Simple models for dynamic hysteresis loops calculation: Application to hyperthermia optimization

To optimize the heating properties of magnetic nanoparticles (MNPs) in magnetic hyperthermia applications, it is necessary to calculate the area of their hysteresis loops in an alternating magnetic field. The three types of theories suitable for describing the hysteresis loops of MNPs are presented and compared to numerical simulations: equilibrium functions, Stoner-Wohlfarth model based theories (SWMBTs) and linear response theory (LRT). Suitable formulas to calculate the hysteresis area of major cycles are deduced from SWMBTs and from numerical simulations; the domain of validity of the analytical formula is explicitly studied. In the case of minor cycles, the hysteresis area calculations are based on the LRT. A perfect agreement between LRT and numerical simulations of hysteresis loops is obtained. The domain of validity of the LRT is explicitly studied. Formulas to calculate the hysteresis area at low field valid for any anisotropy of the MNP are proposed. Numerical simulations of the magnetic field dependence of the area show it follows power-laws with a large range of exponents. Then, analytical expressions derived from LRT and SWMBTs are used for a theoretical study of magnetic hyperthermia. It is shown that LRT is only pertinent for MNPs with strong anisotropy and that SWMBTs should be used for weak anisotropy MNPs. The optimum volume of MNPs for magnetic hyperthermia as function of material and experimental parameters is derived. The maximum specific absorption rate (SAR) achievable is calculated versus the MNP anisotropy. It is shown that an optimum anisotropy increases the SAR and reduces the detrimental effects of size distribution. The optimum anisotropy is simple to calculate and depends on the magnetic field used in the hyperthermia experiments and on the MNP magnetization only. The theoretical optimum parameters are compared to the one of several magnetic materials.Comment: 35 pages, 1 table, 11 figure

A frequency-adjustable electromagnet for hyperthermia measurements on magnetic nanoparticles

We describe a low-cost and simple setup for hyperthermia measurements on colloidal solutions of magnetic nanoparticles (ferrofluids) with a frequency-adjustable magnetic field in the range 5-500 kHz produced by an electromagnet. By optimizing the general conception and each component (nature of the wires, design of the electromagnet), a highly efficient setup is obtained. For instance, in a useful gap of 1.1 cm, a magnetic field of 4.8 mT is generated at 100 kHz and 500 kHz with an output power of 3.4 W and 75 W, respectively. A maximum magnetic field of 30 mT is obtained at 100 kHz. The temperature of the colloidal solution is measured using optical fiber sensors. To remove contributions due to heating of the electromagnet, a differential measurement is used. In this configuration the sensitivity is better than 1.5 mW at 100 kHz and 19.3 mT. This setup allows one to measure weak heating powers on highly diluted colloidal solutions. The hyperthermia characteristics of a solution of Fe nanoparticles are described, where both the magnetic field and the frequency dependence of heating power have been measured

Magnetic anisotropy determination and magnetic hyperthermia properties of small Fe nanoparticles in the superparamagnetic regime

We report on the magnetic and hyperthermia properties of iron nanoparticles synthesized by organometallic chemistry. They are 5.5 nm in diameter and display a saturation magnetization close to the bulk one. Magnetic properties are dominated by the contribution of aggregates of nanoparticles with respect to individual isolated nanoparticles. Alternative susceptibility measurements are been performed on a low interacting system obtained after eliminating the aggregates by centrifugation. A quantitative analysis using the Gittleman s model allow a determination of the effective anisotropy Keff = 1.3 * 10^5 J.m^{-3}, more than two times the magnetocristalline value of bulk iron. Hyperthermia measurements are performed on agglomerates of nanoparticles at a magnetic field up to 66 mT and at frequencies in the range 5-300 kHz. Maximum measured SAR is 280 W/g at 300 kHz and 66 mT. Specific absorption rate (SAR) displays a square dependence with the magnetic field below 30 mT but deviates from this power law at higher value. SAR is linear with the applied frequency for mu_0H=19 mT. The deviations from the linear response theory are discussed. A refined estimation of the optimal size of iron nanoparticles for hyperthermia applications is provided using the determined effective anisotropy value

Magnetic hyperthermia in single-domain monodisperse FeCo nanoparticles: Evidences for Stoner-Wohlfarth behaviour and large losses

We report on hyperthermia measurements on a colloidal solution of 15 nm monodisperse FeCo nanoparticles (NPs). Losses as a function of the magnetic field display a sharp increase followed by a plateau, which is what is expected for losses of ferromagnetic single-domain NPs. The frequency dependence of the coercive field is deduced from hyperthermia measurement and is in quantitative agreement with a simple model of non-interacting NPs. The measured losses (1.5 mJ/g) compare to the highest of the literature, though the saturation magnetization of the NPs is well below the bulk one.Comment: 14 pages, 3 figure

Magnetoresistance and collective Coulomb blockade in super-lattices of ferromagnetic CoFe nanoparticles

We report on transport properties of millimetric super-lattices of CoFe nanoparticles surrounded by organic ligands. R(T)s follow R(T) = R_0.exp(T/T_0)^0.5 with T_0 ranging from 13 to 256 K. At low temperature I(V)s follow I=K[(V-V_T)/V_T]^ksi with ksi ranging 3.5 to 5.2. I(V) superpose on a universal curve when shifted by a voltage proportional to the temperature. Between 1.8 and 10 K a high-field magnetoresistance with large amplitude and a strong voltage-dependence is observed. Its amplitude only depends on the magnetic field/temperature ratio. Its origin is attributed to the presence of paramagnetic states present at the surface or between the nanoparticles. Below 1.8 K, this high-field magnetoresistance abruptly disappears and inverse tunnelling magnetoresistance is observed, the amplitude of which does not exceed 1%. At this low temperature, some samples display in their I(V) characteristics abrupt and hysteretic transitions between the Coulomb blockade regime and the conductive regime. The increase of the current during these transitions can be as high as a factor 30. The electrical noise increases when the sample is near the transition. The application of a magnetic field decreases the voltage at which these transitions occur so magnetic-field induced transitions are also observed. Depending on the applied voltage, the temperature and the amplitude of the magnetic field, the magnetic-field induced transitions are either reversible or irreversible. These abrupt and hysteretic transitions are also observed in resistance-temperature measurements. They could be the soliton avalanches predicted by Sverdlov et al. [Phys. Rev. B 64, 041302 (R), 2001] or could also be interpreted as a true phase transition between a Coulomb glass phase to a liquid phase of electrons

Influence of a transverse static magnetic field on the magnetic hyperthermia properties and high-frequency hysteresis loops of ferromagnetic FeCo nanoparticles

The influence of a transverse static magnetic field on the magnetic hyperthermia properties is studied on a system of large-losses ferromagnetic FeCo nanoparticles. The simultaneous measurement of the high-frequency hysteresis loops and of the temperature rise provides an interesting insight into the losses and heating mechanisms. A static magnetic field of only 40 mT is enough to cancel the heating properties of the nanoparticles, a result reproduced using numerical simulations of hysteresis loops. These results cast doubt on the possibility to perform someday magnetic hyperthermia inside a magnetic resonance imaging setup.Comment: 6 pages, 3 figure

Voltage and Temperature Dependence of High-Field Magnetoresistance in Arrays of Magnetic Nanoparticles

Huge values of high field magnetoresistance have been recently reported in large arrays of CoFe nanoparticles embedded in an organic insulating lattice in the Coulomb blockade regime. An unusual exponential decrease of magnetoresistance with increasing voltage was observed, as well as a characteristic scaling of the magnetoresistance amplitude versus the field-temperature ratio. We propose a model which takes into account the influence of paramagnetic impurities on the transport properties of the system to describe these features. It is assumed that the non-colinearity between the core spins inside the nanoparticles and the paramagnetic impurities can be modelled by an effective tunnel barrier, the height of which depends on the relative angle between the magnetization of both kind of spins. The influence on the magnetotransport properties of the height and the thickness of the effective tunnel barrier of the magnetic moment of the impurity, as well as the bias voltage are studied. This model allows us to reproduce the large magnetoresistance magnitude observed and its strong voltage dependence, with realistic parameters.Comment: 19 pages, with 6 figures, references and figure caption

Analysis of a new class of Forward Semi-Lagrangian schemes for the 1D Vlasov-Poisson Equations

International audienceThe Vlasov equation is a kinetic model describing the evolution of charged particles, and is coupled with Poisson's equation, which rules the evolution of the self-consistent electric field. In this paper, we introduce a new class of forward Semi-Lagrangian schemes for the Vlasov-Poisson system based on a Cauchy Kovalevsky (CK) procedure for the numerical solution of the characteristic curves. Exact conservation properties of the first moments of the distribution function for the schemes are derived and a convergence study is performed that applies as well for the CK scheme as for a more classical Verlet scheme. The convergence in L1 norm of the schemes is proved and error estimates are obtained

A charge preserving scheme for the numerical resolution of the Vlasov-Ampère equations

International audienceIn this report, a charge preserving numerical resolution of the 1D Vlasov-Ampère equation is achieved, with a forward Semi-Lagrangian method introduced in \cite{4respaud}. The Vlasov equation belongs to the kinetic way of simulating plasmas evolution, and is coupled with the Poisson's equation, or equivalently under charge conservation, the Ampère's one, which self-consistently rules the electric field evolution. In order to ensure having proper physical solutions, it is necessary that the scheme preserves charge numerically. B-Spline deposition will be used for the interpolation step. The solving of the characteristics will be made with a Runge-Kutta 2 method and with a Cauchy-Kovalevsky procedure