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

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

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

Common fixed point theorems for compatible and weakly compatible mappings

Results on common fixed points for pairs of single and multivalued mappings on a complete metric space are examined. Our work establishes a common fixed point theorem for a pair of generalized contraction self-maps and a pair of set-valued mappings

Quantum Ignition of Intramolecular Rotation by Means of IR+UV Laser Pulses

Quantum ignition of intramolecular rotation may be achieved as follows: First, a few-cycle infrared (IR) laser pulse excites the torsional vibration in an oriented molecule. Subsequently, a well timed ultrashort ultraviolet (UV) laser pulse induces a Franck-Condon type transition from the electronic ground state to the excited state with approximate conservation of the intramolecular angular momentum. As a consequence, the torsional motion is converted into a unidirectional intramolecular rotation, with high angular momentum (≈ 100 h). The mechanism is demonstrated by means of representative laser driven wave packets which are propagated on ab initio potential energy curves of the model system (4-methyl-cyclohexylidene)fluoromethane

Large specific absorption rates in the magnetic hyperthermia properties of metallic iron nanocubes

We report on the magnetic hyperthermia properties of chemically synthesized ferromagnetic 11 and 16 nm Fe(0) nanoparticles of cubic shape displaying the saturation magnetization of bulk iron. The specific absorption rate measured on 16 nm nanocubes is 1690+-160 W/g at 300 kHz and 66 mT. This corresponds to specific losses-per-cycle of 5.6 mJ/g, largely exceeding the ones reported in other systems. A way to quantify the degree of optimization of any system with respect to hyperthermia applications is proposed. Applied here, this method shows that our nanoparticles are not fully optimized, probably due to the strong influence of magnetic interactions on their magnetic response. Once protected from oxidation and further optimized, such nano-objects could constitute efficient magnetic cores for biomedical applications requiring very large heating power

Particle interactions in liquid magnetic colloids by zero field cooled measurements: effects on heating efficiency

The influence of magnetic interactions in assemblies formed by either aggregated or disaggregated uniform gamma-Fe_2O_3 particles are investigated as a function of particle size, concentration, and applied field. Hyperthermia and magnetization measurements are performed in the liquid phase of colloids consisting of 8 and 13 nm uniform gamma-Fe_2O_3 particles dispersed in water and hexane. Although hexane allows the disagglomerated obtaining particle system; aggregation is observed in the case of water colloids. The zero field cooled (ZFC) curves show a discontinuity in the magnetization values associated with the melting points of water and hexane. Additionally, for 13 nm gamma-Fe_2O_3 dispersed in hexane, a second magnetization jump is observed that depends on particle concentration and shifts toward lower temperature by increasing applied field. This second jump is related to the strength of the magnetic interactions as it is only present in disagglomerated particle systems with the largest size, i.e., is not observed for 8 nm superparamagnetic particles, and surface effects can be discarded. The specific absorption rate (SAR) decreases with increasing concentration only for the hexane colloid, whereas for aqueous colloids, the SAR is almost independent of particle concentration. Our results suggest that, as a consequence of the magnetic interactions, the dipolar field acting on large particles increases with concentration, leading to a decrease of the SAR