Deconvolution of ferromagnetic resonance spectrum of magnetic nanoparticle assembly using genetic algorithm.

The ferromagnetic resonance (FMR) spectra of dilute random assemblies of magnetite nanoparticles with cubic magnetic anisotropy and various aspect ratios are calculated using the stochastic Landau-Lifshitz equation at a finite temperature, T = 300 K, taking into account the thermal fluctuations of the particle magnetic moments. Particles of non-spherical shape in the first approximation are described as elongated spheroids with a given semiaxes ratio a/b, where a and b are the long and transverse semiaxes of a spheroid, respectively. A representative database of FMR spectra is created for assemblies of randomly oriented spheroidal magnetite nanoparticles with various transverse diameters D = 5-25 nm, moderate aspect ratios a/b = 1.0-1.8, and magnetic damping constants κ = 0.1, 0.2. The basic FMR spectra of assemblies with D = 25 nm at different aspect ratios can be considered as representatives of assemblies of single-domain magnetite nanoparticles with transverse diameters D > 25 nm. The database is calculated at exciting frequency f = 4.9 GHz (S-band) to clarify the details of the FMR spectrum that depend on the particle magnetic anisotropy nature. The data obtained make it possible to analyze arbitrary combined FMR spectra constructed as weighted linear combinations of FMR spectra of the base assemblies. In addition, using a genetic algorithm, the corresponding inverse problem is solved. The latter consists in determining the volume fractions of the base assemblies in some arbitrary nanoparticle assembly, which is represented by its FMR spectrum.

Towards optimal thermal distribution in magnetic hyperthermia.

A linear combination of spherically symmetric heat sources is shown to provide optimal stationary thermal distribution in magnetic hyperthermia. Furthermore, such spatial location of heat sources produces suitable temperature distribution in biological medium even for assemblies of magnetic nanoparticles with a moderate value of specific absorption rate (SAR), of the order of 100-150 W/g. We also demonstrate the advantage of using assemblies of spherical magnetic nanocapsules consisting of metallic iron nanoparticles covered with non magnetic shells of sufficient thickness in magnetic hyperthermia. Based on numerical simulation we optimize the size and geometric structure of biocompatible spherical capsules in order to minimize the influence of strong magneto-dipole interaction between closely spaced nanoparticles. It is shown that assembly of capsules can provide sufficiently high SAR values of the order of 250-400 W/g at moderate amplitudes H0 = 50-100 Oe and frequencies f = 100-200 kHz of alternating magnetic field, being appropriate for application in clinics.

Properties of assembly of superparamagnetic nanoparticles in viscous liquid.

Detailed calculations of the specific absorption rate (SAR) of a dilute assembly of iron oxide nanoparticles with effective uniaxial anisotropy dispersed in a liquid are performed depending on the particle diameters, the alternating (ac) magnetic field amplitude H0 and the liquid viscosity. For small and moderate H0 values with respect to particle anisotropy field Hk the SAR of the assembly as a function of the particle diameter passes through a characteristic maximum and then reaches a plateau, whereas for sufficiently large amplitudes, H0 ~ Hk, the SAR increases monotonically as a function of diameter. The realization of viscous and magnetic oscillation modes for particle unit magnetization vector and director for moderate and sufficiently large H0 values, respectively, explains this behavior. It is found that the SAR of the assembly changes inversely with the viscosity only in a viscous mode, for nanoparticles of sufficiently large diameters. In the magnetic mode the SAR of the assembly is practically independent of the viscosity, since in this case the nanoparticle director only weakly oscillates around the ac magnetic field direction. The conditions for the validity of the linear response theory have been clarified by comparison with the numerical simulation data.

Equilibrium properties of assembly of interacting superparamagnetic nanoparticles.

The stochastic Landau-Lifshitz equation is used to investigate the relaxation process and equilibrium magnetization of interacting assembly of superparamagnetic nanoparticles (SPMNPs) uniformly distributed in a nonmagnetic matrix. For weakly interacting assembly, the equilibrium magnetization is shown to deviate significantly from the Langevin law at moderate and large magnetic fields under the influence of their magnetic anisotropies. For dense assemblies with noticeable influence of the magneto-dipole interaction, a significant dependence of the initial susceptibility on the assembly density is revealed. The difference between the initial susceptibility and the corresponding Langevin susceptibility can serve as an indication of appreciable influence of the magneto-dipole interaction on the assembly properties. A new self-consistent approach is developed to explain the effect of mutual magneto-dipole interaction on the behavior of dense assembly of SPMNPs. The probability densities of the components of random magnetic field acting on magnetic NPs are calculated at thermodynamic equilibrium. The self-consistent probability densities of these components are found to be close to Gaussian distribution. A decreasing equilibrium assembly magnetization as a function of its density can be explained as a disorienting effect of the random magnetic field on the NPs magnetic moments.

Multi-domain structures in spheroidal Co nanoparticles.

The structure of multi-domain micromagnetic states in hcp cobalt nanoparticles of spheroidal shape has been studied using numerical simulation in the range of diameters 20-200 nm. The single-domain diameters of the particles are determined depending on their aspect ratio. The complicated vortex structure of domain walls for two- and three-domain micromagnetic configurations is investigated. It has been shown that three domain states are actually strongly deformed two vortex states. In hcp cobalt particles of sufficiently large sizes two types of three-domain micromagnetic states with close total energies have been obtained. They differ in different magnetization directions of the exchange cores of the vortex domain walls. The remanent magnetization of particles has been calculated for two- and three-domain micromagnetic states. The single-domain diameters of fcc cobalt nanoparticles with cubic type of magnetic anisotropy were also calculated.

Magnetic Vortices as Efficient Nano Heaters in Magnetic Nanoparticle Hyperthermia.

Magnetic vortices existing in soft magnetic nanoparticles with sizes larger than the single-domain diameter can be efficient nano-heaters in biomedical applications. Using micromagnetic numerical simulation we prove that in the optimal range of particle diameters the magnetization reversal of the vortices in spherical iron and magnetite nanoparticles is possible for moderate amplitudes of external alternating magnetic field, H0 < 100 Oe. In contrast to the case of superparamagnetic nanoparticles, for the vortex configuration the hysteresis loop area increases as a function of frequency. Therefore, high values of the specific absorption rate, on the order of 1000 W/g, can be obtained at frequencies f = 0.5-1.0 MHz. Because the diameter D of a non single-domain particle is several times larger than the diameter d of a superparamagnetic particle, the volume of heat generation for the vortex turns out to be (D/d)3 times larger. This shows the advantage of vortex configurations for heat generation in alternating magnetic field in biomedical applications.

Interaction Effects in Assembly of Magnetic Nanoparticles.

A specific absorption rate of a dilute assembly of various random clusters of iron oxide nanoparticles in alternating magnetic field has been calculated using Landau-Lifshitz stochastic equation. This approach simultaneously takes into account both the presence of thermal fluctuations of the nanoparticle magnetic moments and magneto-dipole interaction between the nanoparticles of the clusters. It is shown that for usual 3D clusters, the intensity of the magneto-dipole interaction is determined mainly by the cluster packing density η = N p V/V cl , where N p is the average number of the particles in the cluster, V is the nanoparticle volume, and V cl is the cluster volume. The area of the low frequency hysteresis loop and the assembly-specific absorption rate have been found to be considerably reduced when the packing density of the clusters increases in the range of 0.005 ≤ Î· < 0.4. The dependence of the specific absorption rate on the mean nanoparticle diameter is retained with an increase of η, but becomes less pronounced. For fractal clusters of nanoparticles, which arise in biological media, in addition to a considerable reduction of the absorption rate, the absorption maximum is shifted to smaller particle diameters. It is found also that the specific absorption rate of fractal clusters increases appreciably with an increase of the thickness of nonmagnetic shells at the nanoparticle surfaces.