Understanding the influence of dipolar interactions in magnetic hyperthermia (MH) experiments is of crucial importance for a fine optimization of nanoparticle (NP) heating power. In this study, we use a kinetic Monte-Carlo algorithm to calculate hyst
eresis loops, so both time and temperature are correctly taken into account. It is demonstrated that this algorithm correctly reproduces the high-frequency hysteresis loop of both superparamagnetic NPs and ferromagnetic ones without any ad-hoc parameters. The algorithm is easily parallelizable so calculation on several processors decreases considerably calculation time. The specific absorption rate (SAR) of NPs dispersed inside spherical lysosomes is studied as a function of several key parameters: volume concentration, applied magnetic field, lysosome size, NP diameter and anisotropy. The influence of these parameters is illustrated and comprehensively explained. In summary, the effect of magnetic interactions is to increase the coercive field, saturation field and hysteresis area of major loops. However, for small amplitude magnetic field such as the ones used in MH, the heating power as function of concentration can increase, decrease or display a bell shape, depending of the relationship between the applied magnetic field and the coercive/saturation fields of the NPs. The hysteresis area is found to be well correlated to the parallel or antiparallel nature of the dipolar field acting on each NP. It is shown that the heating power increases or decreases sharply in the vicinity of the lysosome membrane. The amplitude of variation reaches more than one order of magnitude in certain conditions. Finally, implications of these various findings are discussed in the framework of MH optimization. It is concluded that feedbacks on specific points from biology experiments are required for further advance on the optimization of NPs for MH.
A low-cost and simple setup for measuring the high-frequency hysteresis loops of magnetic samples is described. An AMF 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 appr
oach 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 MNPs for magnetic hyperthermia applications.
When magnetic nanoparticles (MNPs) are single-domain and magnetically independent, their magnetic properties and the conditions to optimize their efficiency in magnetic hyperthermia applications are now well-understood. However, the influence of magn
etic interactions on magnetic hyperthermia properties is still unclear. Here, we report hyperthermia and high-frequency hysteresis loop measurements on a model system consisting of MNPs with the same size but a varying anisotropy, which is an interesting way to tune the relative strength of magnetic interactions. A clear correlation between the MNP anisotropy and the squareness of their hysteresis loop in colloidal solution is observed : the larger the anisotropy, the smaller the squareness. Since low anisotropy MNPs display a squareness higher than the one of magnetically independent nanoparticles, magnetic interactions enhance their heating power in this case. Hysteresis loop calculations of independent and coupled MNPs are compared to experimental results. It is shown that the observed features are a natural consequence of the formation of chains and columns of MNPs during hyperthermia experiments: in these structures, when the MNP magnetocristalline anisotropy is small enough to be dominated by magnetic interactions, the hysteresis loop shape tends to be rectangular, which enhance their efficiency. On the contrary, when MNPs do not form chains and columns, magnetic interactions reduces the hysteresis loop squareness and the efficiency of MNPs compared to independent ones. The present work should improve the understanding and interpretation of magnetic hyperthermia experiments.
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 temper
ature 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.
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 desc
ribing 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.
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 co
ntribution 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.
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 i
s 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.
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 k
si 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.
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 ferromag
netic 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.
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 gen
eral 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.
