B. Mehdaoui

Simple models for dynamic hysteresis loop calculations of magnetic single-domain nanoparticles: Application to magnetic 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 separation between “relaxation losses” and “hysteresis losses” presented in several articles is artificial and criticized here. The three types of theories suitable for describing hysteresis loops of MNPs are presented and compared to numerical simulations: equilibrium functions, Stoner–Wohlfarth model based theories (SWMBTs), and a linear response theory (LRT) using the Neel–Brown relaxation time. The configuration where the easy axis of the MNPs is aligned with respect to the magnetic field and the configuration of a random orientation of the easy axis are both studied. Suitable formulas to calculate the hysteresis areas 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 the LRT and numerical simulations of hysteresis loops is obtained. The domain of validity of the LRT is explicitly studied. Formulas are proposed to calculate the hysteresis area at low field that are valid for any anisotropy of the MNP. The magnetic field dependence of the area is studied using numerical simulations: it follows power laws with a large range of exponents. Then analytical expressions derived from the LRT and SWMBTs are used in their domains of validity 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 weakly anisotropic MNPs. The optimum volume of MNPs for magnetic hyperthermia is derived as a function of material and experimental parameters. Formulas are proposed to allow to the calculation of the optimum volume for any anisotropy. The maximum achievable specific absorption rate (SAR) is calculated as a function of the MNP anisotropy. It is shown that an optimum anisotropy increases the SAR and reduces the detrimental effects of the size distribution of the MNPs. The optimum anisotropy is simple to calculate; it depends only on the magnetic field used in the hyperthermia experiments and the MNP magnetization. The theoretical optimum parameters are compared to those of several magnetic materials. A brief review of experimental results as well as a method to analyze them is proposed. This study helps in the determination of suitable and unsuitable materials for magnetic hyperthermia and provides accurate formulas to analyze experimental data. It is also aimed at providing a better understanding of magnetic hyperthermia to researchers working on this subject.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.

A Simple Chemical Route toward Monodisperse Iron Carbide Nanoparticles Displaying Tunable Magnetic and Unprecedented Hyperthermia Properties

We report a tunable organometallic synthesis of monodisperse iron carbide and core/shell iron/iron carbide nanoparticles displaying a high magnetization and good air-stability. This process based on the decomposition of Fe(CO)(5) on Fe(0) seeds allows the control of the amount of carbon diffused and therefore the tuning of nanoparticles magnetic anisotropy. This results in unprecedented hyperthermia properties at moderate magnetic fields, in the range of medical treatments.

Increase of magnetic hyperthermia efficiency due to dipolar interactions in low-anisotropy magnetic nanoparticles: Theoretical and experimental results

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 magnetic 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.

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.

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.

Complex Nano-objects Displaying Both Magnetic and Catalytic Properties: A Proof of Concept for Magnetically Induced Heterogeneous Catalysis

Addition of Co2(Co)9 and Ru3(CO)12 on preformed monodisperse iron(0) nanoparticles (Fe(0) NPs) at 150 °C under H2 leads to monodisperse core-shell Fe@FeCo NPs and to a thin discontinuous Ru(0) layer supported on the initial Fe(0) NPs. The new complex NPs were studied by state-of-the-art transmission electron microscopy techniques as well as X-ray diffraction, Mössbauer spectroscopy, and magnetic measurements. These particles display large heating powers (SAR) when placed in an alternating magnetic field. The combination of magnetic and surface catalytic properties of these novel objects were used to demonstrate a new concept: the possibility of performing Fischer-Tropsch syntheses by heating the catalytic nanoparticles with an external alternating magnetic field.

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.

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

We report on the magnetic and hyperthermia properties of 5.5 nm in diameter iron nanoparticles synthesized by organometallic chemistry, which display the bulk magnetization. Quantitative analysis of alternative susceptibility measurements allows the determination of the effective anisotropy Keff=1.3×105 J m−3. Hyperthermia measurements are performed at a magnetic field up to 66 mT and at frequencies in the range of 5–300 kHz. Maximum measured specific absorption rate (SAR) is 280 W/g. 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 μ0H=19 mT. These results are discussed in the light of linear response theory.