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.     

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.     

Investigation of the non-linear loss properties of magnetic fluids subject to large alternating fields

The non-linear relaxational properties of a water-based magnetic fluid are investigated by means of measuring the frequency dependent complex susceptibility, χ(ω) in the presence of an external potential. The results obtained are discussed in terms of the magnetic analogue of the Coffey and Paranjape model as modified by Déjardin. The loss processes in the magnetic fluid in the non-linear region are investigated in the context of the loss tangent, tan(δ), and the power dissipation per unit volume. These measurements are of importance because of the continuing interest in the clinical applications of magnetic fluids, where large alternating magnetic fields can be applied to magnetic fluids to induce loss processes and heating effects, often driving the magnetic fluid into the non-linear region of magnetisation. We evaluate the increment of the susceptibility, Δχ, due to the non-linear response, through measurement of χ(ω), and extend this formulism to the non-linear increment of the loss tangent, Δ tan(δ) and the increment of the heating rate, ΔU_heat.     

The resonance decay function method in the determination of the pre-factor of the Néel relaxation time of single-domain nanoparticles

In its simple form, the relaxation time of the Néel relaxation process of the magnetic moment of single-domain particles is given by τ_N=τ_0Nexp(σ), σ being the ratio of anisotropy energy to thermal energy. The pre-factor, τ_0N, is normally given a value of 10⁻⁹ s, but values ranging from 10⁻⁸ to 10⁻¹² s have been reported in literature. Here, by means of the field and frequency dependence of the complex magnetic susceptibility, χ(ω,H)=χ′(ω,H)−iχ″(ω,H), of a magnetic fluid sample, in the MHz-GHz range, in conjunction with the determination of the sample decay function, b(t), the pre-factor τ_0N is determined. b(t) is readily obtained through the inverse Fourier transformation relationship, which exists between b(t) and χ″(ω).     

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.     

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.     

Magnetic properties of RPd5Al2 (R=Y, Ce, Pr, Nd, Sm, Gd)

Polycrystalline samples of a new rare-earth series RPd₅Al₂ crystallizing in the tetragonal ZrNi₂Al₅-type structure have been prepared. Their physical properties by electrical resistivity ρ, magnetic susceptibility χ, magnetization M and specific heat C_p measurements are reported. The ingots are composed of elongated grains preferentially aligned in the c direction; therefore, measurements were conducted parallel and perpendicular to the grains. Antiferromagnetic ordering appears in R=Ce, Nd, Gd, and Sm at low temperatures. CePd₅Al₂ has two AFM transitions at 4.1 and 2.9 K and ρ(T) indicates a Kondo metal behavior with large anisotropy. In PrPd₅Al₂ no magnetic transition was observed down to 0.4 K. The C_p(T) shows a broad peak around 13 K due to the CEF effect, suggesting a non-magnetic singlet ground state. In NdPd₅Al₂, χ(T) shows anisotropy and the C_p(T) shows a sharp peak at 1.2 K. The magnetic entropy at 3 K is very close to Rln2, indicating a Kramers doublet ground state. In SmPd₅Al₂, C_p(T) shows a magnetic transition at 1.7 K. C_p(T) for GdPd₅Al₂ shows a peak at 6 K, followed by a broad anomaly around 3 K. Within this series, T_N's for CePd₅Al₂ and NdPd₅Al₂ clearly deviate from the relation predicted by de Gennes scaling, which is ascribed to the CEF effect.     

Magnetite-cobalt ferrite nanoparticles for kerosene-based magnetic fluids

Due to the magnetic anisotropy introduced by the Co²⁺ ion in octahedral sites of cubic spinel ferrites, it is possible to tailor the magnetic properties by changing the cobalt content. Magnetic fluids with magnetite-cobalt ferrite nanoparticles given by the formula Co_(x)Fe_(3−x)O₄ with x=0, 0.2 and 0.4 were prepared. Kerosene and oleic acid were used as liquid carrier and surfactant, respectively. Spherical magnetic nanoparticles were obtained by coprecipitation from metal salts and ammonium hydroxide; afterwards the magnetic fluids were obtained by a peptization process. Powder properties were characterized by X-ray diffraction (XRD), nitrogen adsorption–desorption isotherma (BET), vibrating sample magnetometry (VSM) and fluids by transmission electron microscopy (TEM), thermogravimetric analyzer (TGA), VSM and the short-circuited transmission line technique.     

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.     

Phase transition in the Heisenberg ferromagnet Cu(NH4)2Br4·2H2O in a magnetic field

The effect of a magnetic field on phase transitions in the Heisenberg ferromagnet Cu(NH₄)₂Br₄·2H₂O is investigated. It is found that the singularity shift of the susceptibility χ(P, T) in a magnetic field is approximated by power functions with the indexes ω = 2.5 and ? = 0.58.     

Optical characterization of nano-structured Cu2ZnSnS4 thin films deposited by GLAD technique

In this paper, Cu₂ZnSnS₄ (CZTS) thin films were elaborated at room temperature by thermal evaporation method using Glancing Angle Deposition (GLAD) technique at different incident angles γ = 00°, 20°, 40°, 60°, 75° and 85°. XRD, Raman scattering analysis, (SEM) and UV-Visible-NIR spectroscopy were used to characterize the crystalline structure, morphology and optical properties of CZTS samples. The results have showed that the ellipsometric analysis leaded to an optical anisotropy due to the structural anisotropy for CZTS samples deposited at γ = 85°. All Cu₂ZnSnS₄ samples exhibited a high absorption coefficient (α > 10⁴ cm⁻¹) and a direct optical transition varied between 1.48 eV and 2.05 eV for CZTS thin films deposited at γ = 00° and 85°, respectively. The value of the Urbach energy increased with incident angle, indeed, its value increased from 58 meV (γ = 00°) to 604 meV (γ = 75°) and decrease to be 368 meV for γ = 85°. This result is correlated with the Raman analysis. From transmittance data of CZTS thin films deposited at γ = 00°, 20° and 40° Swanepoel's method was used, to estimate the refractive index n. It allows us, using the Wemple-DiDomenico and Spitzer-Fan models, to calculate other optical parameters such as the oscillator energy E₀, dispersion energy E_d, zero frequency refractive index n₀, high frequency dielectric constant ε_∞ and the electric susceptibility χ_e. On the other hand, to have an idea about the evolution of the nonlinear optical character, the nonlinear susceptibility χ⁽³⁾ and the nonlinear refractive index n₂ of CZTS thin films deposited at γ = 00°, 20° and 40° were investigated. Ellipsometric measurements of CZTS thin films has leaded to an optical anisotropy for γ = 85°. In addition, the generalized ellipsometry in Jones formalism have proved this property, which can be related to the nano-columnar slanted structure as revealed by (SEM) analysis.     

Theory for the nonlinear optical response at noble-metal surfaces with nonequilibrium electrons

We present a theory for the electron-temperature dependence T _el of optical second harmonic generation (SHG). Such an analysis is required to study the dynamics of metallic systems with many hot electrons not at equilibrium with the lattice. Using a tight-binding theory for the nonlinear susceptibility χ ⁽²⁾(ω,T _e1) and the Fresnel coefficients we present results for the SHG intensity I ⁽²⁾(ω,T _e1) and its dependence on T _el for Cu. Note, χ ⁽²⁾(ω,T _e1) rather than the Fresnel coefficients determines essentially this temperature dependence. Most interestingly we find frequency ranges where I ⁽²⁾(ω,T _e1) increases for small light intensities, while it decreases for large light intensities. Our theory yields also that SHG probes effects due to hot electrons more sensitively than linear optics. The results of our calculations are compared with recent experiments on Cu and Au.     

Dynamical susceptibility of the ising model in a transverse magnetic field

An approximate expression is obtained for the dynamical susceptibility, χ_zz(q, ω), of the spin one half, simple cubic Ising model in a transverse magnetic field, which is appropriate to the disordered state (〈S_z〉 = 0). The susceptibility along the direction of the field is shown to contain a thermal part with a relative weight proportional to the difference between the isothermal and adiabatic susceptibilities and a width determined by the thermal diffusion constant.     

Paramagnetic susceptibilities, crystal field Stark energies and hyperfine properties of Eu in europium trifluoromethanesulfonate nonahydrate

Hexagonal single crystals of europium trifluoromethanesulfonate nonahydrate (EuTFMS) have been prepared. The paramagnetic susceptibility perpendicular to the symmetry axis (c-axis, χ_⊥) and the principal magnetic anisotropy (Δχ=χ_||−χ_⊥) were measured in the temperature range of 300-13 and 300-80 K, respectively. The paramagnetic susceptibility parallel to the c-axis (χ_||) was calculated using the values of χ_⊥ and Δχ. χ_|| and χ_⊥ increase slowly with decrease of temperature and below ∼93 K, χ_⊥ is more or less constant. But χ_|| levels off below ∼137 K. The calculated value of the effective magnetic moment (P_eff) of Eu³⁺ in the crystalline environment of EuTFMS decreases with lowering of temperature. The Raman and Fourier transform infrared (FTIR) spectra of EuTFMS were recorded in the wavenumber range of 10-1800 and 370-6000 cm⁻¹, respectively. A good theoretical simulation of the observed magnetic properties including the CF Stark energies of the ground term (⁷F) extracted from the Raman and FTIR spectra of Eu³⁺ in EuTFMS have been achieved using one electron crystal field (CF) analysis. The electronic specific heat and other relevant CF dependent hyperfine properties, viz, nuclear quadrupole splitting and hyperfine specific heat have been computed.     

Characterization of different magnetite–cobalt nanoparticles in hydrocarbon-based magnetic fluids by means of static and dynamic magnetization measurements

Magnetic nanoparticles with different compositions (Co_xFe_3−xO₄, 0?x?0.1) were synthesized from metal salts using a coprecipitation technique to produce magnetic fluids following a peptization technique. The liquid carrier was the hydrocarbon Isopar M and the surfactant was oleic acid. The colloidal-sized ferrimagnetic nanoparticles produced were found to be superparamagnetic. Measurements of the complex magnetic susceptibility were carried out to evaluate the resonant frequency f_res, the anisotropy constant K, and anisotropy field H_A. f_res was found to be a linear function of the cobalt content of the magnetic nanoparticles over the range of cobalt content studied.     

Anisotropy and FOMP in Tb3 (Fe28−xCox) V1.0 (x=0, 3 and 6) compounds

In this work, the structural and magnetic properties of Tb₃ (Fe_28−xCo_x) V_1.0 (x=0, 3, 6) compounds have been investigated. The structural characterization of compounds by X-ray powder diffraction is an evidence for a monoclinic Nd₃(Fe, Ti)₂₉-type structure (A2/m space group). The refined lattice parameters a and b (but not c) and the unit cell volume V, obtained from the XRD data by the Rietveld method, are found to decrease with increasing Co concentration. The unit cell parameters behavior has been attributed to the smaller Co atoms and a preferential substitution of Fe by Co. The anisotropy field (H_a) as well as critical field (H_cr) was measured using the singular point detection (SPD) technique from 5 to 300 K in a pulsed magnetic field of up to 30 T. At T=5 K, a FOMP of type 2 was observed for all samples and persists at all temperatures up to 300 K. For sample x=0, H_cr=10.6 and 2.0 T at 5 and 300 K, respectively, is equal to that reported earlier. The occurrence of canting angles between the magnetic sublattices during the magnetization process instead of high-order anisotropy contributions (at room temperature are usually negligible) has been considered to explain the survival of the FOMP at room temperature. The anisotropy and critical fields behave differently for samples with x=0, 3 compared with x=6. The observed behavior has been related to the fact that the Co substitution for Fe takes place with a preferential entrance in the inequivalent crystallographic sites of the 3:29 structure. The contribution of the Tb-sublattice in the Tb₃(Fe, V)₂₉ compound with uniaxial anisotropy has been scaled from the anisotropy field measured on a Y₃(Fe, V)₂₉ single crystal with easy plane anisotropy.     

Axial-field-dependent circular susceptibility in Fe-rich amorphous wires

The longitudinal magnetic field dependence of low-frequency circular susceptibility, χ(H), is measured for (Fe_1−xCr_x)_77.5Si_7.5B₁₅ (x=0,0.05,0.1, and 0.15) amorphous wires of radius r₀=0.07 mm. In order to explain the experimental results, on the basis of the widely accepted core–shell model, we consider that there are a constant axial anisotropy K_c in the core and a radius-dependent radial anisotropy K_s∝r⁸/r₀⁸ in the shell, both K_c and K_s being functions of stress-energy constant λ_sσ₀. A formula for χ(H) is derived from this model. The experimental data fits indicate that the magnetic structure can be well described by the improved core–shell model with reasonable values of λ_s.     

What is measured in a time-resolved stimulated Raman experiment?

We have performed four-beam time-resolved stimulated Raman measurements on liquid CS₂. To interpret our results we have applied the response formalism for the third-order polarization to such an experiment. It turns out that the measured quantity is proportional to (a convolution of) Abs[χ⁽³⁾(-ω_s, ω_s, ω_l, -ω_l)]. As a consequence in this four-beam e xperiment one picks up electronic contributions in contrast to a two-beam experiment where Im[χ⁽³⁾] is observed.     

Crystal field investigation on the magnetic properties of Yb in Yb(CF3SO3)3·9H2O

Ytterbium tri-fluoromethanesulfonate (YbTFMS) single crystals are prepared from the slow evaporation of the aqueous solution of YbTFMS and the principal magnetic susceptibility perpendicular to the c-axis of the hexagonal crystal (χ_⊥) is measured from 300 K down to 13 K. Principal magnetic anisotropy Δχ(=χ_∥−χ_⊥) is measured from 300 K down to 80 K which provides principal magnetic susceptibility parallel to the c-axis (χ_∥) down to 80 K. Very good theoretical simulation of the observed magnetic properties of YbTFMS has been obtained using one electron crystal field (CF) analysis having C_3h site symmetry. No signature of ordering effect in the observed magnetic data is noticed down to the lowest temperature (13 K) attained, indicating the inter-ionic interaction to be of predominantly dipolar type. The calculated g-values are found to be g_∥=2.67 and g_⊥=2.51, respectively. CF analysis provides the electronic specific heat which gives two Schottky anomalies in its thermal variation down to ∼13 K. The temperature dependences of quadrupole splitting and hyperfine heat capacity are studied from the necessary information obtained from the CF analysis.