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We present the results of micromagnetic study of magnonic band structures for exchange spin waves propagating in two-dimensional magnonic crystal waveguides. The studied waveguides are in the form of a regular square lattice array of square dots of a ferromagnetic material embedded in a matrix of another ferromagnetic material. Large magnonic bandgaps with widths of tens of GHz are observed. The bandgaps are also studied as a function of in-plane applied magnetic field, and the width of the square dots. The widths of the first three bandgaps are dependent on the material configurations of the waveguides, but are independent of applied field strength.

We report a micromagnetic investigation of the propagation of spin waves in bi-component magnonic crystal waveguides. The investigated nanostructured waveguides are in the form of regular square lattice arrays of circular Fe dots embedded in a yttrium iron garnet matrix. Magnonic bandgaps of the order of 10 GHz are observed in both calculated frequency power spectra and dispersion curves of spin wave. The effect of the variation of the period along the direction perpendicular to spin wave propagation on magnonic band structures of magnonic crystal waveguides has been investigated. Micromagnetic simulations show that the first bandgap is more sensitive to variations of period than the second bandgap.

Most experimental investigations into magnonic bandgaps are based on structures composed of single-constituent magnetic materials. Here we report Brillouin and numerical studies of the spin dynamics of a bi-component magnonic crystal, viz. a one-dimensional periodic array of alternating permalloy and cobalt 150 nm-wide nanostripes. Our measurements, together with those for a similar crystal composed of 250 nm-wide nanostripes, suggest that for a stripe width ratio of 1:1, the bandgap width of such magnonic arrays increases with crystal lattice constant. The bandgap parameters are strongly dependent on external magnetic field. This magnetic-field tunability of the bandgap is expected to be a crucial property of devices based on magnonic crystals. The agreement between numerical calculations, based on finite element analysis, and the experimental data is generally good.

The intriguing optical and catalytic properties of metal-silica core-shell nanoparticles, inherited from their plasmonic metallic cores together with the rich surface chemistry and increased stability offered by their silica shells, have enabled a wide variety of applications. In this work, we investigate the confined vibrational modes of a series of monodisperse Ag@SiO(2) (cubic core)-shell nanospheres synthesized using a modified Stöber sol-gel method. The particle-size dependence of their mode frequencies has been mapped by Brillouin light scattering, a powerful tool for probing hypersonic vibrations. Unlike the larger particles, the observed spheroidal-like mode frequencies of the smaller ones do not scale with inverse diameter. Interestingly, the onset of the deviation from this linearity occurs at a smaller particle size for higher-energy modes than for lower-energy ones. Finite element simulations show that the mode displacement profiles of the Ag@SiO(2) core-shells closely resemble those of a homogeneous SiO(2) sphere. Simulations have also been performed to ascertain the effects that the core shape and the relative hardness of the core and shell materials have on the vibrations of the core-shell as a whole. As the vibrational modes of a particle have a bearing on its thermal and mechanical properties, the findings would be of value in designing core-shell nanostructures with customized thermal and mechanical characteristics.

The low-frequency acoustic dynamics of multilayer graphene flakes, on SiO 2 /Si substrate, have been studied by polarized Brillouin light scattering. Interference enhancement affords the first observation of both the in-plane longitudinal and transverse acoustic bulk modes near the Γ-point of the Brillouin zone. The experimental data yielded information on the acoustic and elastic properties of multilayer graphene. Additionally, the measured phonon dispersion is found to be in good accordance with that evaluated for graphene, based on first-principles calculations within the generalized gradient approximation. Our findings strongly suggest that the interaction between layers in multilayer graphene is weak.

The localized acoustic modes of single isolated polymethyl methacrylate (PMMA) and polystyrene nanospheres have been studied by micro-Brillouin light scattering. The measured mode frequencies are analyzed on the basis of the Lamb theory formulated for a sphere under free boundary conditions. By measuring light scattering from single isolated particles, placed atop a piece of polished silicon wafer, the free-surface conditions are almost experimentally realized. The observed spectral peaks are attributed to localized eigenvibrations whose frequencies scale as inverse sphere diameter, in accordance with Lamb's theory. The Young's moduli and Poisson ratios of the polymer spheres studied have been evaluated from fits to the experimental data. We have demonstrated that micro-Brillouin spectroscopy is a powerful technique for probing the acoustic dynamics and mechanical properties of nanostructures.

Regular arrays of oval-shaped permalloy nanorings have been fabricated using deep ultraviolet lithography and their spin dynamics measured by Brillouin light scattering with the magnetic field applied along long (easy) axes of the rings. The dispersionless behavior of the spin wave modes observed reveals their standing wave nature. Two-dimensional simulations and analytical calculations have been performed for a single isolated nanoring. Results reveal that the observed modes can be interpreted in terms of quantized Damon–Eshbach modes due to lateral confinement in the finite size rings.

Spin-wave nonreciprocity arising from dipole-dipole interaction is insignificant for magnon wavelengths in the sub-100 nm range. Our micromagnetic simulations reveal that for the nanoscale magnonic crystals studied, such nonreciprocity can be greatly enhanced via synthetic antiferromagnetic coupling. The nonreciprocity is manifested as highly asymmetric magnon dispersion curves of the magnonic crystals. Furthermore, based on the study of the dependence of the nonreciprocity on an applied magnetic field, the antiparallel alignment of the magnetizations is shown to be responsible for the enhancement. Our findings would be useful for magnonic and spintronics applications. MOE (Min. of Education, S’pore) Published version

Brillouin measurements have been made of the spin dynamics of high-density two-dimensional hexagonally ordered 20 nm diameter Fe48Co52 nanowire arrays, with various interwire spacings, as a function of longitudinal magnetic field. The experimental data are analyzed within the Arias-Mills theory based on interwire dipolar couplings in the arrays. The results provide conclusive evidence of collective spin waves arising from the dipolar coupling which is manifested as a reduction in spin wave frequency with decreasing interwire spacing.

Brillouin scattering from aggregates of monodisperse polystyrene spheres has been measured as a function of their diameters (20 - 990nm). In this range of sphere sizes studied, confined acoustic modes and two types of bulk longitudinal acoustic modes are observed. One type exists within larger spheres (diameter > 700 nm), while the other propagates in aggregates of smaller spheres (diameter ≤ 80 nm) which are considered as polystyrene-air composites. The frequencies of the confined acoustic modes are found to be proportional to inverse sphere diameter, in accordance with Lamb's theory.

The coercivity of magnetic thin film having a two-dimensional easy-axis distribution is investigated within the framework of a simple micromagnetic model. It is found that the coercivity decreases from 0.14H(K) to a minimum of 0.07H(K) as thickness increases, where H(K) is the anisotropy field. It is substantially lower than that given by the Stoner-Wohlfarth model and is consistent with available experimental data. The calculated hysteresis loop and the initial magnetization curve are also in good agreement with experiments.

We present our simulated initial magnetization curves for nanostructured permanent magnets based on a simple hybrid model. The model assumes that the reversible change in the magnetization curves obeys the Stoner–Wohlfarth (SW) model while the irreversible part can be attributed to the motion of the transition region (TR), which is a domain-wall-like magnetic moment distribution formed in the grain boundary due to exchange interaction between neighboring grains with different easy axis orientations. The calculated full hysteresis coercivity Hcm (=0.14HK) is in reasonable agreement with available experimental data, where HK is the anisotropy field. Both the calculated remanence Mr and coercivity Hc increase rapidly with the maximum applied field Hm at lower field (Hm

Novel procedures to determine the parallel upper critical field Bc2 (one-dimensional, 1D) have been proposed within a continuous Ginzburg–Landau model. Unlike conventional methods, where Bc2 is obtained through the determination of the smallest eigenvalue of an appropriate eigen equation, the square of the magnetic field is treated as eigenvalue problems by two procedures so that the upper critical field can be directly deduced. The two procedures proposed are extended to determine the upper critical field in the c–a crystal plane (two-dimensional, 2D) with an arbitrary angle θ tilted from the c-axis. The calculated Bc2 from the two procedures are consistent with each other in both 1D and 2D cases. Moreover, the values of Bc2 near the direction parallel to the layers obtained in the 2D case well approximate the counterparts in the 1D case. The properties of the calculated Bc2 are in reasonably good agreement with existing theories and experiments. The profiles of the order parameters associated with Bc2 for both 1D and 2D cases are Gaussian-like, further validating the methodology proposed.

The velocity angular dispersion of Rayleigh surface and bulk acoustic modes propagating parallel to the surfaces of (100), (110) and (111) SrTiO3 plates has been measured by surface Brillouin scattering. Transverse bulk acoustic modes propagating in certain directions are not detected in the scattering geometry employed. The nonobservation of these modes is consistent with results of a calculation of their scattering coefficient. A simultaneous fit to the experimental data on the bulk acoustic modes for the three crystal orientations yields elastic constants that are used to accurately predict the various velocity angular dispersion branches of the Rayleigh surface mode.

The velocity angular dispersion of bulk acoustic modes propagating parallel to the surfaces of X-, Y- and Z-cut crystal plates of LiNbO3 has been measured by Brillouin scattering. The elastic and piezoelectric stress constants of LiNbO3 at hypersonic frequencies, determined from a simultaneous fit to data from the three crystal cuts, are found to be only marginally more accurate than those based on only the X-cut data. Calculations based on the constants fitted to the X-cut data alone predicted accurately the velocity angular dispersion of the surface Rayleigh wave measured simultaneously. The first leaky surface wave on the Z-cut crystal is also experimentally observed whose velocity angular dispersion agrees with the theoretical dispersion computed from the fitted constants. Evidence of dispersion between ultrasonic and hypersonic velocities is found for both surface and bulk acoustic waves.

The particle-size dependence of the eigenfrequencies of confined acoustic modes of aggregates of highly monodisperse silver nanocubes has been measured by Brillouin light scattering. Four Brillouin peaks are observed whose frequencies scale with inverse cube edge length. They are assigned to the D d 1 , D d 2 , D s 1 (symmetric breathing vibration) and D s 2 dilatational modes, labeled using the Demarest classification scheme. The assignment, which is based on numerically simulated frequencies and displacement profiles of the modes, as well as their calculated scattering cross-sections, differs from those of earlier studies on nanocubes. The elastic moduli of the silver cubes, with mean edge lengths between 59–102 nm, are found to be comparable to those of the bulk material, indicating the absence of sample defects like pores and cracks.

The interfacial Dzyaloshinskii-Moriya interaction (DMI) in an in-plane anisotropic Pt(4nm)/Co(1.6nm)/Ni(1.6nm) film has been directly observed by Brillouin spectroscopy. It is manifested in the asymmetry of the measured magnon dispersion relation, from which the DMI constant has been evaluated. Linewidth measurements reveal that the lifetime of the magnons is asymmetric with respect to their counter-propagating directions. The lifetime asymmetry is dependent on the magnon frequency, being more pronounced the higher the frequency. Analytical calculations of the magnon dispersion relation and linewidth agree well with experiments., 15 pages, 4 figures

The nonreciprocal propagation of spin waves in an ultrathin Pt/Co/Ni film has been measured by Brillouin light scattering. The frequency nonreciprocity, due to the interfacial Dzyaloshinskii-Moriya interaction (DMI), has a sinusoidal dependence on the in-plane angle between the magnon wavevector and the applied magnetic field. The results, which are in good agreement with analytical predictions reported earlier, yield a value of the DMI constant which is the same as that obtained previously from a study of the magnon dispersion relations. We have demonstrated that our magnon-dynamics based method can experimentally ascertain the DMI constant of multilayer thin films., Comment: 11 pages, 3 figures

The phenomenon of magnetization reversal in a hard magnet is studied analytically within a framework of a simplified energy minimization model for a two grain system. The transition region (a domain wall-like moment structure) is found to play a crucial role in nucleating a reversed domain and in the subsequent formation of a domain wall near the grain boundary. This is shown to result in a considerable reduction in coercivity. Temperature effects are taken into account by considering thermally activated jumps over energy barriers that hinder the motion of the transition region. We found that thermal fluctuations at room temperature can substantially reduce coercivity provided the grains are sufficiently small.

Employing numerical calculations and our recently developed analytical approach, we calculate the lowest bandgaps in one-dimensional magnonic crystals comprising periodic arrays of submicron stripes of two alternating magnetic materials. Using suitable approximations, we simplify and recast the analytic expressions for their bandgap width and center frequency, formulated in our recent study, into a form that provides insight into the dependence of the bandgap on geometric and magnetic properties of the magnonic crystals. Calculations based on the simplified analytical formulae accord well with numerical calculations.

Using Brillouin spectroscopy, the first observation has been made of the band structures of nanostructured defect magnonic crystals. The samples are otherwise one-dimensional periodic arrays of equal-width Ni80Fe20 and cobalt nanostripes, where the defects are stripes of a different width. A dispersionless defect branch emerges within the bandgap with a frequency tunable by varying the defect stripe width, while the other branches observed are similar to those of a defect-free crystal. Micromagnetic and finite-element simulations performed unveil additional tiny bandgaps and the frequency-dependent localization of the defect mode in the vicinity of the defects., 5 pages, 5 figures

Using Brillouin scattering, we have measured the velocity angular dispersion of the surface and bulk acoustic waves in X-cut and 36° Y-cut LiTaO3. The complete set of twelve independent acoustic physical constants at hypersonic frequencies is evaluated using a simultaneous fit to only the velocity angular dispersion data on both surface Rayleigh and bulk acoustic waves. In comparison to physical constants determined in the ultrasonic frequency range, our acoustic constants yield better agreement between theory and experiment for the angular dispersion of the surface Rayleigh and second leaky wave velocities. Additionally, computation based on these acoustic constants has accurately predicted the velocity angular dispersion of the bulk waves and their scattering coefficients.

In this paper, we report our extensive investigations of layered superconductors within a continuous Ginzburg-Landau model. The calculated results suggest that the parallel upper critical field generally increases with the transition temperature and may be correlated with the behaviours of the order parameters. The calculated upper critical fields of MgB2 are in reasonably good agreement with experiment. The obtained order parameters of MgB2, YBCO and Hg1223 respectively demonstrate a three-dimensional, quasi-three-dimensional and two-dimensional behaviour, as expected.

The behaviour of the order parameter and its effects in intrinsically-layered superconductors are studied within a continuous Ginzburg-Landau model. A simple model of interlayer coupling is proposed in which we suggest that the coupling strength between superconducting and insulating layers may be qualitatively described by a reciprocal of a difference between the order parameters at the respective layers. The feasibility of such an approach is demonstrated by considering Hussey's magnetization experiments, the case of Tc depression observed in iodine-intercalated and Pb-substituted Bi2Sr2CaCu2O8+δ, and some other properties and experiments in layered superconductors.

We have grown MnSb films on sapphire substrates by hot wall epitaxy. A series of films with thicknesses of 80, 155 and 230 nm was prepared to determine the thickness dependence of their magnetic and magneto-optical properties. Our results indicate that the thinnest and thickest films possess largest coercivity and saturation magnetization, respectively. The largest Kerr rotation angle was also found in the thickest film for both the longitudinal and polar Kerr rotations, reaching a maximum of 0.31°. We attribute this behavior to the thickness dependence of both the film magnetization orientation and its atomic composition.

MnSb(1 0 1) thin films with different thicknesses have been successfully epitaxied on GaAs(1 0 0) substrates by the hot-wall epitaxy method. The effects of substrate-induced lattice strains on the structural, magnetic and magneto-optical properties of these films have been studied. It was found that the coercivity of the film increases (and the saturation magnetization decreases) with decreasing film thickness. Measurements of the Kerr rotation angle were made using a home-made magnetic optical Kerr effect system. The Kerr rotation angle increases with film thickness but no measurable angle is observed when the film thickness is about 27 nm. The shape of the Kerr rotation curve is found to be similar to the magnetic hysteresis loop measured by a vibrating sample magnetometer.

Based on a simple micromagnet model, we show that an analytical expression for reduced remanence in single-phased and single-domain isotropic nanostructured permanent magnetic materials can be written as Mr/MS=0.5+1.8Δ0/L, where M r , M S , Δ 0 , and L are the remanence, saturation magnetization, exchange length and the average grain size, respectively. This formula reveals that our calculated remanence is larger than the predictions of the Stoner–Wohlfarth model for all particle sizes, and that remanence enhancement increases with decreasing grain size. Application of the relation to melt-spun Nd–Fe–B magnets shows good agreement with available experimental and numerical data.

The remanence of an isotropic nanocrystalline exchange-coupled composite system (comprising hard and soft magnetic phases) is investigated analytically within a simple (one-dimensional) micromagnetic model, in which only exchange and anisotropy energies are considered. For a soft grain with size much less than its own Bloch wall width, our analysis shows that the magnetization distribution in the soft phase is linearly dependent upon position, which we show is responsible for the significant enhancement observed in composite systems. Furthermore, we show that a good estimate of the remanence can be provided by a simple formula, which is easily calculated by hand.

The elastic vibrations of spherical nanoparticles have been widely studied by Raman scattering. However, there exist more than one set of selection rules for Raman scattering from these vibrations. For instance, Kanehisa has stated that only torsional modes with angular momentum l = 2 are Raman-active, while Tanaka et al. proposed that spheroidal modes of even l and torsional modes of odd l are Raman-active. These contradict selection rules of Duval which states that only spheroidal modes of l = 0 or 2 are Raman-active. Our present calculations based on a macroscopic model show that all torsional modes have vanishing intensity in the Raman spectrum.

A Comment on the Letter by K.-S. Lee, D.-S. Han, and S.-K. Kim, Phys. Rev. Lett. 102, 127202 (2009). The authors of the Letter offer a Reply.

The two-dimensional transfer function is derived from the Synthetic Aperture Radar (SAR) imaging model. Using this expression, the approximations made in the classical range-Doppler and recent chirp-scaling algorithms are examined. An alternative algorithm to the chirp-scaling algorithm is presented. Unlike the chirp-scaling algorithm, this algorithm does not require the transmitted signal to be a linear FM signal and can be easily incorporated into processors using the range-Doppler algorithm. The processing starts with range compressed data rather than from the raw SAR data. Results from processing simulated point targets and the Seasat Goldstone area data show comparable image quality.

Brillouin scattering from loose silica microspheres has been investigated as a function of their diameter (140 nm to 4 μm). The measured linear dependence of the confined acoustic mode frequencies on the inverse sphere diameters accords well with Lamb’s theory. Bulk acoustic modes are also observed in the larger microspheres, suggesting that the limiting size of a particle for these modes to be observable is about three times their wavelength. Internal consistency in the analyses of the bulk and confined mode data shows the validity of this Brillouin technique in the evaluation of the elastic properties of microspheres. Additionally it also affords a means of sizing the diameters of microspheres.

Phononic and magnonic dispersions of a linear array of periodic alternating Ni80Fe20 and bottom anti-reflective coating nanostripes on a Si substrate have been measured using Brillouin light scattering. The observed phononic gaps are considerably larger than those of laterally patterned multi-component crystals previously reported, mainly a consequence of the high elastic and density contrasts between the stripe materials. Additionally, the phonon hybridization bandgap has an unusual origin in the hybridization and avoided crossing of the zone-folded Rayleigh and pseudo-Sezawa waves. The magnonic band structure features near-dispersionless branches, with unusual vortex-like dynamic magnetization profiles, some of which lie below the highly-dispersive fundamental mode branch. Finite element calculations of the phononic and magnonic dispersions of the magphonic crystal accord well with experimental data.

We theoretically demonstrate linear spin-wave nonreciprocity in a Ni80Fe20 nanostripe waveguide, based on interband magnonic transitions induced by a time-reversal and spatialinversion symmetry breaking magnetic field. An analytical coupled-mode theory of spin waves, developed to describe the transitions which are accompanied by simultaneous frequency and wavevector shifts of the coupled spin waves, is well corroborated by numerical simulations. Our findings could pave the way for the realization of spin-wave isolation and the dynamic control of spin-wave propagation in nanoscale magnonic integrated circuits via an applied magnetic field., Comment: 14 pages and 3 figures

The spin-wave dispersions in nanostructured magnonic crystals with periodic defects have been mapped by Brillouin light scattering. The otherwise perfect crystals are one-dimensional arrays of alternating 460nm-wide Ni80Fe20 stripes and 40nm-wide air gaps, where one in ten Ni80Fe20 stripes is a defect of width other than 460 nm. Experimentally, the defects are manifested as additional Brillouin peaks, lying within the first and second bandgaps of the perfect crystal, whose frequencies decrease with increasing defect stripe width. Finite-element calculations, based on a supercell comprising one defect and nine perfect Py stripes, show that the defect modes are localized about the defects, with the localization exhibiting an approximate U-shaped dependence on defect size. Calculations also reveal extra magnon branches and the opening of mini-bandgaps, within the allowed bands of the perfect crystal, arising from Bragg reflections at the boundaries of the shorter supercell Brillouin zone. Simulated magnetization profiles of the band-edge modes of the major and mini-bandgaps reveal their different symmetries and localization properties. The findings could find application in microwave magnonic devices like single-frequency passband spin-wave filters.

The Asian monsoon is a planetary-scale circulation system powered by the release of latent heat, but important features of deep convection and rainfall distribution cannot be adequately represented by the large-scale patterns. This is mainly due to the strong influences of terrain that are important across a wide range of horizontal scales, especially over the Maritime Continent where the complex terrain has a dominant effect on the behavior of convective rainfall during the boreal winter monsoon. This chapter is a review and summary of published results on the effects on monsoon convection due to interactions between the Maritime Continent terrain and large-scale transient systems. The Maritime Continent topographic features strongly affect both the demarcation of the boreal summer and winter monsoon regimes and the asymmetric seasonal marches during the transition seasons. In the western part of the region, the complex interactions that lead to variability in deep convection are primarily controlled by the cold surges and the synoptic-scale Borneo vortex. The Madden–Julian oscillation (MJO) reduces the frequency of weaker surges through an interference with their structure. It also influences convection, particularly on the diurnal cycle and when synoptic activities are weak. When both surges and the Borneo vortex are present, interactions between these circulations with the terrain can cause the strongest convection, which has included Typhoon Vamei (2001), which is the only observed tropical cyclone that developed within 1.5° of the equator. The cold surges are driven by midlatitude pressure rises associated with the movement of the Siberian high. Rapid strengthening of surge northeasterly winds can be explained as the tropical response via a geostrophic adjustment process to the pressure forcing in the form of an equatorial Rossby wave group. Dispersion of meridional modes leads to a northeast–southwest orientation that allows the surge to stream downstream through the similarly oriented South China Sea. This evolution leads to a cross-equatorial return flow and a cyclonic circulation at the equator, and thus a mechanism for equatorial cyclogenesis. Although the narrow width of the southern South China Sea facilitates strengthening of the cold surge, it also severely restricts the likelihood of cyclone development so that Vamei remains to be the only typhoon observed in the equatorial South China Sea. Climate variations from El Niño–Southern Oscillation to climate change may impact the interactions between the large-scale motion and Maritime Continent terrain because they lead to changes in the mean flow. The thermodynamic effects on the interaction between MJO and the monsoon surges and Borneo vortex over the complex terrain also need to be addressed. These and other questions such as any possible changes in the likelihood of equatorial tropical cyclogenesis as a result of climate change are all important areas for future research.

The magnonic band structures for exchange spin waves propagating in one-dimensional magnonic crystal waveguides of different material combinations are investigated using micromagnetic simulations. The waveguides are periodic arrays of alternating nanostripes of different ferromagnetic materials. Our results show that the widths and center frequencies of the bandgaps are controllable by the component materials, the stripe widths, and the orientation of the applied magnetic field. One salient feature of the bandgap frequency plot against stripe width is that there are n-1 zero-width gaps for the n th bandgap for both transversely and longitudinally magnetized waveguides. Additionally, the largest bandgap widths are primarily dependent on the exchange constant contrast between the component materials of the nanostructured waveguides.

We have employed a parametrized tight-binding molecular-dynamics scheme in the study of the phenomenon of vacancies on the Si(001) c(4*2) surface. Simulated annealing is performed with a 'fictitious-Lagrangian' procedure to determine the optimal structures of a single and a dimer vacancy on this surface. A monovacancy is found to be less stable than a dimer vacancy, which agrees with experimental observations. We also show that there is a possible anisotropy in the surface migration of a dimer vacancy on the surface. The calculated activation energy for dimer-vacancy diffusion is 0.6 eV higher than that estimated experimentally at high temperatures.

Quenching of a liquid Pb droplet containing 8217 atoms to T ∼ 0.65 T m is studied on the nanosecond time scale using molecular dynamics and a “glue” force model. Crystallization takes place, and analysis of the final structure reveals an icosahedral-like shape, even if cuboctahedral single crystal structures are energetically favoured by our potential for all sizes. This result appears to be a consequence of the rapid formation of {111} crystallization fronts at the liquid surface and moving inward, and provides an explanation for the rapid structural fluctuations observed in electron microscopy experiments.

An understanding of the spin dynamics of nanoscale magnetic elements is important for their applications in magnetic sensing and storage. Inhomogeneity of the demagnetizing field in a non-ellipsoidal magnetic element results in localization of spin waves near the edge of the element. However, relative little work has been carried out to investigate the effect of the applied magnetic fields on the nature of such localized modes. In this study, micromagnetic simulations are performed on an equilateral triangular nanomagnet to investigate the magnetic field dependence of the mode profiles of the lowest-frequency spin wave. Our findings reveal that the lowest-frequency mode is localized at the base edge of the equilateral triangle. The characteristics of its mode profile change with the ground state magnetization configuration of the nanotriangle, which, in turn, depends on the magnitude of the in-plane applied magnetic field.

Just as a photonic crystal is a periodic composite composed of materials with different dielectric constants, its lesser known magnetic analogue, the magnonic crystal can be considered as a periodic composite comprising different magnetic materials. Magnonic crystals are excellent candidates for the fabrication of nanoscale microwave devices, as the wavelengths of magnons in magnonic crystals are orders of magnitude shorter than those of photons, of the same frequency, in photonic crystals. Using advanced electron beam lithographic techniques, we have fabricated a series of novel bicomponent magnonic crystals which exhibit well-defined frequency bandgaps. They are in the form of laterally patterned periodic arrays of alternating cobalt and permalloy stripes of various widths ranging from 150 to 500 nm. Investigations by Brillouin light scattering and computer modeling show that the dispersion spectrum of these crystals is strongly dependent on their structural dimensions. For instance, their first frequency bandgap is found to vary over a wide range of 1.4-2.6 gigahertz. Such a functionality permits the tailoring of the bandgap structure which controls the transmission of information-carrying spin waves in devices based on these crystals. Additionally, it is observed that the bandgap width decreases with increasing permalloy stripe width, but increases with increasing cobalt stripe width, and that the bandgap center frequency is more dependent on the stripe width of permalloy than that of cobalt. This information would be of value in the design of magnonic crystals for potential applications in the emerging field of magnonics.

The large errors observed in inverse filter or Wiener filter restorations of images are mainly due to the fact that only a truncated region of image data is available for processing. In the earlier literature, it was suggested that the well-known time-series windows may be generalized for treating these errors. This paper examines the windowing technique for the restoration of general blurred images. Mathematical expressions for the restoration errors that arise from truncated data are derived. Optimal windows for image restoration are then designed on the basis of these expressions. With these optimal windows, near-perfect restorations can be obtained if the images vary gradually in intensity near their borders. Restorations using the optimal windows and some well-known time-series analysis windows are presented for comparison of their performance.

On the basis of a previous analysis of the edge error in image restorations by the authors, two new classes of Fourier-domain restoration methods for motion-blurred images are proposed in this paper. In the spectral interpolation methods, the restoration problem is reduced to the estimation of a number of indeterminate spectral coefficients of the image. If we require that the restored image have the smallest possible variance, all the indeterminate spectral coefficients may be set to zero. Even such a simple implementation of the spectral interpolation method proves to be equivalent to the sophisticated spatial-domain method proposed by Sondhi. This suggests that the spectral interpolation method has great potential when used in conjunction with appropriate sophisticated methods for the interpolation of spectral coefficients. In the pixel difference interpolation method, a restoration is computed on the basis of the estimates of the differences in the intensity of adjacent pixels. A characteristic of this method is that we have the freedom to choose the locations at which the estimates are to be made. For images with patches of uniform intensity, the pixel differences within the regions of uniform intensity are small and can be accurately estimated. This fact may be exploited to obtain near-perfect restoration of such images, as demonstrated in actual restorations of test images. Even for highly textured images, restorations obtained using this method are found to be of a quality comparable to those obtained using Sondhi's and Ku and Hu's methods.

Estimating the PSF of a real-world motion-blurred image is an essential step in the restoration process. To estimate the PSF, some techniques assume that it is a spatially invariant square pulse, and extract the blur extent from the zero-crossings of the averaged power spectrum. Some techniques make use of special features such as isolated point objects or sharp edges in a homogeneous background. Recently, sophisticated methods based on maximum likelihood estimators have been developed for estimation of symmetrical PSFs. In actual applications, we often encountered motion-blurred images which have asymmetrical PSFs. There are also no special features such as isolated points. These images present challenges which are not satisfactorily met by the above techniques. In this paper, we first study the error characteristics due to the use of inappropriate PSFs. On the basis of the results, we develop a procedure for estimating (possibly) asymmetrical PSFs of real-world motion-blurred images. The procedure starts with a preliminary restoration using a ramp PSF. The result will indicate if a ramp PSF, a square pulse PSF, or a trapezoid PSF is appropriate, and also provide an estimate for the blur extent of the appropriate PSF. Images restored according to the procedure are practically free of ghost or ringing patterns. The effectiveness and practicality of the proposed procedure is tested using a few real-world images blurred with unknown PSF.

Selection rules governing Brillouin light scattering from the vibrational eigenmodes of a homogeneous, free-surface submicron sphere have been derived using group theory. The derivation is for the condition where the sphere diameter is of the order of the excitation light wavelength. Well-resolved spectral data obtained from Brillouin light scattering from submicron silica spheres provide experimental verification of the selection rules., 8 pages, 2 figures

Employing Brillouin spectroscopy, strong interfacial Dzyaloshinskii-Moriya interactions have been observed in an ultrathin Pt/CoFeB film. Our micromagnetic simulations show that spin-wave nonreciprocity due to asymmetric surface pinning is insignificant for the 0.8nmthick CoFeB film studied. The observed high asymmetry of the monotonic spin wave dispersion relation is thus ascribed to strong Dzyaloshinskii-Moriya interactions present at the Pt/CoFeB interface. Our findings should further enhance the significance of CoFeB as an important material for magnonic, spintronic and skyrmionic applications., Comment: 12 pages, 4 figures