayers. Our objective is to test the reliability of this novel frequency domain technique with respect to frequency and damping. For this purpose we compare vector network analyzer ferromagnetic resonance to pulsed inductive microwave magnetometry, time resolved magneto-optic Kerr effect (both methods in the time domain), and conventional ferromagnetic resonance (measured in the field domain) in terms of position and width of the ferromagnetic resonance. In addition, we compare the various techniques with respect to the signal to noise ratio of the raw data. All data is obtained using the same well characterized ultrathin magnetic Fe/GaAs (0 0 1) film. Finally, we demonstrate the potential of the vector network analyzer ferromagnetic resonance technique for the investigation of nano-structured magnetic elements having nonuniform magnetization configuration. The absorption spectrum of Permalloy disks with a diameter of 200 nm and a thickness of 15 nm shows up to eight distinct resonance peaks. The spatial structure of the corresponding modes was derived from numerical calculations and reveals that azimuthal modes up to the fifth order have been observed inductively.     

Dynamics of Magnetic Skyrmions in Nanodots

Bloch and Neel magnetic skyrmions have been studied in systems of confined geometry (nanodots, a linear array of nanodots). The spectra of low- and high-frequency excitation modes of a skyrmion state have been calculated. It has been shown that skyrmion spectrum asymmetry, namely, the characteristic difference between the frequencies of the azimuthal modes of the azimuthal skyrmion modes rotating clockwise and counterclockwise, is associated with asymmetry in the magnetization profiles of high-frequency spin waves propagating on the background of a skyrmion state in a nanodot. The low-frequency spectrum contains the only gyrotropic mode localized near the center of a nanodot. The gyrotropic frequency depends on the material parameters of a nanodot and the size of a skyrmion. The eigenfrequency of the gyrotropic mode of an isolated skyrmion in a nanodot in ultrathin films (L ~ 1 nm) does not depend on the internal structure of a skyrmion and is the same for Bloch and Neel skyrmions. The interaction of skyrmions, in particular, in a linear chain of nanodots with the ground skyrmion state, leads to distinctions in low-frequency spectra. The structure of a skyrmion (of Bloch or Neel type) is exhibited as a shift of dispersion curves and a difference between the frequencies of ferromagnetic resonance in a system of interacting skyrmions.     

Angular dependence of the ferromagnetic resonance spectrum in continuous/heterogeneous multilayers

We present here a study of the angular dependence of the ferromagnetic resonance (FMR) spectra in trilayers formed by two continuous ferromagnetic layers, Fe and Ni₈₀Fe₂₀ (permalloy), separated by a granular film of Fe(x)–SiO₂(1–x). The study of the Fe/Fe-SiO₂/Ni₈₀Fe₂₀ trilayer was made for an Fe volume concentration x=0.75 and two thicknesses (t=1 and 18 nm) of the granular layer. One microwave absorption line is in general found close to the field expected for Fe, while the other is coincident with the resonance field of permalloy. However, the Fe-like absorption is considerably wider than what is usually observed in pure Fe films, which suggests the presence of a strong exchange interaction between this layer and the granular spacer. The angular dependence of the resonance field and the line width could be very well fitted with a model that assumes an effective in-plane anisotropy for each layer, indicating that the shape anisotropy dominates the angular response of both modes. When the excitation frequency is increased, the line width of the permalloy-like mode increases by a similar factor. The width of the Fe-like mode is very similar at different frequencies because of the effect of the granular layer.     

Intrinsic Localized Modes in Quantum Ferromagnetic XXZ Chains in an Oblique Magnetic Field

A semiclassical study of intrinsic localized spin-wave modes in a one-dimensional quantum ferromagnetic XXZ chain in an oblique magnetic field is presented in this paper. We quantize the model Hamiltonian by introducing the Dyson-Maleev transformation, and adopt the coherent state representation as the basic representation of the system. By means of the method of multiple scales combined with a quasidiscreteness approximation, the equation of motion for the coherent-state amplitude can be reduced to the standard nonlinear Schrödinger equation. It is found that, at the center of the Brillouin zone, when θ < θ _c a bright intrinsic localized spin-wave mode appears below the bottom of the magnon frequency band and when θ > θ _c a dark intrinsic localized spin-wave resonance mode can occur above the bottom of the magnon frequency band. In other words, the switch between the bright and dark intrinsic localized spin-wave modes can be controlled via varying the angle of the magnetic field. This result has potential applications in quantum information storage. In addition, we find that, at the boundary of the Brillouin zone, the system can only produce a dark intrinsic localized spin-wave mode, whose eigenfrequency is above the upper of the magnon frequency band.     

具有格点各向异性的一维铁磁链中的量子孤子和内禀局域模(英文)

基于Hartree-Fock方法和多标度方法,我们考察了具有格点各向异性的一维铁磁链中的量子孤子和内禀局域模,量子磁振子的波函数由量子包络孤子来描述.在布里渊区边界,量子包络孤子变成了量子内禀局域模,它的量子本征频率在简谐波带的顶部上方,量子磁振子主要集中在中心位置j=j0的附近.     

二维随机增益介质中局域模的模面积和放大

随机激光形成于随机介质中局域模的放大,其放大特性依赖于局域模的空间分布。通过复折射率的虚部将光学增益引入系统,采用时域有限差分(FDTD)法,分析了增益介质中局域模的放大特性,并用模面积描述了局域模空间分布,着重对比分析了模面积对局域模放大特性的影响。模拟结果显示,局域模具有不同的空间分布,直接影响了局域模的放大特性,模面积较小的模式具有较低的损耗,能够获得更多能量,在介质中被优先放大,而模面积较大的模式,由于损耗较大,将获得较少的能量。     

Magnetostatic modes of a lateral ferromagnetic/ferromagnetic superlattice

In this Letter, we calculate the magnetostatic modes of a semi-infinite lateral ferromagnetic/ferromagnetic superlattice with the effective-medium theory and present the general features of the modes. The numerical calculations for Co/Ni superlattice show some interesting properties which different from the lateral ferromagnetic/nonmagnetic superlattice. Two branches of the surface modes appear for the superlattice. Comparing with the surface magnetostatic modes of bulk Ni, one branch of the mode is of high frequency; the other branch of mode is of low frequency.