S. Shtrikman

The theory of the Vogel-Fulcher law of spin glasses

Abstract The law governing the experimental temperature dependence of the relaxation time of spin glasses τ −1 = ƒ o exp [ −A (T − T o ) ] is interpreted in terms of interactions between the magnetic clusters constituting them.

Comparison between computed and measured bandwidth of quarter-wave microstrip radiators

A simple theory based on a cavity model is used to analyze a quarter-wavelength flat element, without a dielectric substrate, which is connected to the ground plane in one of its sides by a metallic wall. The bandwidth of the element is computed from this model. Very good agreement is obtained between the computed and the measured bandwidth for elements in the S-band. >

Moment-method solution of the center-fed microstrip disk antenna invoking feed and edge current singularities

The problem of a microstrip disk antenna excited by a probe at its center is studied using a moment-method approach for the evaluation of the surface current on the disk. The novelty of the work is a careful treatment of the singular effects of the probe and of the disk edge on the surface current on the disk. This is done by including in a proper way an attachment-mode current and an edge current in the surface current on the disk. The inclusion of these two currents accelerates the convergence of the moment-method solution and enables the input impedance to be obtained in a broad frequency range, including the zero-frequency limit. The influence of the probe on the input impedance is taken into account in a correct and accurate way. A comparison between measured and computed results is given, and good agreement is obtained. >

The energy of inclusions in linear media exact shape-independent relations

Abstract W e discuss the energy of an inclusion—a configuration whereby a “polarization” distribution is dictated in a bounded domain, D of a medium with linear-response properties. Such is the case when a stress-free strain is prescribed in a domain of an elastic medium, or when a magnet is introduced into a paramagnetic medium. First we treat elastic inclusions. We find that when an eigenstrain ϵ∗ij is dictated within D the energy cannot exceed W 0 =( 1 2 )∫ D e ∗ ij ( r )C ijkl ( r )e ∗ kl ( r )d 3 r Cijkl being the elastic tensor in the medium. The elastic energy for an inclusion with a constant eigenslrain, ϵ0ij in a homogeneous medium, is described by an energy tensor, I, such that the energy, W, is W=( 1 2 )e 0 ij I ijkl e 0 kl . The components of I—which depend on the geometry (shape and orientation) of the inclusion—satisfy a linear, geometry-independent relation of the form BijklIijkl = 3 V. where B is the inverse of the elastic tensor, and V is the volume of the inclusion. For a certain class of media, which include isotropic ones, a second relation is obeyed: B ikjl I ijkl = V (5 + 3v 2 ) sol [2(1-v 2 )] v is the Poisson ratio). As a special case. the components of the Eshelby tensor are found to obey a new linear relation of the form Sijij = 3. We also treat inclusions in a medium that responds linearly to many coupled scalar potentials, as in the magnetoelectric or thermoelectric effects. We find a bound on the energy (or entropy-generation rate when dealing with dissipative phenomena) of the form W 0 =( 1 2 )∫ D P kλ L -1 kmλβ P mβ d 3 r , where L(r) is the response-matrix of the medium, and Pkxr is the αspace component of the k-type external polarization field in the inclusion. Again, when the polarization fields arc constant. W is described in terms of an energy tensor Ikmxβ. We find that its components satisfy n(n + 1) 2 geometry-independent relations (n is the number of coupled fields) LkmxβImpxβ = δkpV. Analogous bounds and constraints on the energy tensor exist for inclusions in a medium that responds linearly to the most general phenomenon including coupled fields of different tcnsorial ranks, such as a piezoelectric or piezo-magneto-electric medium.

Critical exponents at a Lifshitz point to O(1/n)

Abstract The critical exponents at a general Lifshitz point are calculated in the spherical model limit, as are those of an isotropic Lifshitz point to O(1/ n ). These results are in exact agreement in the overlap region with those obtained using an ϵ-expansion.

A layered‐shell model of isotropic composites and exact expressions for the effective properties

A family of models for multicomponent, isotropic mixtures is suggested and discussed for which the exact values of the effective, linear‐response constants can be calculated: The basic unit of the model is a hollow system of contacting concentric shells, each of which is made of one of the components. Space is packed with such units of different sizes, but the same proportions; the cavity within each such shell system is then packed with similar systems, and this continues in an infinite nesting sequence. We deal with the general case of a linear‐response phenomenon involving n coupled driving fields; the effective response matrix is given in a closed form as a function of the volume fractions and the response matrices of the components. Some subfamilies are treated in more detail. For example, a two‐shell two‐phase family spanned by q, the volume fraction of the shells within the sphere they define. The special case q=1 is the well‐known coated‐sphere model. Varying q between zero and one, we get exact m...

Mössbauer Study of Some 2–17 Lanthanide‐Iron Compounds

We have studied the iron‐rich, rare‐earth‐iron intermetallic compounds R2Fe17 (R = Pr, Gd, Tm, Lu), using the Mossbauer effect in 57Fe. The measured average hyperfine field H(T/Tc) acting on the 57Fe nuclei is a unique, monotonically decreasing function of T/Tc, with no observed irregularity at temperatures corresponding to a suspected ferromagnetic‐antiferromagnetic phase transition in these compounds. The onset of paramagnetism occurs at temperatures close to the upper transition points measured by Strnat et al., namely at Tc = 282°, 472°, 271°, and 263°K for Pr2Fe17, Gd2Fe17, Tm2Fe17, and Lu2Fe17, respectively. Low‐temperature (≃90°K) spectra indicate the presence of at least four magnetically nonequivalent Fe sublattices, while for T>Tc broadened 2‐line absorption spectra typical of 57Fe at noncubic sites in paramagnetic material are observed.

Optical selection rules and structures of cholesteric blue phases

Abstract By deriving optical selection rules for cholesteric blue phases and considering the nature of the phase transitions between them, a structural assignment for the three experimentally observed phases of Johnson et al. is obtained. All three are argued to be bcc. A method of testing this structure assignment directly by polarized light scattering studies is also presented.

On the dynamic stability of the hovering magnetic top

Abstract In this paper we analyze the dynamic stability of the hovering magnetic top from first principles without using any preliminary assumptions. We write down the equations of motion for all six degrees of freedom and solve them analytically around the equilibrium solution. Using this solution we then find conditions which the height of the hovering top above the base, its total mass, and its spinning speed have to satisfy for stable hovering. The calculations presented in this paper can be used as a guide to the analysis and synthesis of magnetic traps for neutral particles.

Magnetic trapping of neutral particles: Classical and quantum-mechanical study of a Ioffe–Pritchard type trap

Recently, we developed a method for calculating the lifetime of a particle inside a magnetic trap with respect to spin flips, as a first step in our efforts to understand the quantum mechanics of magnetic traps. The one-dimensional toy model that was used in this study was physically unrealistic because the magnetic field was not curl free. Here, we study, both classically and quantum mechanically, the problem of a neutral particle with spin S, mass m, and magnetic moment μ, moving in three dimensions in an inhomogeneous magnetic field corresponding to traps of the Ioffe–Pritchard “clover-leaf” and “baseball” type. Defining by ωp, ωz, and ωr the precessional, the axial, and the lateral vibrational frequencies, respectively, of the particle in the adiabatic potential Veff =μ|B|, we find classically the region in the (ωr/ωp)−(ωz/ωp) plane where the particle is trapped. Quantum mechanically, we study the problem of a spin-one particle in the same field. Treating ωr/ωp and ωz/ωp as small parameters for the pe...