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).     

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.     

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.     

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.     

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.     

Magnetic properties of compounds in the system CaBaCo4−x−yZnxAlyO7 (x=0,1,2, y=0,1)

The magnetic properties of four compounds in the series CaBaCo_4−x−yZn_xAl_yO₇ (x=0,1,2, y=0,1) were investigated. Using AC-susceptibility and DC-magnetometry, magnetic transitions (T_fs) were found for all four compositions in the range 50-3 K. The data from the AC measurements proved to be frequency dependent: T_f increases with higher frequencies. An energy-loss in the magnetic coupling, indicated as contributions in the imaginary part of the magnetic susceptibility (χ″), was seen for every compound and its maximum appeared just below the maximum χ′. Modelling the data with Arrhenius-, Vogel-Fulcher-, and the power-law made it possible to relate the four compounds to spin-glass materials. The Casimir-du Pré relation was used to extract average relaxation times at T_f. The DC magnetisations clearly show differences between field-cooled and zero-field-cooled measurements. None of the compounds exhibit any metamagnetic properties up to 8 T. A new method is presented to calculate the saturation fields using DC data. Relaxation measurements on three compounds indicate that the systems relax very fast, in contrast to spin-glasses. Aging does not affect the fast relaxations. The compounds are interpreted as disordered anti-ferromagnets with spin-glass features.     

Acoustic NMR in spin-1 systems

Acoustic magnetic resonance, both pulsed and continuous has been discussed in terms of the Bloch-Wangsness-Redfield formulation of the magnetic resonance phenomenon. The quadrupolar mechanism has been taken for the spin-phonon coupling and the mutual interaction has been treated in the ‘effective field approximation’. The expressions for the power absorbed both for Δm=±1 and Δm=±2 have been obtained. It is found that from the measurements of the relaxation parameters for Δm=±1 and Δm=±2 it is possible to estimate the non-secular contributions to the line-width. The power absorbed in pulse excitation comes out to be small for short pulse (short compared to the relaxation parameter) and it reduces to the value obtained in continuous excitation for a long pulse. It is seen that for a given pulse-width the signal decreases with the increase of the relaxation parameter and this happens as temperature is lowered. The saturation of electromagnetic signal in presence of the acoustic excitation has also been studied. The analysis indicates that the relaxation parameter obtained from the plot of the relative signal (〈〉_ω/〈〉₀) vs the acoustic frequency ω, is always less than its true value which can be determined by observing the frequency dependence of the relative fractional signal defined as [(〈〉₀?〈〉_ω)/〈〉_ω]/[(〈〉₀?〈〉_2ω0)/〈〉_2ω0].     

Kondo behaviour of the solid solution (Ce1−xLax)PtGa

The solid solution (Ce_1−xLa_x)PtGa has been studied through X-ray diffraction, magnetization (σ(B)), magnetic susceptibility (χ(T)), electrical resistivity (ρ(T)), magnetoresistivity (MR) and heat capacity (C_P(T)) measurements. The Néel temperature (T_N=3.3 K) for CePtGa is lowered upon La substitution as observed from χ(T) and ρ(T) measurements. The Kondo temperature T_K as calculated from MR measurements is comparable to T_N and also decreases with La substitution. The volume dependence of T_K is in accordance with the compressible Kondo lattice model and a Doniach diagram of the results is presented. C_P(T) measurements are presented for CePtGa, Ce_0.2La_0.8PtGa and LaPtGa and the results are discussed in terms of the electronic and magnetic properties. Other features of interest are anomalies in ρ(T) and C_P(T) due to crystalline electric field effects and metamagnetism as observed in σ(B) studies for samples with 0≤x≤ 0.3.     

Low field AC susceptibility study of intergranular critical current density in Mg-substituted CuBa2Ca3Cu4O12−y high temperature superconductors

Measurements of the a.c.susceptibility (χ=χ′+iχ″) have been made on the Mg substituted high T_C superconducting system, CuBa₂(Mg_xCa_1−x)₃Cu₄O_12−y (Cu-1234) with x=0, 0.10 & 0.20, at different values of the a.c.field amplitude. Estimates of the intergranular critical current density(J_C) made from the field dependent χ″-T curves show an improvement in the Mg-substituted Cu-1234 system. Results have been analysed in the light of the crystal structure and the superconducting anisotropy factor (γ=ξ_ab/ξ_c) of the Cu-1234 system. Lower superconducting anisotropy emanating from Mg substitution has been found to be significant, resulting in better superconducting properties.     

Hopping conductivity of Ni-doped p-CdSb in strong magnetic fields

Magnetoresistance (MR) of oriented single crystals of the anisotropic semiconductor p-CdSb doped with 2 at% of Ni is investigated between T=1.5 and 300 K in transversal pulsed magnetic fields up to B=30 T. In fields B∼4-15 T at T below 4.2 K, the resistivity obeys the law ln ρ∼η[B?(B)]^1/2 with ?(B)=a(0)/a(B), where a is the carrier localization radius and parameter η depends on a(0), on the acceptor concentration N_A and on the direction of the magnetic field with respect to the crystallographic axes, but does not depend on T. Such behavior gives evidence for MR realized by hopping charge transfer over the nearest-neighbor sites in strong magnetic field. The analysis of the experimental data yields the values of η, agreeing with calculated ones within an error of 10%, taking into account the effects of the anisotropy of the acceptor states and of the explicit dependence of a(B) due to the increase in the activation energy of shallow acceptors in magnetic field and the sensitivity of the metal-insulator transition to B.     

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.     

Quasi-Debye response of ion-hopping conduction at lowest frequencies

On the basis of the relaxation mode theory, quasi-Debye response in the dynamic conductivity by hopping ions is theoretically investigated in three-dimensional random lattices with a uniform distribution of activation energies. It is shown at lowest frequencies that the dynamic conductivity is approximately given by σ(ω)∼σ(0)+A″ω^s″, s″=2−n, where n is a non-integer exponent originated from the mode diffusion length and density of states. The numerical analyses give rise to some values of s″<2, for example s″∼1.5, which behaves as s″→2 with increasing temperature.     

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.     

Critical RF losses in fine particles of La1−xAgyMnO3+δ: Prospects for temperature-controlled hyperthermia

Temperature and frequency dependencies of the real (χ′) and imaginary (χ″) parts of the dynamic magnetic susceptibility were studied experimentally in fine particles of La-Ag manganites prepared by various methods. The samples under study have the Curie points in the range T_C=42-48 °C, which is a medical hyperthermia range of interest. When approaching T_C from below, a critical peak of χ″ was revealed, followed by a steep drop while passing to the paramagnetic phase. The experiments on the magnetic radio-frequency (RF) heating of the manganite aqueous suspensions demonstrated good autostabilization of the temperature near T_C. Peculiar instability is found in the heating kinetics, caused by the observed critical behavior of the RF losses. The prospects of the La-Ag manganites as candidates for application in the temperature-controlled hyperthermia are discussed.     

Brownian rotational relaxation and power absorption in magnetite nanoparticles

We present a study of the power absorption efficiency in several magnetite-based colloids, to asses their potential as magnetic inductive hyperthermia (MIH) agents. Relaxation times τ$\tau$ were measured through the imaginary susceptibility component χ^″(T)${\chi }^{″}(T)$, and analyzed within Debye's theory of dipolar fluid. The results indicated Brownian rotational relaxation and allowed to calculate the hydrodynamic radius close to the values obtained from photon correlation. The study of the colloid performances as power absorbers showed no detectable increase of temperature for dextran-coated Fe₃O₄ nanoparticles, whereas a second Fe₃O₄-based dispersion of similar concentration could be heated up to 12 K after 30 min under similar experimental conditions. The different power absorption efficiencies are discussed in terms of the magnetic structure of the nanoparticles.     

Cluster glass magnetism in the phase-separated Nd2/3Ca1/3MnO3 perovskite

A detailed study of the low-temperature magnetic state and the relaxation in the phase-separated colossal magnetoresistance Nd_2/3Ca_1/3MnO₃ perovskite has been carried out. Clear experimental evidence of the cluster-glass magnetic behavior of this compound has been revealed. Well defined maxima in the in-phase linear ac susceptibility χ′(T) were observed, indicative of the magnetic glass transition at T_g∼60 K. Strongly divergent zero-field-cooled and field-cooled static magnetizations and frequency dependent ac susceptibility are evident of the glassy-like magnetic state of the compound at low temperatures. The frequency dependence of the cusp temperature T_max of the χ′(T) susceptibility was found to follow the critical slowing down mechanism. The Cole–Cole analysis of the dynamic susceptibility at low temperature has shown extremely broad distribution of relaxation times, indicating that spins are frozen at “macroscopic” time scale. Slow relaxation in the zero-field-cooled magnetization has been experimentally revealed. The obtained results do not agree with a canonical spin-glass state and indicate a cluster glass magnetic state of the compound below T_g, associated with its antiferromagnetic–ferromagnetic nano-phase segregated state. It was found that the relaxation mechanisms below the cluster glass freezing temperature T_g and above it are strongly different. Magnetic field up to about μ₀H∼0.4 T suppresses the glassy magnetic state of the compound.     

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.     

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.