Method of a singular point and determination of fields of anisotropy of polycrystalline hexagonal magnets

A numerical computation is performed on the magnetization curves and their derivatives for magnets of hexagonal syngony for isotropic polycrystalline specimens as well as materials with sheet texture in the basis plane. It is shown that investigation of the second derivatives ²M/H² for a degree of texture f_T > 0.4 permits obtaining information about the magnitude of the anisotropy field independently of its type. The singularities of M(H) and ²M/H² are examined for magnetization processes of the first kind. In this case the singular point method permits measuring the magnitude of the critical fields, the critical magnetizations, and the anisotropy field on a textured specimen with f_T>0.7, which yields information about the magnitudes of the high order anisotropy constants in the long run.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 39–42, January, 1989.     

Some properties of an “aesthetic” field theory

We continue our study of the Lorentz-invariant field theory based on the equations _jk;l ⁱ =0 and g_ij;k=0. To first order in a perturbation expansion, we find _jk;l ⁱ =0 reduces to the wave equation. In orders higher than the first, we find that _jk;l ⁱ =0 cannot be linearized. We also find that the simple wave-type equation g^ij2g/xⁱx^j=0 is contained in the theory when an appropriate choice is made for the parameters at the origin point.     

Differential algebras for quantum groups of type B, C, and D

We study higher order bicovariant differential calculi on the quantum groups O_q(N) and Sp _q (N). We show that the second antisymmetrizer exterior algebra _u is the quotient of the universal exterior algebra _u by the principal ideal generated by . Here denotes the unique up to scalars biinvariant 1-form. Moreover is central in _u and _u is an inner differential calculus. We show that the quadratic dual to the left-invariant algebra _{s L} is isomorphic to the reflection equation algebra. Let be an arbitrary left-covariant first order differential calculus. We show that the dimension of the space of left-invariant 2-forms in the universal exterior algebra equals the number of linearly independent quadratic-linear relations in the quantum tangent space.     

Hyperbolic initial-boundary-value problem for magnetic flux compression by plane liners

Based on the (relativistic) Maxwell equations with displacement current E/t, the initial-boundary-value problem for the compression of an initially homogeneous magnetic fieldB={0,B(x,t),0} between a fixed liner atx=0 and a detonation-driven liner atx=s(t) is solved analytically. By homogenizing the boundary conditions at the moving boundary, the transient electromagnetic fields are shown to be a superposition of quasistatic elliptic (E/t=0) and hyperbolic (E/t0) wave solutions. The wave equation is solved by a Fourier expansion in time-dependent eigenfunctionsf _n =f _n [nx/s(t)] for the variable region 0xs(t), where the Fourier amplitudes _n (t) are determined by coupled differential equations of second order. It is concluded that the conventional elliptic flux compression theories (E/t=0) hold approximately for nonrelativistic liner speeds , whereas the hyperbolic theory (E/t0) is valid for arbitrary liner speeds .     

Quantization of the Maxwell field in linear conformal invariant gauges

It is shown that the generalized Lorentz gauges provide all linear conformal invariant gauges, i.e. gauges such that A =0.     

Critical surface of the ising model with first-neighbor,second-neighbor,and four-spin interactions

Exact values are obtained for the slopesK ₁ ^c (0, 0)/K ₂,K ₁ ^c (0, 0)/K ₄ of the critical surface of paramagnetic-ferromagnetic transitionsK ₁ ^c (K ₂,K ₄) for the two-dimensional Ising model on a square lattice with first-neighbor, second-neighbor, and four-spin couplingsK ₁,K ₂, andK ₄, respectively. The results are obtained using universality arguments to relate the slopes to known spin-spin correlation functions forK ₂=K ₄=0. The equivalence of different expressions for the slopes in terms of correlation functions yields sum rules for the divergent part of certain sums over the second-neighbor and four-spin energy-energy correlation functions.     

On the Lax representation for the nonlinear evolution equations

By the classical differential geometry techniques it is shown that a general partial differential equation of the second order with two independent variables can be represented in the Lax operator form [X ₁ X ₂]=0, whereX _i =/x _i – ⁱ ,i=1,2 and ⁱ are the 3×3 matrices. The problem of the introduction of the spectral parameter in this representation is shortly discussed.Presented at the International Symposium Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 14–19, 1981.The author is pleased to thank V. K. Mel'nikov for the discussion of this work.     

Influence of the overall pressure on electrical conductivity of the amorphous semiconductor Ge15Te81S2As2

The experimental results obtained with the chalcogenide glass Ge₁₅Te₈₁S₂As₂ with imposed overall pressure up to 700 MPa are presented. The material exhibits the switching effect and the memory effect. It is shown that the overall pressure changes remarkably d.c. electrical conductivity of the amorphous semiconductor. It is assumed that the changes in conductivity are caused by changes in activation energy. The changes in activation energy within the range of considered pressures are, as follows from our measurements, E/p–10·95×10^–5 eV/MPa +p × 10·41 W 10^–7 eV/MPa². The assumption of the activation energy dependence on pressurep are confirmed also by measurements of dependence In vs. 1/T at various pressures.     

Determination of the strain potential constant by means of the p-InSb photoconductivity spectra under uniaxial compression

The influence of uniaxial pressure (0 < P < 2600 kg/cm2) on the intrinsic photoconductivity (PC) spectrum of p-InSb at 93 and 15°K is investigated. At 77°K the carrier concentration and mobility in the specimens were, respectively, (1.4–3.2)·10¹⁴ cm^–3 and 7000 cm²/V. sec. It is established that the maximum in the PC(E_m) spectra under compression is shifted towards higher energies. In the low-compression range E_m/P=5·10^–6eV·cm²/kg, while E_m/P=1·10^–6eV·cm²/kg for P > 1000 kg/cm². It is shown that the shift of the maximum of the intrinsic PC spectra with pressure is due to the growC;th in the forbidden bandwidth (E_g), and the change in parameters characterizing carrier diffusion in the specimen bulk (the diffusion coefficient, lifetime, surface recombination velocity) plays no part. The change in E_m/P with pressure is explained by the influence of valence band splitting. The deformation potential constants of the valence band |b|=(1.7±0.3) eV and |d|=(4.4±0.8)eV are calculated on the basis of a comparison between experimentally obtained data and theoretical results.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 159–162, February, 1976.     

Anisotropy of the low temperature resistivity of hexagonal single crystalline spin glass systems

The impurity contribution to the resistivity in zero field (T) of dilute hexagonal single crystals of ZnMn, CdMn and MgMn has been studied in the mK range on samples cut parallel () and perpendicular () to thec-axis, using a SQUID technique for the measurements. Typical spin glass behavior is found in (T) as well as (T) for all alloys, with Kondo like logarithmic increases at higher temperatures and maxima atT _m at lower temperatures, indicating the influence of impurity interactions. The differences in the corresponding isotropic resistivity _poly(T) between the three systems can qualitatively be understood within the framework of a theoretical model by Larsen, describing (T) as a function of universal quantitiesT/T _K and _RKKY/T _K , where _RKKY is the RKKY-interaction strength andT _K the Kondo temperature. With respect to the two lattice directions studied, the behavior of (T and (T is anisotropic in the Kondo regime as well as in the range where ordering becomes important. While the anisotropy in the Kondo slope can be understood by an anisotropic unitarity limit, the understanding of the anisotropy in region where impurity interactions are important remains problematic.Dedicated to Prof. Dr. S. Methfessel on the occasion of his 60th birthday     

The magnetic anisotropy of manganate ferrites

The anisotropy constants K₁ for systems Mn_xFe_3–xO₄, with 1x 1·8, are calculated on the basis of the one-ion model and it is shown that the anomalous temperature dependence of the constant K₁ can be explained by the presence of Mn³⁺ ions in octahedral positions. The influence of the spin order on the magnetic anisotropy and the uniaxial anisotropy in systems Mn_xFe_3–xO₄ are discussed.     

The effects of inkomogeneous center structure on the shape of the ESR spectra of alkali-rich glasses

The paper considers the effect of nonuniform structure in the centers on the ESR spectrum for the case of axial anisotropy in the g factor; it is shown that if (² >² , _¦ >), the model enables one to describe fairly completely the spectrum of a glass containing 33% Na₂O and 67% SiO₂. Good agreement with all experimental evidence is not obtained for potassium silicate glasses.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 6, pp. 86–90, June, 1971.     

Ferromagnetic resonance and magnetic crystallographic anisotropy of monocrystalline lithium ferrite films

The crystallographic anisotropy constant K₁ of monociystalline lithium ferrite films was measured by the methods of ferromagnetic resonance and rotational moments. The presence of uniaxial anisotropy in the plane of a film with the constant K_u 10₃ erg · cm^–3 is established experimentally. The nature of the uniaxial anisotropy is explained by the anisotropy of the stresses in the plane of the film, a formula is obtained to compute the angle of deflection of the easy magnetization axis from the crystallographic direction. An estimate is made of the difference in the stresses along the axes (_x–_z) 10¹⁰ dyne · cm^–2.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 16, No. 9, pp. 86–89, September, 1973.     

Determination of rf electric field strengths in deuterium from satellite structure of Balmer lines

In a linear magnetoplasma withn _e5×10¹⁸ m^–3 microwaves with frequencyf=34.8 GHz and powerP100 kW were focussed with a quasi-optical horn-lens system. The profiles of the deuterium lines D, D, and D were recorded from the focus. The profiles show a satellite structure which is generated by the rf electric field. Beside the first order satellites which can be resolved from the main line, even second order satellites were detectable. Comparing the satellites' intensities with theory it is possible to determine the electric field strength in the focus. Due to a sensitive dependence of the satellites' intensities upon the polarization direction one can also determine an unknown polarization direction.     

Inverse Problem for a General Bounded Domain inR3 with Piecewise Smooth Mixed BoundaryConditions

We study the influence of a finite container on an ideal gas. The trace of theheat kernel (t) = _{= 1}exp(–t), where {} _{= 1}are the eigenvalues of the negative Laplacian – ² = – ³ _{= 1}(/x )² in the (x ¹, x ², x ³)-space,is studied for a general bounded domain with a smooth bounding surface S, where afinite number of Dirichlet, Neumann, and Robin boundary conditions on thepiecewise smooth parts S _i (i = 1, ..., n) of S are considered such that S =U _{i = 1} S _i . Some geometrical properties of (the volume, the surface area, the meancurvature, and the Gaussian curvature) are determined. Furthermore,thermodynamic quantities, particularly the energy, for an ideal gas enclosed inthe general bounded domain with Dirichlet, Neumann, and Robin conditionsare examined with the help of the asymptotic expansions of (t) for short timet. We show that these thermodynamic quantities depend on some geometricproperties of .     

A new bundle completion for parallelizable space-times

The Schmidt [9]b-boundaryM, for completing a space-timeM, has several desirable features. It is uniquely determined by the space-time metric in an elegant geometrical manner. The completed space-time is¯M=M M, where¯M= ⁺ M/O ⁺ and ⁺ M is the Cauchy completion (with respect to a toplogical metric induced by the Levi-Cività connection) of a component of the orthonormal frame bundle having structure groupO ⁺. ThenM consists of the endpoints of incomplete curves inM that have finite horizontal lifts in ⁺ M, and ifM= we say thatM isb-complete. It turns out thatM isb-complete if and only ifO ⁺ M is complete. This criterion for space-time completeness is stronger than geodesic completeness and Beem [1] has shown that this remains so even for the restricted class of globally hyperbolic space-times. Clarice [3] has shown that for such space-times the curvature becomes unbounded as theb-boundary is approached.Now ifM, then ⁺ M may contain degenerate fibers; thus the quotient topology for¯M is non-Hausdorff and precludes a manifold structure. Precisely this has been demonstrated by Bosshard [2] for Friedmann space-time, casting doubt on the physical significance of the completion. The only neighborhood of the Friedmann singularity is the whole of¯M, and in the closed model initial and final singularities are identified inM. Similarly, Johnson [7] showed that the completion of Schwarzschild space-time is non-Hausdorff because of degenerate ibers in¯O ⁺ M.Here we introduce a modification of the Schmidt procedure that appears to be useful in avoiding fiber degeneracy and in promoting a Hausdorff completion. The modification is to introduce an explicit vertical component into the metric forO ⁺ M by reference to a standard section, that is, to a parallelizationpMO ⁺ M We prove some general properties of thisp-completion and examine the particular case of a Friedmann space-time where there is a fairly natural choice of parallelization.     

A new geometrical gravitational theory

A geometrical gravitational theory based on the connection ={ } + ln + ln –g ln is developed. The field equations for the new theory are uniquely determined apart from one unknown dimensionless parameter ₂. The geometry on which our theory is based is an extension of the Weyl geometry, and by the extension the gravitational coupling constant and the gravitational mass are made to be dynamical and geometrical. The fundamental geometrical objects in the theory are a metricg and two gauge scalars and. Physically the gravitational potential corresponds tog in the same way as in general relativity, the gravitational coupling constant to ^–2, and the gravitational mass tou(, ), which is a coscalar of power –1 algebraically made of and. The theory satisfies the weak equivalence principle, but breaks the strong one generally. We shall find outu(, )= on the assumption that the strong one keeps holding good at least for bosons of low spins. Thus we have the simple correspondence between the geometrical objects and the gravitational objects. Since the theory satisfies the weak one, the inertial mass is also dynamical and geometrical in the same way as is the gravitational mass. Moreover, the cosmological term in the theory is a coscalar of power –4 algebraically made of andu(, ), so it is dynamical, too. Finally we give spherically symmetric exact solutions. The permissible range of the unknown parameter ₂ is experimentally determined by applying the solutions to the solar system.     

Temperature dependence of the electric field gradient in Er metal

The method of perturbed angular distributions was used to measure the temperature dependence of the electric field gradient in Er single crystal for 98 KT156 K. The I=11^– isomer in Er¹⁵⁴) was used as a probe. ₀ increases monotonically for 98 KT259 K and then decreases. A possible cause for this effect may be short range interactions between the f electrons above the Neel point.Visitor from the Weizmann Institute, Rehovoth, Israel.