Showing papers by "Sheldon Schultz published in 1993"

Photonic band structure and defects in one and two dimensions

Abstract: We present an experimental and numerical study of electromagnetic wave propagation in one-dimensional (1D) and two-dimensional (2D) systems composed of periodic arrays of dielectric scatterers. We demonstrate that there are regions of frequency for which the waves are exponentially attenuated for all propagation directions. These regions correspond to band gaps in the calculated band structure, and such systems are termed photonic band-gap (PBG) structures. Removal of a single scatterer from a PBG structure produces a highly localized defect mode, for which the energy density decays exponentially away from the defect origin. Energy-density measurements of defect modes are presented. The experiments were conducted at 6–20 GHz, but we suggest that they may be scaled to infrared frequencies. Analytic and numerical solutions for the band structure and the defect states in 1D structures are derived. Applications of 2D PBG structures are briefly discussed.

Observation of thermal switching of a single ferromagnetic particle

Abstract: A magnetic force microscope (MFM) has been shown to be able to detect fields emanating from submicrometer permalloy particles with magnetic moments as low as 10−13 emu. We have used this MFM equiped with an in situ electromagnet to study the angular dependence of the switching field Hs(θ), and the probability of thermal switching of a single‐domain permalloy particle as a function of the time duration of an applied magnetic field H. The angular dependence of Hs(θ) is significantly different from that expected for coherent rotation. For applied magnetic fields close to Hs, the time dependence of the probability for not switching cannot be fit with a simple exponential. These data indicate that multiple‐energy barriers of similar height are involved in the thermally activated process responsible for the reversal.

Magnetostatic-mode spectrum of rectangular ferromagnetic particles.

Abstract: Approximate methods for obtaining the magnetostatic mode spectrum of thin rectangular samples have been known for some time. However, our experimental results from lithographic arrays of submicron Permalloy particles show that these methods perform relatively poorly if the (in-plane) applied field is not large compared to 4\ensuremath{\pi}${\mathit{M}}_{\mathit{s}}$. We present an improved method for finding the spectrum that takes into account both the elliptical character of the mode precession and sample edge effects. We show that the case of an infinite magnetic strip can be reduced to a one-dimensional eigenvalue problem which we solve numerically, yielding insight into the more difficult rectangular case. Effects of the nonuniform demagnetization field on the spatial patterns and frequencies of the modes are also studied.

Absence of Cu2+ electron-spin resonance in high-temperature superconductors and related insulators up to 1150 K.

Abstract: One unresolved question in the high-temperature superconductors and their copper oxide parent compounds is the absence of a Cu[sup 2+] electron-spin-resonance (ESR) signal even at temperatures well above the Neel temperature. We have extended the measurements up to 1150 K in both single crystals and ceramic pellets of La[sub 2]CuO[sub 4+[delta]], 0[approx lt][delta][approx lt]0.12, and no ESR signal has been observed. Our data are not compatible with the models based only on magnetic fluctuations which predict an ESR linewidth of a few hundred Oe at such high temperatures. Other suggested explanations for the absence of a Cu[sup 2+] ESR signal are discussed.

Internal magnetic field in La2-xSrxCuO4:Gd observed by electron paramagnetic resonance.

Abstract: We have measured the electron paramagnetic resonance (EPR) of Gd3+ in single crystals of La2-xSrxCuO4+δ, as a function of temperature T, magnetic-field angle, oxygen content, microwave frequency, and Sr concentration (0≤x≤0.024). For temperatures larger than the antiferromagnetic ordering temperature of the Cu lattice, TN, we have identified four different sites of Gd3+ as expected for twinned crystals and we are able to fit the data for all directions of the magnetic field. Samples annealed under vacuum or oxygen show only small changes on their crystal-field parameters and g values. For temperatures smaller than TN, the EPR lines are further split due to the internal magnetic field acting at the Gd site associated with the antiferromagnetic ordering of the Cu lattice. The temperature dependence of the splitting of the resonance lines allow us to calculate the moment per Cu ion. A value of ∼0.6μB per Cu ion at T=0 K is inferred, with the Cu moments lying in the bc plane about 5°from the c axis. The data only can be fit for all the directions of the applied magnetic field if other mechanisms such as a Heisenberg type of exchange between the Cu and Gd moments or a distortion of the lattice below TN are included. © 1993 The American Physical Society.

Noise analysis and image focusing for magnetic force microscopy

Abstract: Magnetic force microscopy (MFM) has been widely utilized to reveal magnetization distributions by sensing the external magnetic‐field distribution very close to the sample. The resolution of MFM is determined by the size of the sensor tip and by the spacing between the tip and the measured sample. A technique is developed to analyze the noise and linearity of a MFM image, and consequently to improve the spatial resolution by reducing the spacing loss. As a demonstration, a series of MFM images of a single permalloy particle is obtained and numerically analyzed. The spacing loss is reduced and a much higher resolution image is obtained.

Further development of a scanned near-field optical microscope for magneto-optic Kerr imaging of magnetic domains with 10nm resolution

Abstract: Work is described on the development of a scanning near-field optical microscope (SNOM) for the primary purpose of imaging magnetic systems with resolution on the order of 10 nm. Since many magnetic materials are optically opaque, it is desired to have a probe which is appropriate for the reflection mode. The near-field probe must be linearly polarizable, since the magneto-optic kerr effect (MOKE) is utilized for magnetic imaging. Data will be presented on the characterization and use of ∼30 nm diameter Ag particles as probes for MOKE-sensitive SNOM. Such small metal particles exhibit a localized plasmon resonance in the visible, which greatly enhances their optical scattering cross-section. We have made a systematic study of the light scattering properties of single Ag particles from 20 to 30 nm in size with a high-sensitivity micro spectrophotometer system, for several reasons: (1) To compare the light scattering properties of individual particles with the predictions of Mie theory; (2) to understand the polarization sensitivity of the optical scattering properties of real aspherical particles; and (3) to optimize the probe-sample separation distance for various magnetic materials of interest Ag particles prepared by colloidal chemistry techniques have been deposited on Bi-doped YIG and silica-coated permalloy to measure the magnitude of near-field MOKE. Near-field MOKE polarization rotations of 1.5 and 6.5 milliradians were measured for permalloy and YIG, respectively.

Photonic band gap resonators for high energy accelerators

Abstract: We have proposed that a new type of microwave resonator, based on photonic band gap (PBG) structures, may be particularly useful for high energy accelerators. We provide an explanation of the PBG concept and present data which illustrate some of the special properties associated with such structures. Further evaluation of the utility of PBG resonators requires laboratory testing of model structures at cryogenic temperatures, and at high fields. We provide a brief discussion of our test program, which is currently in progress. >

Field-induced spin reorientation in Eu2CuO4:Gd studied by magnetic resonance.

Abstract: We report a magnetic-resonance study of Gd-doped ${\mathrm{Eu}}_{2}$${\mathrm{CuO}}_{4}$ single crystals. Cooling the samples in a magnetic field ${\mathbf{H}}_{\mathrm{FC}}$, induces weak ferromagnetism (WF), with a strong out-of-plane anisotropy determined by the Dzyaloshinsky-Moriya (DM) interaction. In addition, there is in-plane anisotropy with an easy-axis parallel to the [110] crystal axis closest to ${\mathbf{H}}_{\mathrm{FC}}$. An intense resonance mode is observed at the X band (9.5 GHz) when ${\mathbf{H}}_{\mathrm{FC}}$ is applied parallel to one of the 〈110〉 axes and the measuring field is rotated by 90\ifmmode^\circ\else\textdegree\fi{} in the ${\mathrm{CuO}}_{2}$ plane. At the Q band (35 GHz), the in-plane resonance modes strongly depend on angle and temperature. We analyze the experimental results in terms of a phenomenological model for the magnetic free energy, which predicts a reorientation transition of the WF component of the magnetization ${\mathbf{m}}_{\mathrm{WF}}$ induced by the external field. Associated with this transition, a softening of the WF magnetic resonance mode occurs when the external field is applied perpendicular to the easy magnetization axis. The resulting angular variation of the resonance modes depends on whether the energy gap for the magnetic excitations is larger or smaller than the microwave energy. From the resonance data we have determined both the out-of-plane and in-plane anisotropy fields, ${\mathit{H}}_{\mathrm{DM}}$(T) and ${\mathit{H}}_{\mathrm{ax}}$(T), respectively.The extrapolated values for T=0 are ${\mathit{H}}_{\mathrm{DM}}$(0)=3.5(5)\ifmmode\times\else\texttimes\fi{}${10}^{5}$ G and ${\mathit{H}}_{\mathrm{ax}}$(0)=12(2) G. Both anisotropy fields decrease with increasing T, vanishing around ${\mathit{T}}_{\mathit{N}}$\ensuremath{\simeq}243 K. The temperature dependence of the peak-to-peak linewidths, \ensuremath{\Delta}${\mathit{H}}_{\mathrm{pp}}$, measured at the X and Q bands is explained in terms of a temperature-independent frequency linewidth, \ensuremath{\Delta}${\mathrm{\ensuremath{\omega}}}_{1/2}$/\ensuremath{\gamma}=1.6(2) kG. Nonresonant absorption losses around the maxima and minima of the \ensuremath{\omega}/\ensuremath{\gamma} vs H curves are also described in terms of this finite width for the resonance modes.

Measurements of Localization and Photonic Band Gap Systems in Two-Dimensions

Abstract: We report the results of experimental investigations of two dimensional periodic and random scattering systems. The systems consist of arrays of dielectric cylindrical scatterers bounded on top and bottom by conducting sheets. We present the results of measurements made on defect modes created by removing part or all of a scatterer from an otherwise perfect lattice. We also present a series of measurements made on localized modes created by randomly removing an increasing number of scatterers. Discussion of applications for photonic band gap structures is included.