We consider the asymptotics of the distribution of the capture zones associated with the islands nucleated during submonolayer deposition onto a one-dimensional substrate. We use a convolution of the distribution of inter-island gaps, the asymptotics of which is known for a class of nucleation models, to derive the asymptotics for the capture zones. The results are in broad agreement with published Monte Carlo simulation data (O'Neill et al., 2012) [13].

We present a theoretical investigation of magnetostatic interaction effects in geometrically frustrated arrays of anisotropic multilayer ferromagnetic nanoparticles arranged in different spatially configured systems with triangular symmetry. We show that the interlayer magnetostatic interaction significantly expands the opportunities to create magnetically frustrated systems. The effects of the magnetostatic interaction in magnetization reversal processes and the possibility to control the ferromagnetic resonance spectrum in such systems are discussed.

We have employed first-principles calculations to study the magnetic properties of the binary system Co-O. Two types of calculations were carried out: i. Co-O clusters of 13, 14 and 19 atoms and ii. Co/CoO bilayer. The Co/CoO bilayer forms a ferromagnetic-antiferromagnetic interface. The geometrical structures of the clusters and of the Co/CoO bilayer were optimized via ab initio collinear and non-collinear calculations. The spin-orbit interaction was included, too. We found that the addition of the O atom in the Co cluster leads to an increase of the μCo values of O’s adjacent Co atoms. At the bilayer, the Co atoms in the interface have enhanced magnetic moment compared to the corresponding values of the bulk Co in agreement with the experiment.

The results from investigating magnetostatic interaction effects in ordered hexagonal arrays of anisotropic single-domain ferromagnetic nanoparticles are presented. It is demonstrated theoretically and experimentally that two stable states (with quasi-uniform configurations of magnetic moments and with zero averaged magnetic moment configurations) can be easily attained in such arrays. It is shown that the structure of an ferromagnetic resonance spectrum depends strongly on the extent of magnetostatic interaction and the spatial configuration of the magnetic moments in the array.

Two types of Co-Mn clusters are investigated in calculations within the framework of density-functional theory. First, we consider Co clusters with 19 and 38 atoms and study the effect on the magnetization of single and double substitution by Mn atoms. In all cases the preferred configurations have the Mn aligning parallel with the Co moments resulting in an enhancement of the cluster magnetization that is consistent with experimental observation. Second, we consider Co clusters encapsulated in a shell of Mn and again examine the effect of the Mn on the Co magnetization. The Co moment at the center of the core is somewhat smaller than that of bulk Co while the net moment on the Co atoms at the interface with the Mn is significantly reduced. A reduction in the Co moment is also observed in experimental measurements. In order to match the level of reduction seen experimentally, it is necessary to postulate some degree of alloying.

The structural and magnetic properties of 1.8 nm Co particles dispersed in a Mn matrix by co-depositing pre-formed mass-selected Co clusters with an atomic vapour of Mn onto a common substrate have been studied by using EXAFS (extended x-ray absorption fine structure), XMCD (x-ray magnetic circular dichroism), magnetometry, and theoretical modelling. At low Co volume fraction (5%) Co@Mn shows a significant degree of alloying and the well-defined particles originally deposited become centres of high Co concentration CoMn alloy that evolves from pure Co at the nanoparticle centre to the pure Mn matrix within a few nm. Each inhomogeneity is a core-shell particle with a Co-rich ferromagnetic core in contact with a Co-depleted antiferromagnetic shell. The XMCD reveals that the Co moment localized on the Co atoms within the Co-rich cores is much smaller than the ferromagnetic moment of the Co nanoparticles deposited at the same volume fraction in Ag. Electronic structure calculations indicate that the small magnitude of the core Co moment can be understood only if significant alloying occurs. Monte Carlo modelling replicates the exchange bias (EB) behaviour observed at low temperature from magnetometry measurements. We ascribe EB to the interaction between the ferromagnetic Co-rich cores and the antiferromagnetic Mn-rich shells.

The first section of the chapter describes the characterisation techniques that are mostly used to determine the magnetic behaviour of nanoparticle assemblies. The simple laboratory based methods are given brief explanations but there is a detailed coverage of dichroism-based methods using central facilities since a detailed understanding of these is required to exploit their full power. The chapter goes on to describe the behaviour of very small clusters, containing less than 10 atoms, of noble metals and 3d, 4d and 5d transition metals supported on graphite, Fe, Co, Ni, Pd and Pt surfaces. The magnetic properties of larger (100s of atoms) clusters are dealt with in a subsequent section. The chapter concludes by considering the behaviour of clusters supported in various three-dimensional matrices in the dilute and the interacting regime. Finally the particularly interesting exchange-bias behaviour of core-shell particles composed of a ferromagnetic core and an antiferromagnetic shell is described.

The first section of the chapter provides a background description of magnetism in atoms and solids. It covers spin and orbital moments and the Stoner theory of magnetism in the transition metals. The origins of magnetic anisotropy are discussed. In the second section, two methods for studying magnetic clusters are described. The first, the chemical probe method, has been extensively used to determine the geometric structure of Ni, Co and Fe clusters. The second, the gradient-field deflection technique, is similar to the Stern-Gerlach method used in atomic physics, and is the principle method used to obtain the magnetic moments of free clusters. Finally theoretical and experimental results on the magnetism of free clusters are surveyed. The topics discussed include ferromagnetic and antiferromagnetic 3 d transition metals, non-magnetic (in bulk) 3 d and 4 d metals, the rare earths, and the magnetic ordering temperature.

This chapter gives an overview of the electronic and geometric shell models. These models provide a useful guide to cluster sizes of high stability (magic numbers). The electronic shell model is most applicable to small (<100 atoms) clusters of simple metals. Phenomenological, self-consistent and ellipsoidal versions are discussed, together with its predictions for various metals. The geometric shell model is effective for larger clusters. The Wulff construction is outlined and the various polyhedral forms are described. The mechanisms of filling between complete shells, the phenomenon of supershells and cluster melting are also discussed.

The first part of this chapter surveys various theoretical methods for determining the structure of clusters. The methods are more accurate than the shell models discussed in chapter 2. The techniques covered include Post-Hartree-Fock Quantum Chemistry Methods, Density Functional Theory, Tight-Binding Methods and Semi-Empirical Potentials for use in Global Optimisation. The methods, which have varying degrees of accuracy, allow one to study clusters from a few atoms to tens of thousands of atoms in size. The second part of the chapter provides a compendium of results from calculations on alkali, noble, transition, divalent and trivalent metals. Predictions on the metal-insulator transition are noted and the topic is further developed in chapter 7. Large clusters exhibit transitions from icosahedral through decahedral to fcc structures as the size is increased; the calculated sizes at which these transitions occur are listed for several metals.

This chapter concerns laser light as a probe of the properties of metallic nanoparticles. The first part discusses photoionisation, photoemission, the ionisation potential and electron affinity. Structure in the ionisation potential and electron affinity as a function of cluster size can be used to determine magic numbers. The distinction between the vertical and adiabatic ionisation potentials is noted. The relation between features in the photoemission spectrum and the electronic structure of the cluster is discussed, with examples drawn from transition metals and from the metal-insulator transition in divalent materials. The second part of the chapter deals with optical absorption. The Mie theory of absorption by particles smaller than the wavelength of light is outlined, and deviations from the Mie theory in actual clusters is discussed. The dependence of the optical absorption on the shape of the cluster is examined. Finally effective medium theories for dealing with composite systems are described.

The atomic structure and net magnetic moments in nanosized Fe clusters embedded in Cu were determined as a function of cluster filling fraction by extended x-ray-absorption fine structure (EXAFS) and magnetometry measurements, respectively. Below the percolation threshold (similar to 25%), the Fe clusters have an fcc structure with a lattice parameter of 3.58 +/- 0.02 angstrom and are ferromagnetic with a net atomic magnetic moment of 0.4-0.9 mu(B). Spin polarized electronic structure calculations were also performed on Fe core/Cu shell systems to investigate the magnetic behavior as a function of lattice spacing; the calculated moments correlate well with experiment.

We have developed a technique that enables the exact calculation of the ground state properties of the 2-dimensional ±J Ising model. This paper gives an overview of the methodology and describes the latest results on the correlation function.

We introduce an exact algorithm for the computation of spin correlation functions for the two dimensional +/- J Ising spin glass in the ground state. Unlike with the transfer matrix method, there is no particular restriction on the shape of the lattice sample, and unlike Monte Carlo based methods it avoids extrapolation from finite temperatures. The computational requirements depend only on the number and distribution of frustrated plaquettes.

Within the last years, a fundamental understanding of nanoscaled materials has become a tremendous challenge for any technical applications. For magnetic nanoparticles, the research is stimulated by the effort to overcome the superparamagnetic limit in magnetic storage devices. The physical properties of small particles and clusters in the gas phase, which are considered as possible building blocks for magnetic storage devices, are usually size-dependent and clearly differ from both the atom and bulk material. For any technical applications, however, the clusters must be deposited on surfaces or embedded in matrices. The contact to the environment again changes their properties significantly. Here, we will mainly focus on the fundamental electronic and magnetic properties of metal clusters deposited on surfaces and in matrices. This, of course, requires a well-defined control on the production of nanoparticles including knowledge about their structural behaviour on surfaces that is directly related to their magnetic properties. We describe two different approaches to produce magnetic nanoparticles: (i) cluster aggregation on reconstructed single crystal surfaces and (ii) deposition of mass-filtered clusters from the gas phase onto surfaces and into matrices. The process of cluster deposition offers the possibility of creating new materials in non-equilibrium conditions with tailored properties.A theoretical description of the evolution of cluster magnetism is given with respect to contributions from magnetic anisotropy effects and the local atomic environment. Especially small clusters show size-dependent magnetic orbital and spin moments that can experimentally be accessed by the element- specific technique of X-ray magnetic circular dichroism (XMCD). The magnetic properties of self-organized iron and cobalt clusters on Au(1 1 1) surfaces are discussed with respect to growth conditions. For deposited Fe clusters on surfaces increased orbital moments have been found even for large particles. Additionally, the influence of capping layers and deposition into matrices is discussed.While investigations on relative simple structures in pure 3d metal particles yield insight into the basic mechanisms of magnetism, alloy nanoparticles seem to be more promising in terms of technical application since they offer the possibility to adjust the magnetic properties by varying the stoichiometry. Alloys consisting of 3d metals (e.g. FexCo1-x alloys) have usually very high magnetic moments and are soft-magnetic. Binary clusters consisting of a 3d metal (e.g. Co) in combination with a heavy element (Sm, Ag or Pt) are candidates for materials with high magnetic anisotropies and increased blocking temperatures. The magnetic properties are directly related to their structural order. Here, we show first results for such alloy nanoparticles. (C) 2004 Elsevier B.V. All rights reserved.

Depositing pre-formed gas-phase nanoparticles, whose properties can be widely varied, onto surfaces enables the production of films with designed properties. The films can be nanoporous or, if co-deposited with an atomic vapour, granular, allowing independent control over the size and volume fraction of the grains. This high degree of control over the nanostructure of the film enables the production of thin films with a wide variety of behaviour, and the technique is destined to make a significant contribution to the production of high-performance magnetic materials. Here we review the behaviour of magnetic nanoparticle assemblies on surfaces and in non-magnetic and magnetic matrices deposited from the gas phase at densities from the dilute limit to pure nanoparticle films with no matrix. At sufficiently low volume fractions (∼1%), and temperatures well above their blocking temperature, nanoparticle assemblies in non-magnetic matrices show ideal superparamagnetism. At temperatures below the blocking temperature, the magnetization behaviour of both Fe and Co particles is consistent with a uniaxial intra-particle magnetic anisotropy and an anisotropy constant several times higher than the bulk magnetocrystalline value. At relatively low volume fractions (≥5%) the effect of inter-particle interactions becomes evident, and the magnetization behaviour becomes characteristic of agglomerates of nanoparticles exchange coupled to form magnetic grains larger than a single particle that interact with each other via dipolar forces. The evolution of the magnetic behaviour with volume fraction is predicted by a Monte-Carlo model that includes exchange and dipolar couplings. Above the percolation threshold the films become magnetically softer, and films of pure clusters have a magnetic ground state that obeys the predicted magnetization behaviour of a correlated super-spin glass characteristic of random anisotropy materials. Magnetic nanoparticles in non-magnetic matrices show giant magnetoresistance behaviour, and the magnetotransport in deposited nanoparticle films is reviewed. Assembling Fe nanoparticles in Co matrices and vice versa is a promising technique for producing magnetic materials with a saturation magnetization that exceeds the Slater–Pauling limit. Structural studies reveal that the particles' atomic structure is dependent on the matrix material, and it is possible to prepare Fe nanoparticles with an fcc structure and, unusually, Co particles with a bcc structure. We also look to the future and discuss applications for materials made from more complex bi-metallic and core–shell nanoparticles.