The voigt-type magneto-kerr effect in cubic semiconductors having ellipsoidal constant energy surfaces

A plane-wave analysis is given for the Voigt orientation of an applied static magnetic field ?B in cubic semiconductors having ellipsoidal constant energy surfaces. The effect is shown to be highly anisotropic with respect to the orientation of ?B (magneto-anisotropy) as well as to the initial polarization direction of the incident wave with respect to ?B (polarization anisotropy). The character and extent of the magneto-anisotropy depends not only on the location of the energy extrema, but on the anisotropy of the energy surfaces and on the energy dependence and anisotropy of the scattering processes.Calculations are given for the cases of propagation along 〈100〉 and 〈110〉 crystallographic directions in n-type germanium. High-field effects and infrared (IR) behavior are considered; however, the low-field quadratic range for microwaves in high-loss material is emphasized. A useful approximation for the high-loss case is given. Particular attention is given to the potential diagnostic applications of the effect.Room-temperature measurements of the Voigt-type Kerr effect for the TE₁₁ circular-waveguide mode at 35 GHz in n-type Ge are presented and compared with plane-wave calculations for propagation along 〈100〉 and 〈110〉 directions. Good quantitative agreement is obtained when the plane-wave calculations are reduced by the same mode-reduction factor as is applicable for the Faraday orientation.     

Effect of constant mismatch on stimulated scattering in laser plasma interactions

The presence of a constant wave number mismatch (Δk) renders the asymptotic steady of the backward scattered wave time dependent. While the pump wave is unaffected by the mismatch, the excited waves (with group velocities v₂, v₃) are modulated at the frequency $\text{[}\text{v}{}_2\text{v}{}_3\text{(v}{}_2\text{+ v}{}_3\text{)}\text{] Δk}$.     

Toroidal hydromagnetics

The complete set of hydromagnetic equations is transformed into Poisson equations and equations of motion for flux densities and their associated variables. The toroidal components of the vector potential A and of the momentum density $\text{a}\text{≠}\text{πv}$ are represented by the po loidal flux densities Ψ and Ψ, respectively, for which the equations of motion are derived. The poloidal components A_⊥ and a_⊥ are represen ed by the potentials atΦ, U and φ, u, for which we obtain Poisson equations in the poloidal plane. Thus one has to solve two Dirichlet and two von Neumann problems at every time step. The source terms of the four Poisson equations define the remaining four variables, namely, $\text{Λ = ▽ ·}\text{A}$,$\text{Ω=(▽×}\text{A}\text{)ζ/R}$, $\text{λ=?·}\text{a}$, and $\text{ω=(?×}\text{a}\text{)ζ/R}$, for which equations of motion are also derived. In the limit of small toroidicity ? we look fo r a selfconsistent scaling of the equations with v_⊥～ε. But the curl of v_⊥×B in Faraday's law creates a toroidal plasma component of B which is one order of magnitude larger than in the case of a low β equilibrium; therefore, the motion becomes fully three-dimensional. Finally, an artificial pressure law is needed to balance the lowest order of the Lorentz force. The conclusion is then that the scaling laws previously used are not applicable for toroidal geometry, and that the effort to obtain numerical solutions is not dramatically higher than without using any scaling law.     

Giant quantum oscillations of acoustoelectric current in Bi

In single crystals of Bi with resistivity ratio R₂₉₃/R_4.2 ≈ 300 by a helium temperature at frequencies 500 MHz of longitudinal sonic wave detected and investigated the longitudinal acoustoelectric effect.In strong magnetic fields if the condition $\text{h}\text{?}$ Ω ? kT,ql ? 1 Ω — cyclotron frequency, k — Boltzman constant) for directions H 6 q 6 y (y— a bissector crystal axis) and H 6 q 6 z (z — a triagonal crystal axis) is fulfilled, giant quantum oscillations of longitudinal acoustoelectric current are detected. Sign of current oscillations is determined by the type of current carriers.     

Anomalously enhanced plasma diffusion transverse to a magnetic field in n-Ge

From the broadening of a narrow plasma sheet drifting along E_x × B, we measured the transverse diffusion coefficient D_⊥ in n-Ge. Contrary to the classical theory, D_⊥ increases with the electric field E_x, increases with the magnetic field B up to μ⁺B ≈ 1, and decreases proportional to $\text{1}\text{B}$ in higher magnetic fields. The transverse drift velocity v_⊥ measured simultaneously shows a classical behavior over the whole field ranges of E_x = 3–110 $\text{V}\text{cm}$ and B = 0.1–2.3T, which were used in our experiment.The results correspond to those gained previously in n-InSb[13,14]. However, whereas in InSb plasma instabilities were observed together with the anomalous diffusion, no instabilities could be found in Ge. Various ways to arrive at an explanation of the anomalous effect are discussed and possible applications are indicated.     

Operator formulation of Regge asymptotic behavior

If the appropriate high-energy limits of the amplitudes $\text{W ≡ ?}\text{d}\text{x}\text{e}{}^{\mathrm{<mtext>i</mtext><mtext>q\; ·\; x</mtext>}}\text{<b|j(x)j′(0)|b′ >}$ are Regge pole dominated, then the large distance (x₀ → ∞, x²fixed) behavior of the current product is completely characterized by an operator expression $\text{R}\text{(x : 0)}$, involving only local operators at 0, which is such that $\text{R ≡ ?}\text{d}\text{x}\text{e}{}^{\mathrm{<mtext>i</mtext><mtext>q\; ·\; x</mtext>}}\text{<b|}\text{R}\text{|b′ >}$ and W have the same high-energy behavior. In the only case (|b> a single particle stateand |b′> the vacuum) where W is not Regge behaved, it is shown that R is identical to W, and so the relation $\text{jj′ →}\text{R}$ is established as a large distance operator expansion, valid between all states. $\text{R}$ is expressed as a differential operation B(□_x, ?_x · ?₀, □₀) on the light-cone expansion and some of its properties are deduced by carrying out the differentiations. A second form of $\text{R}$ is given in terms of non-local “reggeon” field operators R_αm(0) (α is a (fixed) spin index and m is a (variable) helicity index) which might be useful coordinate in reggeon field theories. These operators can be used to define reggeon-particle amplitudes and if conventional double-Regge and triple-Regge behaviors are further assumed, the large distance behaviors of the current-reggeon and reggeon-reggeon field products are specified in terms of other reggeon fields.     

On the definition of the pressure of an infinite system

A microcanonical system $\text{L}$^o_Λ is considered together with a manometer $\text{M}$_Λ. The thermodynamic limit Λ → ∞ is taken for the system $\text{L}$_Λ composed of $\text{L}$^o_Λ and $\text{M}$_Λ. This yields a definition of the pressure P(v, ε) of $\text{{}\text{L}{}^{\mathrm{o}}{}_{\mathrm{\Lambda }}\text{; Λ → ∞}}$ for given values ε and v of the energy and particle densities. P(v, ε) is shown to be equal to the thermodynamic function p(z, β) derived from the grand canonical ensemble for almost all values of ε and v provided the appropriate equilibrium values of the temperature β^?1 and the chemical potential μ = β^?1 log z are inserted.     

Interacting Frenkel defects at high concentration and the superionic transition in fluorite crystals

A spherical cell model is proposed to account for the explicit concentration dependence of Frenkel defects in an ionic system. In the model, the linearized Debye-Hückel equation is soluble exactly, subject to the boundary condition that the electric field is zero at the cell boundary R, related to the concentration c of defects by $\text{R ∝ c}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}$This screened field is used to calculate the chemical potential, which in turn leads to a condition for the instability of the interacting defect assembly. This condition allows one to calculate the enhancement of the concentration of defects above its Arrhenius value at the point of instability in terms of (a) the critical concentration c₀, (b) $\text{a}\text{R}$, where a is the radius of defect and (c) the Debye-Hückel screening length k_c.It is clear from the cell model that this enhancement factor is reduced somewhat in the relevant range of parameters in some of the fluorites from its value in extended Debye-Hückel theory. It is anticipated that the instability discussed here should afford an upper bound to c_v, at the superionic transition, within the range of validity of the model. The excess heat capacity c_p is also discussed briefly.     

Acoustic soft modes of Nb3Sn in high magnetic fields

In single crystal Nb₃Sn the effect of a magnetic field upon the soft sound velocity v_s (110, 1$\text{1}$0) was measured at different temperatures above the structural phase transition point. The observed quadratic variation with field is in accordance with theory. But the magnitude of the field dependence is much smaller than expected and can only be explained by existing theories if the magnetic moment of the electron would vary by as much as a factor of two within an energy interval of some 100 K.     

Excitation of ion cyclotron waves at the difference frequency of two microwave beams in a semiconductor

This paper presents an investigation of the resonant excitation of the electrostatic ion cyclotron wave at the difference frequency of two microwave beams propagating in a magnetoactive solid state plasma, viz. n InSb. The resonant excitation of the electrostatic ion cyclotron wave occurs when the difference frequency of the two microwave beams and the difference of their propagation vectors satisfy the dispersion relation corresponding to the electrostatic ion cyclotron wave. For typical plasma parameters of n InSb and microwave beams of power densities 1 MW cm^?2, the power density of the excited ion cyclotron wave is 0.40 kW cm^?2 when external magnetic field is $\text{1.46 kG (}\text{Ω}{}_{\mathrm{c}}\text{ω}\text{) = 0.1)}$. The power density of the excited ion cyclotron wave increases with the magnetic field. This study may provide new means for the characterisation and diagnostic of semiconductors.     

Multidimensional elastic waves excited by oscillating domain walls

Magnetoelastic excitations with a fine structure in the 50kHz range have been observed in the study of the domain wall resonance (DWR) in magnetic garnet thin films. DWR excites standing transverse elastic waves which have a resonance frequency given by $\text{f=}\text{nv}\text{2d}$, where f is the frequency, n is an integer, v=3.5×10⁵ cm/sec is the transversal velocity of the elastic wave, and d=0.05 cm is thickness of the film/substrate system. A fine structure associated with each of these modes has been identified as due to two dimensional bulk elastic waves by using a set of parallel microstrip lines. The dispersion relation of these elastic waves is ω²=v²(k²₁+k²₂), where ω is the radial frequency, k₁ and k₂ are the wave vectors in the orientation perpendicular and parallel to the sample surface respectively. In the case of k₁?k₂, $\text{f=}\text{f}{}_0\text{+v}{}^2\text{k}{}^2{}_2\text{f}{}_0$, where f₀ is the resonance when k₂=0. The experimental results are in excellent agreement with this model. A linear dispersion, observed when using a shorted slot-line structure, is understood as the excitation of three dimensional modes due to the complex structure of the slot-line and the sample geometry.     

The effect of external electric fields on molecular liquids and induced translational motion

A computer simulation is reported of the enantiomer S CHBrClF subjected in the liquid state to intense external fields of force : i) uniaxial electric field E_Z; ii) circularly polarised field at optical frequencies. The molecular dynamics are quantified in detail at field - on equilibrium in case i) using a range of auto correlation functions. The foremost result of the investigation is that the simple uniaxial field E_Z makes the sample $\text{translate}$ in a well defined direction. The direct effect of E_Z on an isolated molecule of S-CHBrClF is purely rotational, but intramolecular rotation/translation coupling converts this rotation into coherent centre of mass translation. This gives rise to direct, $\text{laboratory frame}$, cross correlations of the type <v(t)$\text{J}$^T(o)> where $\text{v}$ is the molecular centre of mass translational velocity and $\text{J}$^T the transposed molecular angular momentum vector. (The existence of these invalidates the classical theory of the Kerr effect.) The molecular dynamics of the hypothetical chiral ion S-CHBrClF^? are looked at with a view to corroborating the predictions by Baranova et al. concerning their response to electric field treatment. Despite the inherent instability of such an ensemble of like-charged ions the simulation can be used to produce a range of auto and cross-correlation functions with which to characterise the ionic dynamics. The effect of treating the ionic ensemble with a field E_Z is reported briefly in terms of the non-vanishing ensemble averaged centre of mass velocity <v_Z&>;.The induced translation in an electric field may be demonstrated on most liquids using a simple experimental set up. Its importance in optically active systems is such that it may be used to separate a racemic mixture into its enantiomers, the translational motion induced in the one enantiomer is necessarily, by symmetry, opposite to that induced in the other enantiomer. The observation therefore has technological importance. Other applications are discussed.     

Temperature variation of the magnetic cluster structures in an iron-nickel invar alloy

Small-angle scattering of long wavelength neutrons $\text{(λ = 6.42}\text{A}\text{?}\text{)}$ from an Fe₆₅Ni₃₅ single crystal has been measured with the applied magnetic field (6.2 kG) parallel and perpendicular to the scattering vector $\text{K}$ of the elastic scattering over the temperature range from 25 to 422°C (T_c = 227°C). The scattering cross sections due to the longitudinal spin fluctuation have been analyzed by means of Guinier's approximation $\text{(dσ/dω)}{}_0\text{exp}\text{(?κ}{}^2\text{R}{}_{\mathrm{<mtext>g</mtext>}}{}^2\text{3}\text{)}$, where the forward cross section (dσ/dω)₀ is proportional to n, which is the number of atoms in a paramagnetic cluster, and R_g is the radius of gyration of the cluster. The empirical relation between n and R_g is = 0.298 × R_g^2.34 to be compared with that calculated for a simple spherical cluster model n = 1.274 R_g³.     

Transition amplitudes and probabilities for the Weinberg-Salam model

Transition probabilities for the processes vv?vv, vv?, $\text{vv}$?$\text{vv}$, and spin-dependent transition amplitudes for the processes ve?ve, vē?vē, v?e?v?e, $\text{ve}$?$\text{ve}$ and vv??eē are calculated in lowest order for the Weinberg-Salam model.     

Magnetic field induced changes in linear and nonlinear optical properties of Ti incorporated Cr2O3 nanostructured thin film

We report the magnetic field effect on the linear and nonlinear optical properties of pulse laser ablated Ti-incorporated Cr₂O₃ nanostructured thin film. Optical properties have been experimentally analyzed under Voigt geometry by performing ultraviolet-visible spectroscopy and closed aperture Z-scan technique using a continuous wave He–Ne laser source. Nonlinear optical response reveals a single peak-valley feature in the far field diffraction pattern in absence of magnetic field ($\mathrm{B}=0$) confirming self-defocussing effect. This feature switches to a valley-peak configuration for $\mathrm{B}=5000\text{G}$, suggesting self-focusing effect. For $\mathrm{B}\le 750\text{G}$, oscillations were observed revealing the occurrence of higher order nonlinearity. Origin of nonlinearity is attributed to the near resonant d-d transitions observed from the broad peak occurring around 2 eV. These transitions are of magnetic origin and get modified under the application of external magnetic field. Our results suggest that magnetic field can be used as an effective tool to monitor the sign of optical nonlinearity and hence the thermal expansion in Ti-incorporated Cr₂O₃ nanostructured thin film.     

Quantum oscillations in screening in a two-dimensional electron gas

The static dielectric constant of a two-dimensional electron gas is studied as a function of the strength of a dc magnetic field applied normal to the plane of the electron gas. At high temperatures $\text{(kT ?}\text{h}\text{?}\text{ω}{}_{\mathrm{c}}\text{)}$ the static dielectric function is independent of magnetic field, and for long wavelengths is given by ? ? ?₀ + 2n_vme²/q, where ?₀ is the background dielectric constant and n_v is the valley degeneracy. At low-temperatures, quantum oscillations become important and dramatically modify the screening.     

Phase transition in strongly inhomogeneous ferromagnets

A field theoretical model is proposed to describe the critical behaviour of a strongly inhomogeneous spin system with a position dependent concentration of magnetic atoms C(R) and magnetisation M(R). Assuming a finite number of $\text{n}$ Fouriermodes $\text{C}{}_{\mathrm{<mtext>Q</mtext>}}{}_{\mathrm{<mtext>v</mtext>}}\text{v}\text{= 1}$,..., $\text{n}$, to express C(R), the quenched randomness requires to interpret {$\text{Q}{}_{\mathrm{<mtext>v</mtext>}}\text{|}\text{Q}{}_{\mathrm{<mtext>v</mtext>}}\text{|}{}^2$} on a set of invariant or marginal lengths. As consequence, M(R) can be described by n Fourier-modes M_Qv, where $\text{n ?}\text{n}$. For short range spin-spin interaction, we find for strong inhomogeneity, i.e. large n, the critical exponent between those of the related homogeneous system and those of the spherical model.     

A phenomenological investigation of the shower particle pseudorapidity fluctuations in hadron-nucleus collisions

From the experimental matrix $\text{?(N}{}_{\mathrm{<mtext>g</mtext>}}\text{; n}{}_{\mathrm{<mtext>s</mtext>}}\text{, Δη}{}_{\mathrm{i}}\text{)}$ (the number of events with a given number N_g of particles with velocity 0.3c<v<0.7c, and n_s, the number of shower particles (v > 0.7c) in a pseudo-rapidity interval Δη_i) obtained from the Heidelberg-Igel hadron-nucleus experiment at CERN, we extract the shower particle multiplicity distributions as a function of ν, the number of nucleons that interacted with the projectile. We use a theoretically justified statistical correlation between ν and N_g (recoil protons) and the assumption that the correlation between n_s and N_g is given merely through ν. The data used are for incoming energies 50 and 150 GeV with a proton or pion as the projectile and Cu or Pb as the target. We find that the shower particle multiplicity distributions are of a Poissonian character in each η bin and for each value of ν. The average multiplicities $\text{〈n}{}_{\mathrm{<mtext>s</mtext>}}\text{〉(ν)}\text{Δη}{}_{\mathrm{i}}$ are approximately the same for the two targets and for the different projectile, possibly with a small excess for the pion projectile.The results are compared to a rather general theoretical model of the soft interaction type. The predictions from this model for the shower particle pseudorapidity distributions are very close to the derived values.