Field-induced structures in a ferrofluid with well-defined magnetite nanoparticles with a permanent magnetic dipole moment are analyzed on a single-particle level by in situ cryogenic transmission electron microscopy (2D). The field-induced columnar phase locally exhibits hexagonal symmetry and confirms the structures observed in simulations for ferromagnetic dipolar fluids in 2D. The columns are distorted by lens-shaped voids, due to the weak interchain attraction relative to field-directed dipole-dipole attraction. Both dipolar coupling and the dipole concentration determine the dimensions and the spatial arrangement of the columns. Their regular spacing manifests long-range end-pole repulsions that eventually dominate the fluctuation-induced attractions between dipole chains that initiate the columnar transition. DOI: 10.1103/PhysRevLett.97.185702 PACS numbers: 64.70.Nd, 75.50.Mm, 82.70.Dd Nanoparticles dispersed in a solvent and with a sufficiently large permanent magnetic dipole moment selfassemble into a variety of magnetic equilibrium structures such as (flux-closure) rings and wormlike, branched dipole chains [1,2]. The morphology of these clusters, formed in absence of an external field, has been examined in detail, together with a determination of pair correlation functions and chain-length distributions [3]. In contrast, much less is known about the structural transitions induced by an external (homogeneous) magnetic field for fluids of permanent dipoles. Interestingly, magnetic colloids in an external field are nevertheless frequently encountered in practical applications [4] and biomedicine [5,6].The structure formation and phase behavior of colloidal systems in reduced dimensions is not necessarily equivalent to that of three-dimensional (3D) systems [7][8][9]. In particular, for permanent dipolar spheres confined to two dimensions (2D) a field-induced transition to a columnar phase with local hexagonal symmetry was predicted [10], although a conclusive experimental real-space analysis is still lacking. Elongated iron-particle clusters have been imaged [1] but the irregular particle shape and the bidisperse size distribution obstruct the wanted single-particle analysis. Parallel structures have also been observed for maghemite ferrofluids dried in the presence of a homogeneous field [11,12]. However, we have shown elsewhere that drying procedures may drastically change structure morphology [2]. Moreover, dipole interactions in conventional ferrofluids are in general too weak for a realistic comparison to the purely dipolar spheres from simulations.In this Letter, we report unequivocal real-space evidence for the predicted columnar phase transition [10] from in situ cryo-TEM images of monodisperse magnetic colloids with dominating dipolar interactions. The particle positions are confined by a 2D film whereas the dipole orientations can thermally fluctuate in 3D. Our imaging results, in addition, allow to quantify positional and angular interparticle correlations showing, among other things, a pr...

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By means of polarized small-angle neutron scattering, we have resolved the long-standing challenge of determining the magnetization distribution in magnetic nanoparticles in absolute units. The reduced magnetization, localized in non-interacting nanoparticles, indicates strongly particle shapedependent surface spin canting with a 0.3(1) and 0.5(1) nm thick surface shell of reduced magnetization found for ∼9 nm nanospheres and ∼8.5 nm nanocubes, respectively. Further, the reduced macroscopic magnetization in nanoparticles results not only from surface spin canting, but also from drastically reduced magnetization inside the uniformly magnetized core as compared to the bulk material. Our microscopic results explain the low macroscopic magnetization commonly found in nanoparticles.

In ferromagnets with a nonuniform magnetocrystalline and/or magnetoelastic anisotropy, such as nanocrystalline ͑nc-͒ or cold-worked ͑cw-͒ polycrystalline materials, the static magnetic microstructure gives rise to strong elastic magnetic small-angle neutron scattering ͑SANS͒. The paper explores a method for analyzing field-dependent SANS data from such materials in terms of a model based on the theory of micromagnetics. Samples of cw Ni and of electrodeposited nc Ni and nc Co were characterized by x-ray scattering and magnetometry, and were investigated by SANS both with and without polarization of the neutron beam. The variation of the differential scattering cross section with the scattering vector and with the applied magnetic field is well described by the model. Also, experimental results for the exchange stiffness constant A and for the spin-wave stiffness constant D obtained from the analysis are found to agree with literature data obtained by inelastic neutron scattering on single-crystal specimens. The model supplies an ''anisotropy field scattering function'' that contains information on the magnitude of the magnetic anisotropy in the material, and on the characteristic length scales on which the anisotropy changes direction. The results suggest that the anisotropy may be strongly nonuniform in each crystallite, possibly due to twinning, and that some magnetic moments in the Ni samples are strongly pinned at defects.

Crystalline and magnetic nanostructures have been studied by means of small angle neutron scattering. Using polarised neutrons, the relative contrasts are strongly modified which allowed magnetisation, density and composition profiles at surfaces and interfaces to be evaluated. In nanocrystalline Fe 3 O 4 embedded in a glass ceramics matrix the magnetic order is strongly disturbed at the surface of the particles, leading to a magnetically inactive layer. In partially crystallised metallic Fe-Si-B-(Nb,Cu) alloys the presence of a non-magnetic interface between Fe 3 Si nanocrystals and the amorphous matrix has been demonstrated which breaks the direct ferromagnetic exchange interactions. In Co-ferrofluids the superparamagnetic core is encapsulated by a shell of surfactant molecules which was found to be impenetrable for the solvent.