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

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

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

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

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

Hysteretic properties of a magnetic particle with strong surface anisotropy

We study the influence of surface anisotropy on the zero-temperature hysteretic properties of a small single-domain magnetic particle, and give an estimation of the anisotropy constant for which deviations from the Stoner-Wohlfarth model are observed due to non-uniform reversal of the particle's magnetisation. For this purpose, we consider a spherical particle with simple cubic crystalline structure, a uniaxial anisotropy for core spins and radial anisotropy on the surface. The hysteresis loop is obtained by solving the local (coupled) Landau-Lifschitz equations for classical spin vectors. We find that when the surface anisotropy constant is at least of the order of the exchange coupling, large deviations are observed with respect to the Stoner-Wohlfarth model in the hysteresis loop and thereby the limit-of-metastability curve, since in this case the magnetisation reverses its direction in a non-uniform manner via a progressive switching of spin clusters. In this case the critical field, as a function of the particle's size, behaves as observed in experiments.Comment: 12 pages, 15 eps figure

Spin dephasing in n-typed GaAs quantum wells in the presence of high magnetic fields in Voigt configuration

We perform a many-body study of the spin dephasing due to the D'yakonov-Perel' effect in n-typed GaAs (100) quantum wells under high magnetic fields in the Voigt configuration by constructing and numerically solving the kinetic Bloch equations. We include all the spin conserving scattering such as electron-phonon, the electron-nonmagnetic impurity as well as the electron-electron Coulomb scattering in our theory and investigate how the spin dephasing time (SDT) is affected by the initial spin polarization, impurity, and magnetic field. The dephasing obtained from our theory contains not only that due to the effective spin-flipping scattering first proposed by D'yakonov and Perel' [Zh. Eksp. Teor. Fiz. {\bf 60}, 1954 (1971)[Sov. Phys.-JETP {\bf 38}, 1053 (1971)]], but also the recently proposed many-body dephasing due to the inhomogeneous broadening provided by the DP term [Wu, J. Supercond.:Incorp. Novel Mechanism {\bf 14}, 245 (2001); Wu and Ning, Eur. Phys. J. B {\bf 18}, 373 (2000)]. We are able to investigate the spin dephasing with extra large spin polarization (up to 100 %) which has not been discussed both theoretically and experimentally. A huge anomalous resonance of the SDT for large spin polarizations is predicted under the high magnetic field we used.Comment: 8 pages, Revtex, 7 figures in EPS forma

Boundary and finite-size effects in small magnetic systems

We study the effect of free boundaries in finite magnetic systems of cubic shape on the field and temperature dependence of the magnetization within the isotropic model of D-component spin vectors in the limit D \to \infty. This model is described by a closed system of equations and captures the Goldstone-mode effects such as global rotation of the magnetic moment and spin-wave fluctuations. We have obtained an exact relation between the intrinsic (short-range) magnetization M = M(H,T) of the system and the supermagnetization m = m(H,T) which is induced by the field. We have shown, analytically at low temperatures and fields and numerically in a wide range of these parameters, that boundary effects leading to the decrease of M with respect to the bulk value are stronger than the finite-size effects making a positive contribution to M. The inhomogeneities of the magnetization caused by the boundaries are long ranged and extend far into the depth of the system.Comment: 15 pages, 5 figures, To appear in Physica