Frequency Hysteresis Loops Research Articles

Tuning magnetic heating efficiency of colloidal dispersions of iron oxide nano-clusters by varying the surfactant concentration during solvothermal synthesis

Magnetic fluid hyperthermia (MFH) is being actively sought as a supplementary cancer therapy, where enhancing the MFH efficiency is essential for reducing dosage and field exposure. Owing to the superior magnetic properties, magnetic nano-clusters (MNCs) are being developed as MFH agents, where the role of synthesis routes, colloidal stability and magneto-structural properties on MFH efficiency requires further attention. In this article, we report the tuning of MFH efficiency of water and diethylene glycol-based magnetic nanofluids containing iron-oxide MNCs of sizes ∼ 125 to 539 nm, obtained by varying the surfactant concentration. Magnetite MNCs are prepared via solvothermal route, where the primary nano-crystallite (MNP) size is varied from 7.4 ± 0.7 to 25.0 ± 0.8 nm by reducing the sodium citrate (surfactant) concentration from 29 to 0.29 mg/mL. With decreasing surfactant concentration, the amount of sodium citrate absorbed on the surface of the freshly formed nano-seeds reduces, which lowers the electrostatic stabilization in polar media and favours the growth of larger MNPs that results in comparatively larger MNCs. Transmission electron microscopy and atomic force microscopy based studies indicate the monodisperse spherical morphology of the MNCs, consisting of several primary nano-crystallites. Room temperature isothermal magnetization measurements indicate high saturation magnetization and superparamagnetic nature of the MNCs, which are beneficial for MFH applications. Magneto-calorimetry experiments are performed for the accurate estimation of the MFH efficiency of the colloidal dispersions of the MNCs. Experimental findings indicate that the heating efficiency increases from 15.24 ± 1.22 to 193.8 ± 5.2 W/gFe (i.e., an enhancement of ∼ 12.7 times), at a field exposure condition of 33.1 kA/m and 126 kHz, when the primary nano-crystallite size is increased by ∼ 3.4 times by reducing the surfactant concentration. It is observed that the heating efficiency decreases linearly with the logarithm of surfactant concentration in all the cases, which is attributed to the variations in primary nano-crystallite sizes and the resultant magnetic losses. Magneto-calorimetric experiments, using MNCs immobilized in high viscosity agar matrix, indicate insignificant contributions from the whole-scale Brownian relaxation, and the heating efficiency is found to be solely dependent on the magnetic losses of the primary nano-crystallites. With increasing primary nano-crystallite size, augmentation of heating efficiency is due to the increase in magnetization and dynamic coercivity, which is confirmed from theoretical calculations using the high frequency hysteresis loops and sweeping rate modified Stoner Wohlfarth model. The obtained results indicate the possibility of tuning hyperthermia efficiency of MNCs by varying the surfactant concentration, which is beneficial for designing colloidally stable dispersions of MNCs with improved MFH efficiency.

Time-dependent AC magnetometry and chain formation in magnetite: the influence of particle size, initial temperature and the shortening of the relaxation time by the applied field.

Magnetite nanoparticles (MNPs) with 12, 34 and 53 nm sizes have been measured by AC-magnetometry at 50 kHz and 57 mT maximum applied field. The MNPs form chains under the AC-field, and the dynamics of the formation can be studied by measuring hysteresis cycles at different times. The measurement time has been varied from 5 ms to 10 s and for different initial temperatures of 5, 25 and 50 °C. The chain formation, identified by the increase of susceptibility and remanence with the measurement time, appears only for 34 nm particles. It has been observed that saturation, remanence and susceptibility at low (high) fields increase (decrease) with time. For the other two samples, these magnitudes are independent of time. At low fields, the heating efficiency is higher at 5 °C than at 50 °C, whereas it shows an opposite behaviour at higher fields; the origin of this behaviour is discussed in the article. Additionally, the relaxation times, τN and τB, have been calculated by considering the influence of the applied field. Chain formation requires translation and rotation of MNPs; therefore, the Brownian mechanism plays a fundamental role. It is found that magnetic reversal for 12 nm MNPs is mainly due to Néel relaxation. However, in the case of 34 nm MNPs, both mechanisms, Néel and Brownian relaxation, can be present depending on the amplitude of the field; for μ0H < 22 mT, the physical rotation of the particle is the dominant mechanism; on the other hand, for μ0H > 22 mT, both mechanisms are present within the size distribution. This highlights the importance of taking the field intensity into account to calculate relaxation times when analysing the relaxation mechanisms of magnetic colloids subjected to AC fields.

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.

An air-cooled Litz wire coil for measuring the high frequency hysteresis loops of magnetic samples--a useful setup for magnetic hyperthermia applications.

A setup for measuring the high-frequency hysteresis loops of magnetic samples is described. An alternating magnetic field in the range 6-100 kHz with amplitude up to 80 mT is produced by a Litz wire coil. The latter is air-cooled using a forced-air approach so no water flow is required to run the setup. High-frequency hysteresis loops are measured using a system of pick-up coils and numerical integration of signals. Reproducible measurements are obtained in the frequency range of 6-56 kHz. Measurement examples on ferrite cylinders and on iron oxide nanoparticle ferrofluids are shown. Comparison with other measurement methods of the hysteresis loop area (complex susceptibility, quasi-static hysteresis loops, and calorific measurements) is provided and shows the coherency of the results obtained with this setup. This setup is well adapted to the magnetic characterization of colloidal solutions of magnetic nanoparticles for magnetic hyperthermia applications.

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 &amp;lt; 10 – 12 nm, and rather large, D &amp;gt; 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&amp;gt;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.

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.

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).

Domain wall pinning in amorphous CoZrNb films

A series of CoZrNb amorphous films, with thickness t ranging from 200 to 630 nm, has been studied by using several techniques: Kerr imaging, dc and audio frequency hysteresis loops, field dependence of the permeability, torque balance, broadband frequency susceptometer (1 kHz≤f≤500 MHz). Only samples with t≤500 nm have simple domain structures typical of an in-plane anisotropy (with a small dispersion of the easy axis). Although domain walls (DW) are visible, they do not contribute to the initial permeability in the observed frequency range (even in the favorable case where the magnetic field is parallel to the easy axis), but they do play a role on the irreversible magnetization processes as shown by the existence of a critical field Hcr, typical of the onset of irreversible DW motion. These observations are consistant with a model which assumes that the DW are pinned at the film surfaces: the calculations give a negligible DW bulging contribution to the initial permeability, and predict the occurence of a DW unpinning field, thickness dependent as observed.

Effect of gaussian irradiance profile on the switching characteristics and the bit size of the fe/pc memory device

In the ferroelectric/photoconductor (FE/PC device, the effect of a gaussian irradiance profile is to give rise to a variable series resistance, in series with the ferroelectric. Low and high frequency hysteresis loops and the FE-switching transients are obtained as a function of series resistance for pulses of fixed amplitude and variable pulse width. Using a four-quadrant plot, the spatial distribution of the charge switched is estimated. Bit size is defined as the distance between the points where the switched polarization drops to half the amount of polarization switched at the center. The bit sizes are calculated for different photoconductor sensitivities and for different drive pulses. The sublinear lux-ampere characteristic of the photoconductor combined with the gaussian irradiance profile causes the recorded bit size to be larger than the light beam diameter.