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.     

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.     

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.     

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).     

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.     

Low-frequency alternative-current magnetic susceptibility of amorphous and nanocrystalline Co60Fe20B20 films

This investigation experimentally studies the low-frequency alternating-current magnetic susceptibility (χ_ac) of amorphous and nanocrystalline CoFeB films by measuring the magnetic field established by passing currents of various frequencies through such films of various thicknesses (t_f). A CoFeB film is sputtered onto a glass substrate with t_f from 100 Å to 500 Å under the following conditions: (a) As-deposited films were maintained at room temperature (RT) and (b) films were post-annealed at T_A=150 °C for 1 h. The samples thus obtained are analyzed in a magnetic field that was generated by an alternating current (AC) at various frequencies from 10 Hz to 25,000 Hz. The experimental results demonstrate that the χ_ac declines as the thickness of the as-deposited sample and the post-annealed sample (T_A=150 °C) increases because the lower coercivity (H_c) of thinner CoFeB films is similar to a soft magnetic characteristic and is associated with a higher χ_ac value. The best χ_ac value is obtained at a thickness of 100 Å under both conditions. The χ_ac value of the post-annealed sample exceeds that of the RT sample at thicknesses from 100 Å to 500 Å because the magneto crystalline anisotropy of the post-annealed sample yields the highest χ_ac value at the optimal resonance frequency (f_res), at which the spin sensitivity is maximal. The X-ray diffraction patterns (XRD) of as-deposited CoFeB films reveal their amorphous structure. The XRD results for the post-annealed films include a main peak at 2θ=44.7° from the body-centered cubic (BCC) nanocrystalline CoFe that indicated a (110) textured structure. Post-annealing treatment caused that the amorphous structure to become more crystalline by a thermally driven process, such that the χ_ac value of the post-annealed sample exceeded that of the RT sample. This experimental result demonstrates that the χ_ac value decreased as the thickness of the thin film increased. Finally, the CoFeB thin films had the best χ_ac at low frequency (<50 Hz) following post-annealing treatment. The results obtained under the two conditions indicate that the maximum χ_ac value and the optimal f_res of a 100 Å-thick CoFeB thin film were 1.6 and 30 Hz, respectively, following post-annealing at T_A=150 °C for 1 h, suggesting that a 100 Å-thick CoFeB thin film that has been post-annealed at T_A=150 °C can be utilized as a gage sensor and in transformer applications at low frequencies.     

Frequency Dependence of the Dielectric Loss Angle in Disordered Semiconductors in the Terahertz Frequency Range

Frequency dependence of the real part of the conductivity σ₁(ω) in the region of the transition from almost linear (s < 1) to quadratic (s ≈ 2) can indicate a change in the conduction mechanism (the transition from the variable-range to the fixed-range hopping with increasing frequency); in this case, the sharpness of the change in the slope of the frequency characteristic is related to the dependence of the preexponential factor of the resonance integral on the intercenter distance in the pair. The frequency dependence of the imaginary part of the conductivity σ₂(ω) has no kink in the vicinity of the transition frequency ωcr, remaining almost linear. A large dielectric loss angle |cotγ| = |σ₂|/σ₁ can indicate that the imaginary part of the conductivity at ω < ω_cr is defined by the larger zero-phonon contribution in σ₂^res the region of weak variation in the loss angle γ(ω), which significantly exceeds the relaxation contribution σ₂^res.     

XPS and thermomagnetic characterization of the CeNi4Cr compound

The magnetic, thermodynamic and electronic structure properties are discussed for the CeNi₄Cr compound. The X-ray photoemission spectra (XPS) provide an evidence of a mixed valence behavior with the occupancy of the f states n_f=0.89 and their hybridization with the conduction electrons Δ=30 meV. These values reproduce well the magnetic susceptibility χ(T=0), which is enhanced compared to similar CeNi₄M (M=Al, B, Cu) compounds. In combination with a slightly increased electronic specific heat coefficient (up to 100 mJ mol⁻¹ K⁻²), this compound can be classified as being on the border of the heavy fermion and mixed valence behavior. Using a small magnetic field in the χ(T) measurements reveals a presence of magnetically ordered impurity phase, which is easily damped by higher fields and it is shown that the contribution of this phase is minor. The question of the dependence of the electronic specific heat coefficient on the magnetic field is also addressed and the observations agree well with theoretical predictions based on the Anderson model.     

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.     

Neutron scattering of iron-based superconductors

Low-energy spin excitations have been studied on polycrystalline LaFeAsO_1?xF_x samples by inelastic neutron scattering. The Q-integrated dynamical spin susceptibility χ″(ω) of the superconducting samples is found to be comparable to that of the magnetically ordered parent sample. On the other hand, χ″(ω) almost vanishes at x = 0.158, where the superconducting transition temperature T_c is suppressed to 7 K. In addition, χ″(ω) in optimally doped LaFeAsO_0.918F_0.082 with T_c = 29 K exhibits a spin resonance mode. The peak energy, E_res, when scaled by k_BT_c is similar to the value of about 4.7 reported in other high-T_c iron-based superconductors. This result suggests that there is intimate relationship between the dynamical spin susceptibility and high-T_c superconductivity in iron-based superconductors, and is consistent with a nesting condition between Fermi surfaces at the Γ and M points.     

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.     

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.     

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.     

Spin-glass behavior and magnetocaloric effect in melt-spun TbCuAl alloys

Magnetic properties and magnetocaloric effects of amorphous and crystalline TbCuAl ribbons are investigated by measuring their ac susceptibilities including a nonlinear term and dc magnetizations. The in-phase third harmonic ac susceptibility is found to be negative. It can be well fitted by the expression at high temperatures, indicating a spin-glass behavior in amorphous TbCuAl alloy. ΔT_f(ω)/[T_f(ω)Δlog₁₀ω], a possible distinguishing criterion to judge the presence of a spin-glass behavior is ∼0.011. The frequency-dependent data can be well fitted by the conventional critical slowing down law and the spin-glass transition temperature is obtained to be 20.1 K. The maximum of magnetic entropy change reaches 4.5 J kg⁻¹ K⁻¹ for a field change of 0-50 000 Oe, while the crystalline TbCuAl compound experiences a simple ferromagnetic-to-paramagnetic phase transition. The peak value of magnetic entropy change is obtained at the Curie temperature and reaches 14.4 J kg⁻¹ K⁻¹ for the same field change, which is much larger than that of amorphous TbCuAl alloy.     

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.     

Magnetic properties of ball-milled Mn nanoparticles

Nanoparticles of Mn of sizes  < 500 Å were prepared by the ball-milling technique. The temperature dependence of the magnetic susceptibility χ showed systematic variation with particle size. Peaks observed in χ were attributed to the magnetic ordering of the oxides Mn₃O₄and MnO. Peaks found in ∂(χT) / ∂T were associated with the Neel temperature ofα -Mn. We estimated that our samples contain about 0.4% of Mn₃O₄. This low concentration of Mn₃O₄was not detected by X-ray diffraction experiments but contributed significantly to the magnetization measurements.     

The non-linear paramagnetic effect in CdCr2Se4 near the Curie temperature

Results are presented of measurements made of alternating current susceptibility changes Δχ = χ_B - χ₀ induced by external application of a constant magnetic field using the beat method (f ～ 1MHz). For 1 K < (T ? T_c) < 50 K and taking the appropriate values of magnetic fields the relation Δχ ～ B² was satisfied. Making use of the Debye theory adapted for the non-linear dielectric effect, it was shown that the mean number n of elementary cells in a cluster varies with temperature according to the relation n ～ (T ? T_c)^-1.31.     

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.