Components Of Susceptibility Tensor Research Articles

Dispersion of the quadratic optical susceptibility and crystal structure of lithium tantalate

An investigation was made of the dispersion of the components of the quadratic susceptibility tensor of lithium tantalate on approach of the sum frequency of nonlinearly interacting light waves to the absorption edge of the crystal. The experimentally observed features of the dispersion of the various components of the susceptibility tensor were related to the structure of lithium tantalate.

Dispersion of the quadratic optical susceptibility of meta-toluylenediamine crystals

An investigation was made of the dispersion (wavelength dependences) of all independent components of the quadratic susceptibility tensor of molecular crystals of meta-toluylenediamine on approach of the sumfrequency wavelength to the edge of the absorption band of these crystals. The nature of the dispersion of the tensor components agreed with the main ideas of the oscillator model and it ensured effective addition of frequencies in the converted-radiation wavelength range 347–532 nm.

Ordering of Co(HCOO)2·2H2O Studied by Proton NMR –Magnetic Sandwich System of Antiferromagnetic Planes with Paramagnetic Ions

Proton NMR of an approximate magnetic sandwich system Co(HCOO) 2 ·2H 2 O is investigated. From the analysis of angular dependence of the resonance frequency, we determine all the components of paramagnetic sublattice susceptibility tensors and of spontaneous sublattice magnetizations which can not be obtained by the other experiments such as susceptibility, magnetization or torque measurement. These sublattice magnetizations show that exchange interactions in A plane and between A and B planes are antiferro- and ferromagnetic, respectively. The temperature dependence of spontaneous staggered magnetizations L A 0 and L B 0 on A and B planes is obtained from that of the resonance frequency. The results | L A 0 |∝ ε β (β=0.13±0.01) and | L B 0 |∝| L A 0 |/ T seem to indicate that the sandwiched paramagnetic ions do not participate cooperatively in the phase transition at T N with the ions on A plane.

Hydrodynamic modes in the spin-flop phase of an antiferromagnet

A linear theory of the hydrodynamic modes in the spin-flop phase of an antiferromagnet is outlined. The theory applies to systems with weak anisotropy in the basal plane. A variety of dynamical correlation functions are calculated in the adiabatic limit. The theory is used to interpret recent nuclear-magnetic-resonance experiments in Mn${\mathrm{F}}_{2}$ by King and Rohrer which show evidence of a low-lying electronic mode near the spin-flop-paramagnetic phase boundary. The mode is identified as a zone-center magnon which is coupled to the nuclear spins through off-diagonal components of the dynamic electronic susceptibility tensor.

Effect of spin-flip scattering on magnetic properties of metals

The itinerant-electron model is used to derive magnetic properties of paramagnetic and ferromagnetic metals in which nonmagnetic impurities are embedded. The results are valid for various relative strengths of the spin-flip and spin-independent scattering caused by the impurities. Essentially $s$-wave scattering by impurities is considered in the second-order Born approximation. Starting from a Hamiltonian the kinetic equations for the density-matrix elements are derived in the presence of an external magnetic field, and in the random-phase approximation. The kinetic equations are transformed to the equations of motion for the magnetization components. The longitudinal and transverse components of the rf susceptibility tensor are calculated. For the case of very small spin-flip scattering known results are obtained, whereas for other cases of spin-flip scattering the results obtained here are new. Conditions are found to obtain Bloch-like equations. Explicit expressions for the parameters of the Bloch-like equations are obtained, such as the relaxation "destination" of the longitudinal and transverse components of the magnetization and their spin-lattice relaxation times. Measurable shifts in the $g$ factor of the itinerant electrons caused by the spin-flip scattering of the impurities are obtained. Expressions for the static shifts in the magnetic excitations, paramagnons, and magnons are calculated.

Nonlinear optical properties of molecular crystals of metatolylenediamine

An investigation was made of the absorption spectra of polarized light, dispersion of principal refractive indices, and collinear phase matching in the generation of the second harmonic of λ = 1.06 μ laser radiation in molecular crystals of meta-tolylenediamine. The relative values of all the independent components of the quadratic susceptibility tensor were determined for these crystals and the value of the second-harmonic conversion coefficient was found. It was concluded that meta-tolylenediamine crystals were promising frequency doublers.

Some optical properties of silver thiogallate single crystals

Silver thiogallate (AgGaS2) single crystals of high optical quality were prepared. A study was made of the main optical properties of these crystals, including refractive indices, absorption spectra, components of the nonlinear susceptibility tensor, and phase-matching angles for the generation of second harmonics of CO2 and He-Ne laser radiations of wavelengths λ = 10.6 and 3.39 μ, respectively. Optical activity was observed in the 0.5 μ range and this activity had a resonance at λmax = 497.3 nm.

Description of Nonlinear Optics on an Atomic Scale

An examination is made of charge motion on an atomic scale in response to an applied electric field at optical frequencies to demonstrate the physical origin of nonlinear optical effects. In particular, second harmonic generation in a crystal of zinc blende structure is considered, and the zero and nonzero components of the nonlinear susceptibility tensor are obtained. Also, an estimate of the magnitude of the nonlinear susceptibility is made.

External susceptibility tensor of magnetized ferrite ellipsoid in terms of uniform-mode ellipticity

In the paper, the components of the external susceptibility tensor in finite ellipsoidal shapes are given in terms of the uniform-mode ellipticity. This notation besides introducing the uniform-mode ellipticity simply relates the form of the external susceptibility tensor to the internal one. Measurement of the uniform-mode ellipticity provides an alternative method to the usual Kittel resonance method by which the properties of single-crystal ferrites can be obtained. The uniform-mode ellipticity is also important because it is responsible for lineshape asymmetry at low frequencies. A final advantage is that it allows a single rule for introducing the Landau-Lifshitz form of damping into the loss free components of both the internal and external susceptibilities. The paper concludes with experimental results for a hexagonal single-crystal ferrite with planar anisotropy which is biased in the easy plane.

Frequency doubling of laser light in an isotropic medium with electrically destroyed centre of inversion

The non-zero non-linear susceptibility tensor components χστυ2ω (E0)which account for frequency doubling of laser light in a naturally isotropic medium immersed in a DC efectric field (E0) are discussed. The conditions for extremal second harmonic generation (SHG) are derived, which depend onE0 and on the incident laser intensity but primarily on the microstructure of the medium. With growingE0, the susceptibilities χστυ2ω (E0) increase for cigar-like microsystems but decrease for disc-shaped ones, according to whether the induced dipole helps or hinders the permanent dipole in reorienting the microsystem along (E0). Non-linear electronic distortion alone is insufficient for explaining the anomalous experimental results.

Theory and Method for Magnetic Resonance Measurements

The boundary-value problems involving a usual spherical ferromagnetic sample and commonly used cavity geometries are virtually impossible to solve so that perturbation theory must be used to interpret the results of resonance measurements. However, we have succeeded in solving the problem of a spherical sample in a spherical cavity under the assumption of uniform and circularly polarized magnetic field within the sample. Using the results of this calculation, it is possible to measure all components of the intrinsic susceptibility tensor of the medium. Furthermore, they enable the determination of the limits of validity of perturbation theory with regard to sample size, dielectric constant, and susceptibility. The calculation is self-consistent in that uniform and circularly polarized magnetic field within the sample is assumed and verified for a certain range of parameters by results of the calculation itself. Dimensional resonance, characterized by cavity-like resonances within the sample, is found to occur if the sample has a high susceptibility. In the case of ferromagnetic materials with small linewidths, this dimensional-resonance effect can be sufficiently serious as to render the usual interpretation via perturbation theory completely invalid. A measurement technique for determining the magnetic properties of a sample by use of our theory is described. It has been found that use of our solution makes it possible to relax the restriction of very small sample size as implied by perturbation theory. The use of a larger sample is highly desirable, since the change in frequency and Q would be greater, and less refined instruments would be required for making the measurements.

Observation of the T m169 nuclear magnetic resonance in thulium gallium garnet

The observation of the Tm 169 nuclear magnetic resonance (NMR) at T = 4° K in single crystals of thulium gallium garnet is reported. A study of the angular dependence of the Tm 169 NMR clearly shows that the symmetry of the Tm 3+ crystal field interaction is orthorhombic. An analysis of the NMR data yields values for the components of the orthorhombic susceptibility tensor. An experimental value 〈 r −3〉 = 11.7 ± 0.2 a. u. is also obtained.

Magnetic Properties of Hydrogen Fluoride. II. Susceptibility

A method is outlined for the calculation of the magnetic susceptibility χ from the ground-state wave function of 1Σ molecules. The diamagnetic contribution χd is obtained directly by first-order perturbation theory and the paramagnetic contribution χp is determined by a variational technique based on minimizing the second-order energy in an external magnetic field. When applied to an SCF—LCAO—MO function for hydrogen fluoride, the theoretical result is 〈χ〉Av=—8.74×10—6 erg gauss—2 mole—1, in excellent agreement with the experimental value of —8.6×10—6 erg gauss—2 mole—1. The separate contributions, with respect to the fluorine as origin, are somewhat more in error, with 〈χd〉Av=—9.58×10—6 erg gauss—2 mole—1 (exp: —9.2×10—6 erg gauss—2 mole—1) and 〈χp〉Av=0.855×106 erg gauss—2 mole—1 (exp: 0.609×10—6 erg gauss—2 mole—1, as obtained from the rotational magnetic moment). For the isoelectronic atoms F— and Ne (in which there is only a diamagnetic term), analytic Hartree-Fock functions yield 〈χ〉Av values equal to —12.7×10—6 erg gauss—2 mole—1 (exp: ∼—12×10—6) and —7.48×10—6 erg gauss—2 mole—1 (exp: —6.7 to —7.7×10—6), respectively. By a comparison of the results obtained with different molecular wave functions for hydrogen fluoride (one-center and two-center approximations), the sensitivity of the magnetic-susceptibility components (especially the paramagnetic terms) to the form of the wave function is clearly demonstrated. This suggests that χ and its components can serve as useful criteria for the accuracy of electron distributions and indicates the need for refinements in the hydrogen fluoride functions. Finally, the availability of a method for the theoretical evaluation of the susceptibility tensor components suggests that additional measurements should be done to improve the experimental values.

Low-Level Garnet Limiters

S- and L-band low-level passive limiters preselectors using polished single crystals of narrow line-width yttrium-irongarnet have been developed. The S-band limiter employed unsubstituted YIG and has an insertion loss of 0.6 db, a limiting threshold of -26 dbm, and a dynamic range greater than 30 db. The L-band limiter used specially grown gallium-substituted YIG crystals, which, when ground into spheres and polished to a high finish, exhibited extremely narrow line widths. The L-band limiter had an insertion loss of 1.1 db, a limiting threshold of -21 dbm, and a dynamic range greater than 25 db. A tuning range from 1120 to 1305 Mc was obtained. Data on frequency sensitivity and SWR are given and indicate that such limiters have a high off-band rejection and a fair power-handling capability. A leading-edge spike of 0.1μ-sec duration was observed. The decline of the various components of the magnetic susceptibility tensor can be used to construct other novel types of limiters. The operation of three such devices-electronically-tunable preselectors, and cavity-type and comb-type limiters-will be described and experimental data given.

Measurement of Susceptibility Tensor in Ferrites

Experimental techniques for measuring the magnetic susceptibility tensor components in microwave cavities are described. General expressions for the perturbation of microwave cavities by the magnetic properties of ferrites are developed. Experimental results are given for Ferramic 1331 measured at 9165 Mcps. Since these results indicate that both the real and imaginary parts of the tensor components χ and κ are approximately equal to each other in the resonance region, only measurement of the diagonal components may suffice to specify the complete tensor. However, whenever the small differences between χ and κ are desired, measurement of the tensor susceptibility in a degenerate cavity will be necessary. An attempt has been made to compare the experimental results with the Bloch-Bloembergen magnetic resonance theory as applied to circularly polarized excitation.