On the high-frequency measurement of the dynamic properties of nano-particle colloids

Measurement of the magnetic complex susceptibility, χ(ω)=χ′(ω)−iχ″(ω) by means of the transmission line technique, is a well established method for the determination of the dynamic properties of nano-particle colloids, such as magnetic fluids. From polarising studies one can obtain accurate data on the anisotropy constant, K, anisotropy field, H_A, gyromagnetic constant γ, and the damping parameter, α. From data on χ(ω), one can determine the loss tangent, tan δ, of the samples and also a value of the precessional decay time, τ₀. From polarized studies, one can investigate the presence of any hysteresis. The technique is also suitable for the investigation of the magnetic properties of composite samples. In this paper a review of the above mentioned topics are presented with examples of results obtained for a number of magnetic fluids.     

An experimental study of the dynamic properties of nanoparticle colloids with identical magnetization but different particle size

Measurements of the frequency dependent complex magnetic susceptibility, χ(ω)=χ′(ω)−iχ″(ω), have been used to determine the dynamic properties of three specially prepared 400 G (0.04 T) magnetic fluids. The samples, denoted by sample 1, sample 2 and sample 3, consisted of magnetite particles of mean diameter 6.4 nm, 7.5 nm and 9 nm respectively and were identical in terms of carrier liquid, surfactant and particle material.     

An improved technique for the measurement of the complex susceptibility of magnetic colloids in the microwave region

Measurements by means of the short-circuit (S/C) and open circuit (O/C) transmission line techniques are well established methods for investigating the magnetic and dielectric properties of magnetic colloids, respectively. In particular, the S/C technique has been used in the investigation of the resonant properties of ferrofluids; resonance being indicated by the transition of the real component of the magnetic complex susceptibility, χ(ω)=χ′(ω)−iχ″(ω), from a positive to a negative value at a frequency, f_res. However, under certain circumstances, the accuracy of the S/C technique is affected by the dielectric properties of the sample, hence incurring errors in the measurement of χ(ω) and indeed of f_res. Here we present a model which, by combining short-circuit and open circuit measurements, is developed in a manner in which the permeability, μ, and the permittivity, ε, contribute simultaneously to the calculation of χ(ω), thereby providing superior experimental results in comparison to those obtained by the S/C technique alone. For the two ferrofluid samples measured it is demonstrated that the dielectric properties affect the high frequency content of the susceptibility spectrum.     

Frequency dependence of the complex susceptibility for a spin-1 Ising model

The complex susceptibility or the dynamic susceptibility (χ(ω)=χ′(ω)−iχ″(ω)) for a spin-1 Ising system with bilinear and biquadratic interactions is obtained on the basis of Onsager theory of irreversible processes. If the logarithm of the susceptibilities is plotted as a function of the logarithm of frequency, then the real part (χ′) displays a sequence of plateau regions and the imaginary part (χ″) has a sequence of maxima in the ordered or ferromagnetic phase. On the other hand, only one plateau region in χ′ and one maximum in χ″ is observed in the disordered or paramagnetic phase. Argand or Cole-Cole plots (χ″−χ′) for a selection of temperatures are also shown, and a sequence of semicircles is illustrated in the ordered phase and only one semicircle for the disordered phase in these plots.     

χ polarization induced in molecular glass of conjugated compound by all-optical poling

The paper presents the first report on χ⁽²⁾ polarization induced in molecular glass of conjugated compound by all-optical poling. Transparent thin film of molecular glass of 1,4-bis[2-[4-[N,N-di(p-tolyl)amino]phenyl]vinyl]benzene (BTAPVB) was prepared using a spin-cast technique. Dipolar as well as octupolar components in BTAPVB contributed to the formation of photoinduced χ⁽²⁾ polarization. Growth rate of χ⁽²⁾ polarization has good linear relation with E_ω⁴E_2ω, which suggested that the simultaneous processes of two-photon (ω + 2ω) and three-photon (ω + ω + ω) excitation on the same electronic level contributed to the formation of photoinduced χ⁽²⁾ polarization.     

Influence of mobile space charges on electrical properties of ferroelectric Bi3.5La0.5Ti3O12 thin films

Lanthanum-substituted bismuth titanate, Bi_3.5La_0.5Ti₃O₁₂ (i.e., x=0.5 in Bi_4−xLa_xTi₃O₁₂), thin films have been grown on Pt/Ti/SiO₂/Si substrates using pulsed laser deposition. The frequency dependence of the real part ε′(ω) and the imaginary part ε″(ω) of the dielectric constant has been studied. The ε′(ω) does not show any sudden change within the frequency range of 10²-10⁶ Hz. In contrast, the ε″(ω) shows a large dispersion as frequency decreases. The observed relaxation behavior in ε″(ω) can be explained in terms of a migration of oxygen vacancies in (Bi₂O₂)²⁺ layers, not in Bi₂Ti₃O₁₀ perovskite layers.     

The vibrational spectrum of thiazole between 600 and 1400 cm revisited: A combined high-resolution infrared and theoretical study

The Fourier transform infrared gas-phase spectrum of thiazole, C₃H₃NS, has been recorded in the 600-1400 cm⁻¹ wavenumber region with a resolution around 0.0030 cm⁻¹. Nine fundamental bands (ν₅(A′) to ν₁₁(A′), ν₁₅(A″), and ν₁₆(A″)) are analysed employing the Watson model. Ground-state rotational and quartic centrifugal distortion constants as well as upper state spectroscopic constants have been obtained from the fits. A detailed analysis of perturbations identified in the ν₁₁(A′) band at 866.5 cm⁻¹ enables a definitive location of the very weak ν₁₀(A′) and ν₁₄(A″) bands at 879.3 and 888.7 cm⁻¹, respectively. The three levels are analysed simultaneously by a model including Coriolis resonance using an ab initio predicted first order c-Coriolis coupling constant; second and higher order Coriolis parameters are determined. Qualitative explanations in terms of Coriolis resonances are given for a number of crossings observed in ν₅(A′), ν₆(A′), and ν₇(A′) at 1383.7, 1325.8, and 1240.5 cm⁻¹, respectively. The rotational constants, anharmonic frequencies, and vibration-rotation constants (alphas, ) calculated by quantum chemical calculations using a cc-pVTZ and TZ2P basis with B3LYP methodology, have been compared with the present experimental data. The rotation constant differences for each vibrational state, from the ground state values, are closer to experiment from the TZ2P calculations relative to those using cc-pVTZ. The values for Δ_J, Δ_JK, Δ_K, δ_J, and δ_K are close to experiment with both basis sets.     

High-resolution infrared spectra of bicyclo[1.1.1]pentane

Infrared spectra of bicyclo[1.1.1]pentane (C₅H₈) have been recorded at a resolution (0.0015 cm⁻¹) sufficient to resolve for the first time individual rovibrational lines. This initial report presents the ground state constants for this molecule determined from the detailed analysis of three of the ten infrared-allowed bands, ν₁₄(e′) at 540 cm⁻¹, ν₁₇ (a₂″) at 1220 cm⁻¹, ν₁₈(a₂″) at 832 cm⁻¹, and a partial analysis of the ν₁₁(e′) band at 1237 cm⁻¹. The upper states of transitions involving the lowest frequency mode, ν₁₄(e′), show no evidence of rovibrational perturbations but those for the ν₁₇ and ν₁₈ (a₂″) modes give clear indication of Coriolis coupling to nearby e′ levels. Accordingly, ground state constants were determined by use of the combination-difference method for all three bands. The assigned frequencies provided over 3300 consistent ground state difference values, yielding the following constants for the ground state (in units of cm⁻¹): B₀ = 0.2399412(2), D_J = 6.024(6) × 10⁻⁸, D_JK = −1.930(21) × 10⁻⁸. For the unperturbed ν₁₄(e′) fundamental, more than 3500 transitions were analyzed and the band origin was found to be at 540.34225(2) cm⁻¹. The numbers in parentheses are the uncertainties (two standard deviations) in the values of the constants. The results are compared with those obtained previously for [1.1.1]propellane and with those computed at the ab initio anharmonic level using the B3LYP density functional method with a cc-pVTZ basis set.     

Scaling laws and approximate expressions for the dynamic magnetic susceptibility of Brownian nanoparticles

We present simplified expressions for the out-of-phase component of the dynamic susceptibility χ″ of lognormal-sized magnetic nanoparticles under Brownian rotation. These expressions are based on transforming the general integral functions used for χ″ in the convolution of gaussian functions. χ″ can thus be expressed as a sum of gaussians with parameters directly related to those of the size distribution and to the saturation magnetization. The gaussian fit of χ″(ω) (where ω is the ac field frequency) is a simpler way to determine these structural and magnetic parameters as it avoids fitting χ″(ω) to an integral function. The expressions derived for χ″ suggest that χ″T data collapses in a ωη(T)/T scale (where T is the temperature and η the fluids viscosity), which is confirmed by numerical calculations. We also discuss the limits of validity of these approximations in real systems where both Néel and Brownian relaxation mechanisms coexist and we present further approximations for the relation of ω_χ with the average volume (being ω_χ the frequency at which χ″ is maximum). The ωη(T)/T scale can be used to qualitatively evaluate the dominance of the Brownian relaxation mechanism.     

Third-order optical harmonic coefficients of atomic hydrogen at low frequencies

The analytical expression is derived for the third-order optical harmonic coefficients χ⁽³⁾₁₁₁₁ (ω, ω, ω) = χ⁽³⁾₂₂₂₂ (ω, ω, ω) = χ⁽³⁾₃₃₃₃ (ω, ω, ω) of the atomic hydrogen at very low frequencies ω → 0.     

Structural and ac electrical properties of a newly synthesized single phase rare earth double perovskite oxide: Ba2CeNbO6

A single phase rare earth double perovskite oxide Ba₂CeNbO₆ (BCN) is synthesized by solid-state reaction technique for the first time. The X-ray diffraction pattern of the sample at room temperature shows monoclinic structure, with the lattice parameters, a=5.9763 Å, b=5.975 Å and c=8.48 Å and β=90.04°. Impedance spectroscopy is used to study the ac electrical behavior of this material as a function of frequency (10²-10⁶ Hz) at various temperatures (30-450 °C). A relaxation is observed in the entire temperature range. Conduction mechanism is investigated by fitting the complex impedance data to Cole-Cole equation. Complex impedance plane plots show only one semicircular arc, indicating only the grain contribution of dielectric relaxation. The scaling behavior of imaginary part of electric modulus (M″) and imaginary part of electrical impedance (Z″) suggests that the relaxation describes the same mechanism at various temperatures. The frequency dependence of conductivity is interpreted in terms of the jump relaxation model and is fitted to Jonscher's power law. The values of dc conductivities extracted from the Jonscher power law varies from 2.79×10⁻⁷ to 3.5×10⁻⁵ Sm⁻¹ with the increase in temperature from 100 to 450 °C. The activation energies (0.37 eV) extracted from M″(ω) and Z″(ω) peaks are found to follow the Arrhenius law.     

The effect of gamma irradiation on electrical and dielectric properties of Al-TiW-Pd2Si/n-Si Schottky diode at room temperature

The effects of ⁶⁰Co (γ-ray) irradiation on the electrical and dielectric properties of Al-TiW-Pd₂Si/n-Si Schottky diodes (SDs) have been investigated by using capacitance-voltage (C-V) and conductance-voltage (G/ω-V) measurements at room temperature and 500 KHz. The corrected capacitance and conductance values were obtained by eliminating the effect of series resistance (R_s) on the measured capacitance (C_m) and conductance (G_m) values. The high-low frequency capacitance (CHF-CLF) method given in [12] as N_ss = (1/qA) [((1/C_LF) − (1/C_ox))⁻¹ −  ((1/C_HF) − (1/C_ox))⁻¹] was successfully adapted to the before-after irradiation capacitance given in this report as N_ss = (1/qA) [((1/C_bef) − (1/C_ox))⁻¹ − ((1/C_after) − (1/C_ox))⁻¹] for the analyzing the density of interface states. The N_ss-V plots give a distinct peak corresponding to localized interface states regions at metal and semiconductor interface. The experimental values of the ac electrical conductivity (σ_ac), the real (M′) and imaginary (M″) parts of the electrical modulus were found to be strong functions of radiation and applied bias voltage, especially in the depletion and accumulation regions. The changes in the dielectric properties in the depletion and accumulation regions stem especially from the restructuring and reordering of the charges at interface states and surface polarization whereas those in the accumulation region are caused by series resistance effect.     

Phase transition in Ising, XY and Heisenberg magnetic films

The phase transition and magnetic properties of a ferromagnet spin-S, a disordered diluted thin and semi-infinite film with a face-centered cubic lattice are investigated using the high-temperature series expansions technique extrapolated with Padé approximants method for Heisenberg, XY and Ising models. The reduced critical temperature of the system τ_c is studied as function of the thickness of the thin film and the exchange interactions in the bulk, and within the surfaces J_b, J_s and J_⊥, respectively. It is found that τ_c increases with the exchange interactions of surface. The magnetic phase diagrams (τ_c versus the dilution x) and the percolation threshold are obtained. The shifts of the critical temperatures T_c(l) from the bulk value (T_c(∞)/T_c(l) − 1) can be described by a power law l^−λ, where λ = 1/υ is the inverse of the correlation length exponent.     

Change in the shape of a symmetric light pulse passing through a quantum well

A theory for the response of a 2D two-level system to irradiation by a symmetric light pulse is developed. Under certain conditions, such an electron system approximates an ideal solitary quantum well in a zero field or a strong magnetic field H perpendicular to the plane of the well. One of the energy levels is the ground state of the system, while the other is a discrete excited state with energy ?ω₀, which may be an exciton level for H=0 or any level in a strong magnetic field. It is assumed that the effect of other energy levels and the interaction of light with the lattice can be ignored. General formulas are derived for the time dependence of the dimensionless “coefficients” of the reflection ?(t), absorption A(t), and transmission ?(t) for a symmetric light pulse. It is shown that the ?(t), A(t), and ?(t) time dependences have singular points of three types. At points t ₀ of the first type, A(t ₀)=T(t ₀)=0 and total reflection takes place. It is shown that for γ_r?γ, where γ_r and γ are the radiative and nonradiative reciprocal lifetimes, respectively, for the upper energy level of the two-level system, the amplitude and shape of the transmitted pulse can change significantly under the resonance ω_l=ω₀. In the case of a long pulse, when γ_l<γ_r, the pulse is reflected almost completely. (The quantity γ_l characterizes the duration of the exciting pulse.) In the case of an intermediate pulse duration γ_l?γ_r, the reflection, absorption, and transmission are comparable in value and the shape of the transmitted pulse differs considerably from the shape of the exciting pulse: the transmitted pulse has two peaks due to the existence of the point t ₀ of total reflection, at which the transmission is zero. If the carrier frequency ω_l of light differs from the resonance frequency ω₀, the oscillating ?(t), A(t), and ?(t) time dependences are observed at the frequency Δω=ωl?ω₀. Oscillations can be observed most conveniently for Δω?γ_l. The position of the singular points of total absorption, reflection, and transparency is studied for the case when ω_l differs from the resonance frequency.     

Domain growth dynamics in multicomponent vesicles composed of BSM/DOPC/cholesterol

We have investigated the domain growth dynamics in vesicles composed of BSM/DOPC/cholesterol using fluorescence microscopy. A ternary mixture of equimolar BSM, DOPC, and cholesterol was employed, and two fluorescent dyes were added for comparison studies. We found that in the early stage the number of the domains on the vesicle surface, N(t), decayed with time as N(t)∼t^−2/3, which confirmed previous theoretical prediction and numerical simulation, while in the late stage N(t) decreased more quickly, as ∼t^−β, with β≈2. We discuss the faster growth dynamics based on the collision-induced collision mechanism.     

High-resolution study of the bΣ(b0)→XΣ(X10) transition of PI

Emission spectra of the b¹Σ⁺(b0⁺)→X³Σ⁻(X₁0⁺) transition of phosphorus iodide have been measured with a high-resolution Fourier-transform spectrometer. The PI radicals were generated and excited in a fast-flow system by reaction of phosphorus vapor (P_x) with iodine and microwave-discharged oxygen. Four sequences, Δv=0,+1,−1,−2, of the b¹Σ⁺(b0⁺)→X³Σ⁻(X₁0⁺) transition of PI comprising 28 bands were observed. Six bands were measured at high spectral resolution. Vibrational and rotational analyses have yielded accurate spectroscopic constants of the X₁0⁺ and b0⁺ states (in cm⁻¹): X₁0⁺: ω_e=371.296(4), ω_ex_e=1.3302(9), B_e=0.1194117(2), α_B=−0.0005676(7), D_e=4.56(2) ×10⁻⁸; b0⁺: T_e=11136.921(4), ω_e=400.165(6), ω_ex_e=1.345(2), B_e=0.1239237(2), α_B=−0.0005540(2), D_e=4.84(5) × 10⁻⁸, where the numbers in parentheses are the standard deviations of the parameters. No emissions of the b0⁺→X₂1 sub-system nor of the a¹Δ(a2)→X³Σ⁻(X₂1) transition have been observed leaving PI the only group Va halide for which the spin splitting in the X³Σ⁻ ground state is still unknown.     

Spatial-temporal dispersion of the kinetic coefficients near the Anderson transition

A generalization of the Vollhardt-Wölfle localization theory is proposed to make it possible to study the spatial-temporal dispersion of the kinetic coefficients of a d-dimensional disordered system in the low-frequency, long-wavelength range (ω?_F and q?k _F ). It is shown that the critical behavior of the generalized diffusion coefficient D(q,ω) near the Anderson transition agrees with the general Berezinskii-Gor’kov localization criterion. More precisely, on the metallic side of the transition the static diffusion coefficient D(q,0) vanishes at a mobility threshold λ _c common for all q: D(q, 0)∝t=(λ _c ?λ)/λ _c →0, where λ=1/(2π?_F τ) is a dimensionless coupling constant. On the insulator side, q≠0 D(q,ω)∝?iω as ω→0 for all finite q. Within these limits, the scale of the spatial dispersion of D(q,ω) decreases in proportion to t in the metallic phase and in proportion to ωξ ², where ξ is the localization length, in the insulator phase until it reaches its lower limit ～λ _F. The suppression of the spatial dispersion of D(q,ω) near the Anderson transition up to the atomic scale confirms the asymptotic validity of the Vollhardt-Wölfle approximation: D(q,ω)?D(ω) as |t|→0 and ω→0. By contrast, the scale of the spatial dispersion of the electrical conductivity in the insulator phase is of order of the localization length and diverges in proportion to |t|^?v as |t|→0.     

Dynamic hysteresis of magnetic aggregates with non-integer dimension

We investigate the dynamic hysteresis of nanoscale magnetic aggregates by employing Monte Carlo simulation, based on Ising model in non-integer dimensional space. The diffusion-limited aggregation (DLA) model with adjustable sticking probability is used to generate magnetic aggregates with different fractal dimension D. It is revealed that the exponential scaling law A(H₀, ω)∼H₀^α·ω^β, where A is the hysteresis area, H₀ and ω the amplitude and frequency of external magnetic field, applies to both the low-ω and high-ω regimes, while exponents α and β decrease with increasing D in the low-ω regime and keep invariant in the high-ω regime. A mean-field approach is developed to explain the simulated results.     

Crystal field study and magnetic properties of [TbCu6(μ3OH)3(HL)2(L)4](ClO4)2·25H2O (H2L=imino-diacetic acid)

A crystal field (CF) investigation of the magnetic properties of [TbCu₆(μ₃-OH)₃(HL)₂(L)₄](ClO₄)₂·25H₂O (H₂L=imino-diacetic acid) has been carried out. An enhancement of the average magnetic susceptibility (defined by =(χ_||+2χ_⊥)/3, where χ_|| and χ_⊥ are the magnetic susceptibilities parallel and perpendicular to the symmetrical axis of the cluster) with respect to the Tb³⁺ free ion value has been noticed and is attributed to the Tb-Cu interaction. The CF parameters obtained for the system for the first time have been exploited to find the Stark splitting of the ⁷F manifold of Tb³⁺, paramagnetic resonance g-values, and the heat capacity. Two anomalies are obtained in the heat capacity at 40 and 5 K; the peak values are 3.1 and 5.98 J mol⁻¹ K⁻¹, respectively.     

Phase separation, ferromagnetism and magnetic irreversibility in La1−xSrxMn1−yFeyO3

Magnetic susceptibility, χ(T), is investigated in ceramic La_1−xSr_xMn_1−yFe_yO₃ (LSMFO) samples with x=0.3 and y=0.15−0.25. A ferromagnetic (FM) transition observed in LSMFO is accompanied with an appreciable decrease of the transition temperature with increasing y, which is connected to breaking of the FM double-exchange interaction by doping with Fe. Strong magnetic irreversibility, observed in low (B=10 G) field, gives evidence for frustration of the magnetic state of LSMFO. The FM transition, which is expanded with increasing B, is more pronounced in the samples with y=0.15-0.20 and broadens considerably at y=0.25, where the irreversibility is increased. Well above the transition, χ(T) exhibits a Curie-Weiss asymptotic behavior, yielding very large values of the effective Bohr magneton number per magnetic ion, incompatible with those of Mn or Fe single ions. At y=0.15 and 0.20 a critical behavior of χ⁻¹(T)∼(T/T_C−1)^γ in the region of the FM transition is characterized by influence of two different magnetic systems, a 3D percolative one with γ₌γ_p≈1.8 and T_C=T_C^(p), and a non-percolative 3D Heisenberg spin system, with γ=γ_H≈1.4 and T_C=T_C^(H), where T_C^(p)<T_C^(H). At y=0.25 the percolative contribution to the critical behavior of χ(T) is not observed. The dependence of χ on T and y gives evidence for phase separation, with onset already near the room temperature, leading to generation of nanosize FM particles in the paramagnetic host matrix of LSMFO. The ferromagnetism of LSMFO is attributable to percolation over the system of such particles and generation of large FM clusters, whereas the frustration is governed presumably by a system of smaller weakly-correlated magnetic units, which do not enter the percolative FM clusters.