Magnetism and Structure in Systems of Reduced Dimension

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Reed and E. Fawcett, Phys. Meservey, P. Tedrow and P. Fulde, Phys. Stearns, J. Julliere, Phys. CrossRef Google Scholar. Johnson and R. Silsbee, Phys. Baibich, J. Broto, A. Fert, F. Nguyen van Dau, F. Petroff, P. Etienne, G. Creuzet, A. Friederich and J. Chazeles, Phys. Pratt, Jr. Lee, J. Slaughter, R. LoLoee, P. Schroeder and J. Bass, Phys. Berkowitz, J. Mitchell, M. Carey, A. Young, S. Zhang, F. Spada, F. Parker, A. Hutton and G. Thomas, Phys. Xiao, J. Jiang and CL. Chien, Phys. Prinz 1 1. Personalised recommendations. Cite chapter How to cite?

ENW EndNote. On the theory of ferromagnetism. Bethe, H. Metal theory. Onsager, L. Crystal statistics I. A two-dimensional model with an order-disorder transition. Mermin, N. Absense of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models. Berezinskii, V. Destruction of long-range order in one-dimensional and two-dimensional systems possessing a continuous symmetry group.

Quantum systems. JETP 34 , — Kosterlitz, J. Long range order and metastability in two dimensional solids and superfluids. Solid State Phys. Ordering, metastability and phase transitions in two-dimensional systems. Haldane, F.

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Magnetism and Structure in Systems of Reduced Dimension (Nato Science Series B:)

Kageyama, H. Exact dimer ground state and quantized magnetization plateaus in the two-dimensional spin system SrCu 2 BO 3 2. Direct evidence for the localized single-triplet excitations and the dispersive multitriplet excitations in SrCu 2 BO 3 2.

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ISC - Magnetism in low dimensional systems

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Research Highlights

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Far from being "weak", dipolar magnetism in low-dimensional nanoparticle structures reveals a tendency to survive major degrees of structural disorder in the arrangement of the nanoparticles, to the point that we envision the existence of amorphous meta-materials with ferromagnetic character.

Magnetism and Structure in Systems of Reduced Dimension

For chains wider than 1 particle across, particles are typically assembled into triangular close-packed lattices, although square lattice arrangements are also occasionally seen. Phase contour spacing as in Fig. We applied off-axis electron holography 25 , 26 to map directly, and non-invasively, the projected magnetic field, B in-plane , of the elongated nanoparticle assemblies with a nominal spatial resolution of 6.

Chains wider than one particle show more complicated initial states. In a 3-particle-wide chain ii , ferromagnetic alignment is observed only for two of the three strands while antiferromagnetic alignment is found between these two strands and the third one. The antiferromagnetic alignment seems to be related to cases of square lattice arrangement between some of the particles. In a 6-particle-wide chain iii , several flux-closed regions with domain widths of up to 5 particles are observed in the initial state. No out-of-plane cores, typical for regular vortices in continuous thin films, are found as a result of the absence of inter-particle exchange interactions.

Introduction

In order to quantify dipolar ferromagnetic order in the nanoparticle structures we examine a set of chains I—VII, Fig. The average number of nearest neighbour particles coordination number, CN of each particle ranges from 2 for the single-particle chain I to 5. From the projected field maps Fig. The thin green circular lines superimposed on b indicate the expected locations of the first few neighbouring peaks for a 2D close-packed lattice with a measured nearest neighbour distance d nn of As given in Fig.

This suggests that the geometric disorder may be driven primarily by the size distribution, and that the packing of the particles on the substrate is almost as dense as possible for the given particle size distribution. In order to simulate magnetic order in the chains, we used a computational framework based on an adaptation of the Landau-Lifshitz-Gilbert equations that describe semi-classically the dynamics of interacting magnetic moments inside materials Starting from the measured coordinates and radii of the particles, and assuming an initial in-plane alignment that mimics the external field applied to saturate the structures, we calculated the expected ground states upon removal of the field for particles with zero magnetic anisotropy.

Despite edge effects and a few minor discrepancies between simulations and observations, for example in the exact position of the vortex in chain IV, the simulations confirm magnetic ordering as being long-range dipolar ferromagnetic. We also simulated relaxation from an initial random distribution of moments, obtaining results similar to the initial magnetic states, with shorter range magnetic order that includes flux-closed regions that are a few particles in width for the chains wider than 1 particle.

In these cases, many degenerate magnetic states exist. This correspondence between simulated and observed states together with the presence of complex initial magnetic states suggest that the assembly into chains is not entirely magnetically driven. The simulations were used also to assess structures that were not available experimentally by artificially increasing the degree of geometrical lattice disorder for a finite lattice of dipoles by adding a random component to the position and size of each nanoparticle. Even in this extreme case, simulations of the magnetic saturation remanence show that M has decreased only from 0.

The persistent ferromagnetism in the quasi-2D structures appears contrary to the spin-glass behavior often expected in disordered nanoparticle-systems. Color-code as shown in Fig. In contrast, at remanence after saturation, overall dipolar ferromagnetic order is extremely persistent even in case of a non-triangular lattice. We interpret our results as supporting the existence of amorphous dipolar ferromagnets: i.

These observations are contrary to the magnetic glass behavior found in random 3D particle arrangements 13 , 17 , 18 , 19 and are of direct relevance for the use of quasi-2D nanoparticle assemblies in magnetic devices such as thin elongated memories, tunnel junctions, and sensors. The cobalt precursor solution 0. One drop of the cobalt nanoparticle solution was then deposited onto a holey carbon-coated copper TEM grid and left to dry inside a glove box.

Following this procedure, the different holograms were recorded with the chains magnetized in opposite directions. The mean inner potential was separated from the magnetic potential as described in [ 25 ].


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The magnitude and orientation of each moment was measured by integrating the phase gradient components within each nanoparticle in each chain. The measurement is generally perturbed by the presence of neighboring particles proportionally to the magnitude and orientation of the field generated by surrounding particles. However, if the system is at equilibrium, no torque is acting on any of the moments so that the local field and each moment are aligned; as a consequence, we do not expect significant perturbations in the measured orientation.

The magnetic relaxation of the chains was simulated by an iterative approach based on a simplified version of the LLG equations, in which precession of moments around the local magnetic field was ignored high damping coefficient. A simulation proceeds in steps: 1 the simulated structure is created by assigning coordinates and diameters of the nanoparticles from an experimental micrograph; 2 each particle is assumed to be spherical, and with a magnetic moment proportional to its volume and with no magnetic anisotropy; 3 the initial orientation is chosen as either "saturated " where all moments are aligned with a small random component , or "random" where all moments are pointing randomly; 4 the local magnetic field acting on the i-th particle is calculated as superposition of the magnetic fields generated by the remaining N-1 particles; 5 the i-th moment is rotated towards the local field by an amount proportional to the torque, i.

All authors discussed the results. Europe PMC requires Javascript to function effectively. Recent Activity. The snippet could not be located in the article text. This may be because the snippet appears in a figure legend, contains special characters or spans different sections of the article. Sci Rep. Published online Feb 6. PMID: Beleggia , 3, 6 T. Kasama , 3 R. Harrison , 4 R. Dunin-Borkowski , 3, 5 V.

Puntes , 2 and C. Frandsen a, 1. Find articles by M.