The low frequency hysteresis loops and specific absorption rate (SAR) of assemblies of magnetite nanoparticles with cubic anisotropy are calculated in the diameter range of D = 20–60 nm taking into account both thermal fluctuations of the particle magnetic moments and strong magneto–dipole interaction in assemblies of fractal-like clusters of nanoparticles. Similar calculations are also performed for assemblies of slightly elongated magnetite nanoparticles having combined magnetic anisotropy. A substantial dependence of the SAR on the nanoparticle diameter is obtained for all cases investigated. Due to the influence of the magneto–dipole interaction, the SAR of fractal clusters of nanoparticles decreases considerably in comparison with that for weakly interacting nanoparticles. However, the ability of magnetic nanoparticle assemblies to generate heat can be improved if the nanoparticles are covered by nonmagnetic shells of appreciable thickness.

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.

The energy diagram of stationary magnetization states existing in polycrystalline cobalt nanoparticles in the range of diameters 20 ≤ D ≤ 60 nm has been calculated by means of numerical simulation. It is shown that in polycrystalline cobalt nanoparticles in the range of diameters D ≥ 32 nm only vortex states with low average magnetization are present, whereas mostly quasi-uniform states are realized in nanoparticles with diameter D ≤ 24 nm. Thus, the effective single-domain diameter of polycrystalline cobalt nanoparticles is estimated to be Dc = 24 nm. It is approximately two times smaller than the actual single-domain diameter of monocrystalline cobalt nanoparticle, Dc0 = 45 nm. The hysteresis loops of a dilute assembly of polycrystalline cobalt nanoparticles in the range of diameters D ≤ Dc are characterized by a coercive force that is approximately 2.5 times less compared with that of the randomly oriented assembly of monocrystalline cobalt nanoparticles.

Multi-domain structures in spheroidal co nanoparticles n. A. Usov 1,2 ✉ & M. S. nesmeyanov 2 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 twoand three-domain micromagnetic states. the single-domain diameters of fcc cobalt nanoparticles with cubic type of magnetic anisotropy were also calculated. Cobalt nanoparticles attract substantial interest due to their technological significance 1. They were also the first magnetic nanoparticles extensively studied theoretically 2-5. However, the theory of small magnetic particles developed by Kittel 2 , Stoner and Wohlfarth 3 , Brown 4 , and Aharoni 5 is only capable to describe the magnetic properties of single-domain nanoparticles. Meanwhile, magnetic nanoparticles of submicron sizes are often found in practice. For example, the assemblies of magnetic nanoparticles with a wide size distribution are frequently obtained in chemical synthesis 6 , so that the sizes of some particles may exceed the corresponding single domain diameter. Particles of sufficiently large sizes can arise during prolonged annealing of thin-film samples 7 , they can be created as a result of implantation process 8 , etc. It is worth noting that the magnetic properties of submicron-sized nanoparticles play an important role in paleo-magnetism 9. The magnetic properties of nanoparticles in inhomogeneous micromagnetic states differ significantly from those of single-domain ones 1,4,5. However, the characteristics of nanoparticles of sufficiently large sizes are still poorly investigated. In particular, the dependence of the single-domain diameter of a spheroidal cobalt nanoparticle on its aspect ratio is unknown. The upper and lower analytical estimates for the single-domain diameter of magnetic nanoparticle given by Brown 10 are not always close enough. Therefore, in most cases a detailed numerical simulation is necessary to determine the single-domain diameter of particles of various magnetic materials. At present, domain structures in submicron cobalt nanoparticles and cobalt nanowires are experimentally studied using magnetic force microscopy 11,12. In addition, modern electronic holography technique 13-17 allows to study experimentally inhomogeneous micromagnetic distributions in magnetic nanoparticles and nanowires. This revives interest in detailed micromagneti...

The influence of the crystal structure inhomogeneities on the magnetic properties of cobalt nanoparticles with different aspect ratio and spherical nanoparticles of chromium dioxide, cobalt ferrite and magnetite has been studied by means of numerical simulation. The polycrystalline nanoparticles are modeled by means of subdivision of the nanoparticle volume into tightly bound single-crystal granules with randomly distributed directions of the easy anisotropy axes. The probability of appearance of quasi uniform and vortex states in sufficiently large assemblies of polycrystalline nanoparticles of various types have been calculated depending on the nanoparticle diameter. It is shown that the subdivision of a nanoparticle into single-crystal granules with different orientations of the easy anisotropy axes substantially reduces the effective single-domain diameters for particles with uniaxial type of anisotropy of individual granules. However, for particles with cubic type of magnetic anisotropy the influence of the crystal structure inhomogeneities on the equilibrium properties of the particles is not so important even for magnetically hard cobalt ferrite nanoparticles. It is practically absent for magnetically soft magnetite nanoparticles.PACS 75.50.Tt; 75.40.Mg