Low-frequency Hysteresis Loops Research Articles

Ni/Zn ratio and La substitution effect on selected structural and magnetic properties of NiZn ferrites

Auto-combustion process was used for synthetization of Ni1−x Zn x Fe2O4 and Ni1−x Zn x La0.02Fe1.98O4 (x = 0, 0.3, 0.5, 0.64 and 0.7) ferrite samples to investigate their structural and selected magnetic properties. Standard characterization method such as x-ray diffraction, magnetic susceptibility temperature dependencies measurement, low-frequency hysteresis loops recording and complex permeability spectra were used on the research samples. The monophasic ferrite compounds have been prepared. For all samples, with an increase of zinc ions in the content, a decrease of the Curie temperature and coercive field value and an increase of the complex permeability real part value were observed, together with a shift of the ferrimagnetic resonance frequency value to lower ones. Substituted samples showed some differences, such as slightly higher values of the Curie temperature and coercive field, and at the same time slightly lower values of the complex permeability real part and higher values of the ferrimagnetic resonance frequency.

Heating ability of elongated magnetic nanoparticles.

Low-frequency hysteresis loops and specific absorption rate (SAR) of various assemblies of elongated spheroidal magnetite nanoparticles have been calculated for a range of particle semiaxis ratios a/b = 1.0–3.0. The SAR of a dilute randomly oriented assembly of magnetite nanoparticles in an alternating magnetic field of moderate frequency, f = 300 kHz, and amplitude H0 = 100–200 Oe is shown to decrease significantly with an increase in the aspect ratio of nanoparticles. In addition, there is a narrowing and shift of the intervals of optimal particle diameters towards smaller particle sizes. However, the orientation of a dilute assembly of elongated nanoparticles in a magnetic field leads to an almost twofold increase in SAR at the same frequency and amplitude of the alternating magnetic field, the range of optimal particle diameters remaining unchanged. The effect of the magneto-dipole interaction on the SAR of a dilute assembly of oriented clusters of elongated magnetite nanoparticles has also been investigated depending on the volume fraction of nanoparticles in a cluster. It has been found that the SAR of the assembly of oriented clusters decreases by approximately an order of magnitude with an increase in the volume fraction of nanoparticles in a cluster in the range of 0.04–0.2.

Heating ability of magnetic nanoparticles with cubic and combined anisotropy.

The low frequency hysteresis loops and specific absorption rate (SAR) of assemblies of magnetite nanoparticles with cubic anisotropy are calculated in the diameter range of D = 20–60 nm taking into account both thermal fluctuations of the particle magnetic moments and strong magneto–dipole interaction in assemblies of fractal-like clusters of nanoparticles. Similar calculations are also performed for assemblies of slightly elongated magnetite nanoparticles having combined magnetic anisotropy. A substantial dependence of the SAR on the nanoparticle diameter is obtained for all cases investigated. Due to the influence of the magneto–dipole interaction, the SAR of fractal clusters of nanoparticles decreases considerably in comparison with that for weakly interacting nanoparticles. However, the ability of magnetic nanoparticle assemblies to generate heat can be improved if the nanoparticles are covered by nonmagnetic shells of appreciable thickness.

Unraveling viscosity effects on the hysteresis losses of magnetic nanocubes.

Hysteresis losses in magnetic nanoparticles constitute the basis of magnetic hyperthermia for delivering a local thermal stress. Nevertheless, this therapeutic modality is only to be realised through a careful appraisal of the best possible intrinsic and extrinsic conditions to the nanoparticles for which they maximise and preserve their heating capabilities. Low frequency (100 kHz) hysteresis loops accurately probe the dynamical magnetic response of magnetic nanoparticles in a more reliable manner than calorimetry measurements, providing conclusive quantitative data under different experimental conditions. We consider here a set of iron oxide or cobalt ferrite nanocubes of different sizes, through which we experimentally and theoretically study the influence of the viscosity of the medium on the low frequency hysteresis loops of magnetic colloids, and hence their ability to produce and dissipate heat to the surroundings. We analyse the role of nanoparticle size, size distribution, chemical composition, and field intensity in making the magnetisation dynamics sensitive to viscosity. Numerical simulations using the stochastic Landau-Lifshitz-Gilbert equation model the experimental observations in excellent agreement. These results represent an important contribution towards predicting viscosity effects and hence to maximise heat dissipation from magnetic nanoparticles regardless of the environment.

AC Magnetic Technique to Measure Specific Absorption Rate of Magnetic Nanoparticles

The electrodynamic method is applied to determine the specific absorption rate (SAR) of an assembly of superparamagnetic nanoparticles as a function of frequency and magnetic field amplitude. The home made frequency-adjustable electromagnet is used to create a nearly uniform magnetic field in a core gap of a volume 1×3×3 cm3 in the frequency range f=10–150 kHz and for magnetic field amplitudes up to H 0=250 Oe. Two oppositely connected pick-up coils are used to record the electromotive force signal (EMF) generated by magnetic nanoparticles. By integrating the EMF signal one can determine the low-frequency hysteresis loops of the assembly and the assembly SAR. Using this method the measurement of SAR has been carried out for magnetite nanoparticles with an average diameter D=25 nm. The electrodynamic method is shown to be capable of measuring a small amount of magnetic nanoparticles, up to 5×10−5 g, dispersed in a solid matrix. The maximal SAR ∼ 80 W/g has been obtained for the magnetite nanoparticle assembly investigated.

Hysteresis losses in a dense superparamagnetic nanoparticle assembly

The hysteresis losses of a dense assembly of magnetite nanoparticles with an average diameter D = 25 nm are measured in the frequency range f = 10 – 200 kHz for magnetic field amplitudes up to H0 = 400 Oe. The low frequency hysteresis loops of the assembly are obtained by means of integration of the electro-motive force signal arising in a small pick-up coil wrapped around a sample which contains 1 – 5 mg of a magnetite powder. It is proved experimentally that the specific absorption rate diminishes approximately 4.5 times when the sample aspect ratio decreases from 11.4 to 1. Theoretical estimate shows that experimentally measured hysteresis loops can be approximately described only by taking into account appreciable contributions of magnetic nanoparticles of both very small, D < 10 – 12 nm, and rather large, D > 30 nm, diameters. Thus the wide particle size distribution has to be assumed.

Low frequency hysteresis loops of superparamagnetic nanoparticles with uniaxial anisotropy

The low frequency hysteresis loops of superparamagnetic nanoparticles with uniaxial anisotropy are calculated as a function of the particle diameter, alternating magnetic field amplitude H0, frequency, and particle magnetic parameters both for oriented and nonoriented assemblies. The magnetic field frequency is assumed so high, f>50–100 kHz, that the mechanical rotation of a particle in surrounding medium is restricted. Thus, only the Neel–Brown magnetization relaxation process is taken into account. Pronounced dependence of the specific loss power on the particle diameter is found in the linear regime pertaining to small magnetic field amplitudes. For an oriented assembly of Co nanoparticles with optimal diameter D≈6 nm the specific power loss can be as high as 1600 W/g for typical values H0=200 Oe and f=500 kHz. It is three times less for the corresponding nonoriented assembly. Nevertheless, using of particles with low anisotropy field, i.e., particles of soft magnetic type, seems to be preferable for the purpose of magnetic nanoparticle hyperthermia. For such an assembly the nonlinear regime can be easily accessed. Hence the hysteresis loop area increases and is comparable with its maximum possible value.

XRD, HRTEM and magnetic properties of mixed spinel nanocrystalline Ni–Zn–Cu-ferrite

Nanocrystalline Ni 0.4Zn 0.4Cu 0.2Fe 2O 4 samples with different particle sizes are prepared by simple co-precipitation method. The mixed spinel phases of the nanocrystalline materials have been confirmed by X-ray diffractograms (XRD). The sizes of the nanoparticles are estimated from the (3 1 1) peaks of the XRD patterns using Debye–Sherrer equation and are lying in the range of 7–32 nm. High-resolution TEM observations also support the findings obtained from XRD. Specific saturation magnetizations measured by vibrating sample magnetometer (VSM) are found to increase steadily with the increase of average particle size. Nature of variations of the magnetization curves of the different particle sizes samples are of typical superparamagnetic behaviours up to 16 nm beyond which ferrimagnetic ordered particles are dominating over superparamagnetic particles. The coercive field for a sample of particle size 12 nm is interestingly low (87 A/m) where the saturation magnetization is also moderately high (∼50 A m 2/kg). The coercive fields of the different samples obtained from low frequency hysteresis loops observations show that even in case of sample with lowest particle size, a small fraction of particles are not relaxed within the experimental time window.

Dynamics and scaling of low-frequency hysteresis loops in nanomagnets

The magnetic hysteresis and its area for two-dimensional nanomagnets with precessional magnetization reversal, driven by ac magnetic field of frequency $f$ and amplitude ${H}_{0}$, are investigated by numerically solving the Landau-Lifshitz-Gilbert equation. Irregular hysteresis loops are observed when $f$ is low and ${H}_{0}$ is high, indicating the significant contribution of nonadiabatic precession to the magnetization reversal. The frequency dispersion of hysteresis area $A(f)$ shows the double-peaked pattern with the low-$f$ peak caused by the precessional magnetization reversal and the high-$f$ peak originating from the quasichaotic oscillations of the spin precession. The power-law scaling behavior of the hysteresis dispersion, i.e., $A\ensuremath{\propto}{H}_{0}^{\ensuremath{\lambda}}{f}^{\ensuremath{\beta}}$ with exponents $\ensuremath{\lambda}=0.60$ and $\ensuremath{\beta}=0.50$, is observed in the low-$f$ range limit. We present the one-parameter dynamic scaling on the low-$f$ hysteresis dispersions over a broad range of ${H}_{0}$, demonstrating the scalability of the hysteresis dispersion and thus the existence of the unique characteristic time for magnetization reversal process in nanomagnets, given the field amplitude ${H}_{0}$.

Hysteresis and limiting cycles in a high frequency ac field

Numerical solutions of Brown’s Fokker-Planck equation are used to analyze the response of a superparamagnetic particle to an ac applied field. The nature of the response is governed by the rate of intrawell relaxation processes: At low driving frequencies they maintain the system close to a quasistationary state, and the response is Markovian. By contrast, probability redistribution effects taking place at high frequencies lead to a non-Markovian response mode which displays memory phenomena. The high frequency limiting cycles are analyzed in detail, and the transition to conventional low frequency hysteresis loops is discussed.

Power absorption and ferromagnetic resonance in Co-rich metallic glasses

The power absorption of Co-rich metallic glasses in the shape of ribbons and microwires has been measured in the microwave frequency range. The technique employed consists of replacing the dielectric of a coaxial transmission line by the amorphous sample to be measured. The ferromagnetic resonance frequency of the microwires has been obtained by analyzing the absorbed power as a function of an external magnetic field. From the evolution of this resonance frequency, the anisotropy field has been deduced and successfully compared to that obtained from low-frequency hysteresis loops.

Behaviour of Na0.5Bi0.5TiO3 ceramics in the a.c. electric field

The dielectric dispersion and influence of a.c. electric field strength on electric permittivity as well as the hysteresis loops for Na0.5Bi0.5TiO3 ceramics were investigated. The dipolar relaxation of Cole—Cole type below 1 MHz is observed. This relaxation significantly evolves with temperature and is connected with dynamics of polar regions. The increasing strength of a.c. electric field shifts the electric permittivity characteristic towards lower temperatures. This effect can be associated with the reactivation and reversal of the polar regions and mechanical stresses rising because of external field action. Examination of the low-frequency hysteresis loops reveals the occurrence of usual ferroelectric properties below 200°C. The occurrence of deformed hysteresis loops above 200°C is discussed in terms of electro-mechanical interaction between polar regions and nonpolar matrix.

Scaling and dynamics of low-frequency hysteresis loops in ultrathin Co films on a Cu(001) surface.

The hysteresis loops of epitaxially grown ultrathin Co films on a Cu(001) surface with magnetic anisotropy were measured in situ at room temperature under a periodic external field by the surface magneto-optical Kerr-effect technique. A dynamic phase transition occurs at high frequencies. At very low frequencies, \ensuremath{\Omega}, a constant hysteresis loop area exists. We also observed power-law scaling of the loop area, A\ensuremath{\sim}${\mathit{H}}_{0}^{\mathrm{\ensuremath{\alpha}}}$${\mathrm{\ensuremath{\Omega}}}^{\mathrm{\ensuremath{\beta}}}$, for ${\mathit{H}}_{0}$>40 Oe and \ensuremath{\Omega}/2\ensuremath{\pi}90 Hz, with exponents \ensuremath{\alpha} and \ensuremath{\beta} each about 2/3. The observations are consistent with a mean-field Ising model.

Hysteresis loops in the low frequency region of the Clausius-Mossotti polarization factor: the result of non-linear boundary conditions at the particle interface

A mathematical model involving a non-linear displacement vector at the interface of a spherical particle with a linear medium, is developed to explain the recent experimental observations of multiple Clausius-Mossotti factors in the low frequency (10 Hz to 1 kHz) domain in the dielectrophoretic spectrum of tobacco protoplasts. The model is the simplest possible extension of the existing spherical model, and is exactly solvable. This model also clearly demonstrates the active role of the electric field in influencing the physical properties of the medium-particle interface. Suitable choice of the second-order parameters in permittivity and conductivity result in good qualitative agreement with the experimentally observed low frequency hysteresis loops (neglecting anomalous dielectrophoresis).

Very low-frequency hysteresis loops in ferroelectric liquid crystals: A new optical technique

A new optical technique for quantitative studies of switching processes in ferroelectric liquid crystals is reported. The molecular reorientational changes are determined directly as a function of the exciting electric field. By that means, information can be obtained which is similar and complementary to that derived from the polarization current measurements. The method is specially adapted for very low-frequency regimes (≤0.1 Hz). In contrast to the polarization technique, there are no spurious conductive and capacitive contributions. The features of the method are illustrated by studying the switching process of a 9-μm-thick sample of p-(n-decyloxybenzylidene)-p-amino-(2-methyl-buthyl) cinnamate (DOBAMBC) under a triangular wave of 0.03 Hz. The temperature dependence of the coercive fields of these low-frequency cycles is found to obey a power law at the chiral smectic C (Sm C*) phase. The frequency dependence of the coercive fields exhibits a null value at the zero-frequency limit in contrast to that of the solid-state ferroelectrics.

The hysteresis loops of individual domain walls and domain-wall motion in grain-oriented 3% Si-Fe

The Kerr magneto-optical effect has been used to study the very low-frequency hysteresis loops of individual 180° domain walls in grain-oriented Si-Fe sheet. Measurements on a number of walls show that the loops vary widely in shape and show similar non-repeatable properties to those reported previously at higher frequencies. The peak movement appears to be independent of the coercive force of the walls, suggesting a model for wall motion in which the retarding forces on the wall due to a combination of magnetostatic fields and imperfections.

A magnetic amplifier for the visual presentation of low-frequency hysteresis loops of very small ferromagnetic samples

This paper describes a magnetic amplifier based on the principle of permeability tuning, and intended for the amplification of small, low-impedance signals obtained from a small ferromagnetic sample (e.g., a ferrite memory core or a thin film). The apparatus is able to produce a good display of a flux as low as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Delta\phi = 10^{-12}</tex> V/s at 50 c/s. In this case, the signal power applied to the amplifier is of the order of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-16</sup> watts.

Quantitative study of low-frequency hysteresis loops of polarized polycrystalline barium titanate

Ferroelectrics belong to that group of dielectrics which are said to be nonlinear, but a nonlinear dielectric is not necessarily ferroelectric. The statement that a dielectric is nonlinear requires rather careful consideration.1 If the temperature of a ferroelectric ceramic and also the external pressure on it are maintained constant, and if an electric field is applied which is below the saturation level, then the electric displacement D, or equivalently the polarization P, depends not only on the magnitude of the applied field but also on the past history and state of strain of the material. Linear dielectrics are characterized by the unique function D(ω) = ω(ω)E(ω), which does not hold true for nonlinear dielectrics. This implies that when one is dealing with a nonlinear dielectric: (1) frequencies appear in P(t), or in D(t), which are not present in E(t); and/or (2) if E1(t) produces D1(t) and E2 produces D2(t), then A1E1(t) + A2E2(t) does not produce A1D1(t) + A2D2(t).

Ferrite Films—New Logic and Storage Devices

Magnetic devices for storage and switching applications in digital computers have been fabricated in the form of open flux path elements. The geometry employed is that of a planar film with thicknesses in the range of 5 to 50 μ and other dimensions in the fractional inch range. These elements have the advantages of a ferrite composition and of open flux paths without many of the disadvantages present in similar metallic devices. For use in storage systems, these devices possess excellent squareness characteristics and have coincident selection times comparable with ferrite-toroidal devices. Properties of these devices are given in terms of switching curves, low-frequency hysteresis loops, and one to zero-signal ratios. Other aspects that are discussed include disturb sensitivity of storage elements,heating effects due to high pulse repetition frequency, and mechanical properties. For each of these, comparison is made with other types of magnetic elements such as toroids and metallic films. Applications are discussed in terms of drive requirements, packing densities, and switching times.