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.     

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.     

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.     

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.     

Modification of the dielectric properties of copper-doped CdIn2S4 single crystal

The study of the dielectric properties of a CdIn₂S₄〈3 mol % Cu〉 single crystal in alternating-current (ac) electric fields with frequencies f = 5 × 10⁴?3.5 × 10⁷ Hz has revealed the origin of dielectric loss (relaxation loss that is changed by the through current loss at high frequencies). It has been found that CdIn₂S₄〈Cu〉 has permittivity increment Δ?′ = 123, relaxation frequency f _r = 2.3 × 10⁴ Hz, and relaxation time τ = 43 μs. The doping of CdIn₂S₄ single crystal with copper (3 mol %) is established to substantially increase the permittivity (?′), dielectric loss tangent (tanδ), and ac conductivity (σ_ac). In this case, the frequency dispersion of ?′ and tanδ increases and that of σ_ac decreases.     

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).     

Low-field magnetic properties of LaMnO3+δ with 0.065≤δ≤0.154

In a weak magnetic field LaMnO_3+δ exhibits at δ=0.065 below the paramagnetic-to-ferromagnetic (FM) Curie temperature, T_C, a mixed (spin-glass and FM) phase followed by a frustrated FM phase at δ between 0.100 and 0.154. The same behavior is observed in La_1−xCa_xMnO₃ with x between 0 and 0.3. This can be understood by the similar variation of the Mn⁴⁺ concentration, c between ≈0.13 and 0.34, in both materials when x or δ is increased. On the other hand, considerable differences are found between these compounds in the values of the magnetic irreversibility, in the dependencies of T_C(c) and the magnetic susceptibility, χ(c), as well as in the critical behavior of χ(T) near T_C. These differences can be explained by distortions of the cubic perovskite structure, by the reduced lattice disorder and by the more homogeneous hole distribution in LaMnO_3+δ than in La_1−xCa_xMnO₃.     

The magnetic susceptibility of hydrogen-doped partially crystalline (Zr76Ni24)1−xHx metallic glasses

The magnetizations of Zr₇₆Ni₂₄ metallic glass and hydrogen-doped partially crystalline (Zr₇₆Ni₂₄)_1−xH_x metallic glasses have been measured in the temperature range 10-300 K and magnetic fields up to 2 T for various dopant concentrations (x=0, 0.024, 0.043, 0.054). It is found that the samples are paramagnetic and magnetic susceptibility at room temperature, χ(300 K), shows a nonmonotonic behaviour upon hydrogenation. The values of χ(300 K) of the hydrogen-doped partially crystalline (Zr₇₆Ni₂₄)_1−xH_x metallic glasses are reduced with increase in hydrogen content up to x=0.043, whereas for x=0.054, an enhancement of χ(300 K) has been revealed. The magnetic susceptibility is weakly temperature dependent down to 110 K, below which an increase is observed. A shallow minimum exists between 90 and 120 K. The form and magnitude of the observed temperature dependence of the magnetic susceptibility are well accounted for by the sum of the quantum corrections to the magnetic susceptibility. Hydrogen reduces the electronic diffusion constant and influences strongly the quantum interference at defects, slowing down the spin diffusion and enhancing the magnetic susceptibility in the temperature range from 110 down to 10 K.     

A pulse-resonance method for the determination of frequency-dependent magnetic susceptibilities in the microwave region

A simple set-up for the determination of non-diagnonal elements of the magnetic susceptibility tensor in the microwave region is given. The change of the magnetization during microwave absorption (MMA) is detected and leads directly to the susceptibilityχ′ _yx (ω). The method is applicable to magnetic systems having longitudinal relaxation times larger than 10^?6 sec. The MMA-method enables one to decide whether the sample is para-, ferro- or antiferromagnetic and from this magnetic transition temperatures can be measured.     

Dielectric properties of modified As<Subscript>2</Subscript>Se<Subscript>3</Subscript>〈Bi〉<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> layers

The dielectric parameters (permittivity ? and dielectric loss tangent tanδ) for As₂Se₃〈Bi〉 _x layers are calculated using the polarization current relaxation curves measured at different strengths of the applied electric field. It is revealed that the bismuth dopant has a considerable effect on the frequency dependences of ? and tanδ, which is probably associated with the existence of microinhomogeneous regions with an increased dopant concentration.     

Nonlinear optical susceptibilities χ of nitridosilicate powders

Nitridosilicates are of interest as novel nonlinear materials due to their extraordinary chemical and thermal stability. Unfortunately, large nitridosilicate single crystals are presently not available for the investigation of their nonlinear optical properties. The first experiments are presented in which an averaged nonlinear susceptibility χ⁽²⁾ for several nitridosilicates is studied by using two different powder techniques, the Kurtz Perry method and the SHEW method (Second Harmonic Wave generated by an Evanescent Wave). We observe nonlinearities of the new materials which are comparable to those of LiIO₃. The highest averaged M_eff=(χ_eff⁽²⁾)²/4n_2ωn_ω² values found are ∼0.9 pm²/V². The refractive indices of the materials are determined to be between n=2 and 3.     

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.     

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.     

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.     

Effects of competition between the anisotropy and the spin quantum number on the magnon energy gap in a four-layer ferromagnetic superlattice

The magnon energy bands are studied for a four-layer ferromagnetic superlattice, with regard to the effects of the competition between the anisotropy and the spin quantum number. A special attention is also paid on the effects of the symmetry of the system. It is found that three modulated energy gaps exist in the magnon energy band along K_x direction perpendicular to the superlattice plane. The magnetic anisotropy affects significantly the magnon energy gaps. The zero energy gap Δω₂₃ correlates with the conditions between anisotropy constants, D₁+D₃=D₂+D₄ and D₁=D₃ (or D₂=D₄), while the disappearance of the magnon energy gaps Δω₁₂ and Δω₃₄ corresponds to a translational symmetry of x-direction in a unit cell. When the parameters of the system deviate from these conditions, the energy gaps Δω₁₂, Δω₂₃ and Δω₃₄ become larger. There is a competition effect of the anisotropy and the spin quantum number on the magnon energy gaps Δω₁₂ and Δω₂₃. When the symmetry of the system is higher, the competition can achieve a balance to cause the zero energy gap.     

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.     

The permittivity of a monatomic gas with spatial dispersion

The longitudinal, ε^l(ω, k), and transverse, ε^tr(ω, k), permittivities of a monatomic gas were calculated. The frequency ranges in which the permittivity ε(ω) and permeability μ(ω) of a gas without spatial dispersion have a physical meaning were determined. The limiting magnetic susceptibility χ(ω) at ω=0 and the static magnetic susceptibility were found. The question of whether an electromagnetic wave with antiparallel group and phase velocities can propagate through a monatomic gas is discussed.     

Principles of generalized spin-echo spectroscopy

The concept is proposed for determining the total dynamic scattering function of an object under study, representing a sum of odd and even parts measured by the generalized neutron spin-echo method in the form of the signals S _odd(q, t) ～ ΣS(ω, q)sin(ωt)dω and S_even(q, t) ～ ΣS(ω,q)cos(ωt)dω as functions of the momentum q transferred to the neutron and the time t corresponding to the frequency ω and the transferred energy ?ω. The principle of the generalized spin echo and the results of mathematical modeling are confirmed in experiments on inelastic scattering on magnetic fluids and polymer solutions. The developed method makes it possible to study the features of the dynamics of atomic and molecular systems, e.g., to analyze soft vibrational spectra of nanoparticle ensembles against the background of intense relaxation processes, which is inaccessible for classical spin-echo spectrometry.