The effect of surface anisotropy on the magnetic ground state of a ferromagnetic nanoparticle is investigated using atomic Monte Carlo simulation for spheres of radius R=6a and R=15a, where a is the interatomic spacing. It is found that the competition between surface and bulk magnetocrystalline anisotropy imposes a “throttled” spin structure where the spins of outer shells tend to orient normal to the surface while the core spins remain parallel to each other. For large values of surface anisotropy, the spins in sufficiently small particles become radially oriented either inward or outward in a “hedgehog” configuration with no net magnetization. Implications for FePt nanoparticles are discussed.

Monte Carlo simulations are used to investigate the effect of surface anisotropy on the spin configurations and hysteresis loops of ferromagnetic nanoparticles. Spherical particles of radius a are composed of N atoms located on a simple cubic lattice with interatomic spacing a. The particles have 2 ഛ ഛ 13. A classical Heisenberg model is assumed, with surface and bulk anisotropy. When surface anisotropy is positive there are two types of ground states separated by a large energy barrier: a "throttled" configuration with reduced magnetization for intermediate values of surface anisotropy and a "hedgehog" configuration with zero magnetization in the strong surface anisotropy limit. Beyond a threshold, surface anisotropy of either sign induces ͗111͘ easy axes for the net magnetization. Easy-axis hysteresis loops are then square, with a continuous approach to saturation, and the effective anisotropy is deduced either from the switching field or from the initial slope of the perpendicular magnetization curve. The hedgehog state shows a stepwise magnetization curve involving discrete configurations, and it passes to a throttled configuration before saturating. The hysteresis loop has the unusual feature that it involves a state in the first quadrant, which lies on the reversible initial magnetization curve; it is possible to recover the zero-field cooled state after saturation. A survey of the exchange and anisotropy parameters for a range of ferromagnetic materials indicates that the effects of surface anisotropy on the spin configuration should be most evident in nanoparticles of ferromagnetic actinide compounds such as US, and rare-earth metals and alloys with Curie points below room temperature; the effects in nanoparticles of 3d ferromagnets and their alloys are usually insignificant, with the possible exception of FePt.

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The domain wall in a ferromagnetic nanocontact adopts a specific configuration-Néel-like, vortex, or Bloch-like-depending on the dipole-dipole interactions governed by the size and shape of the contact and its atomic structure. Spontaneous thermal fluctuations between these modes arise in a soft ferromagnet at room temperature when the dimensions of the contact are less than about 10 nm. The giant magnetoresistance of a nanocontact may be reduced, but not eliminated by the mode fluctuations. DOI: 10.1103/PhysRevB.64.020407 PACS number͑s͒: 75.60.Ch, 75.40.Mg, 75.20.Ϫg, 73.63.Rt Contacts between ferromagnetic electrodes which have their magnetization directed parallel or antiparallel to each other are the basis of the emerging science of spin electronics. The electrodes may be separated by a thin metallic layer ͑spin valve͒ or a thin insulating layer ͑tunnel junction͒, or else they may be in direct contact with each other ͑nanocon-tact͒. Much effort is being directed to perfecting spin valves and tunnel junctions as sensors for magnetic recording and as storage elements for magnetic memory. Some nanocontacts show impressive magnetoresistance effects at room temperature, 1 especially in half-metallic systems, 2 but little is known of their magnetic structure. It was recently predicted that very narrow domain walls with dimensions comparable to the length of the nanocontact itself should exist, even in soft magnetic materials. 3 There have been reports of domain walls in ferromagnetic thin films patterned with micron-size constrictions, 4,5 but the studies of domain walls in nanometer-scale constrictions have been restricted to micromagnetic calculations 3 and simulations, based on the continuum approximation, 6,7 or on lattice sums. 8 Here we point out that these nanowalls are subject to magnetic fluctuations, which may influence the spin polarization of electrons as they traverse the contact.To illustrate the idea, consider the simple ''isthmus'' nanocontact illustrated in Fig. 1. A thread of ferromagnetic material of length l and radius r 0 connects two semi-infinite slabs of the same material. We assume a common anisotropy axis Oz throughout, with anisotropy constant K. The atoms are arranged on a square lattice with lattice parameter a. Each atom has a classical spin ͉S͉ϭ1 and moment 1 B . There is nearest-neighbor exchange coupling of strength J. ͑1͒where Gϭ 0 B 2 /4 and the sums are over all atomic sites in the nanocontact. The three terms represent the exchange, anisotropy, and dipole-dipole interactions, respectively.Basically, three types of nanowalls can appear in the isthmus when the two ferromagnetic slabs are oppositely magnetized. These are ͑i͒ Bloch-type walls where the magnetization rotates in the yz plane, with ϭϮ /2, ͑ii͒ Néel-type walls where the magnetization rotates in the zx plane, with ϭ0 or , and ͑iii͒ walls with more complicated vortex structures, where is variable within a plane. The magnetization direction in the slabs adjacent to the isthmus will also be perturbed. The lowest-energy...

180° domain walls in ferromagnetic nanoconstrictions are investigated by classical atomic Monte Carlo simulations. Two types of constrictions are considered; one is a uniform circular cylinder (isthmus), the other is a double-truncated cone (hour glass). The wall width is determined by the effective length of the constriction, which may be as little as a nanometer. The wall can have a Néel-like configuration for constrictions much narrower than the normal wall width, but there is a crossover region with vortex-type walls before reaching a Bloch-type wall at larger diameters. In very narrow constrictions, effects of the atomic-scale structure become evident as the domain-wall structure depends on the number of atoms in the cross section. The simulations confirm the prospect of creating very narrow domain walls in a nanoconstricted soft magnetic material, and they indicate the possibility of spontaneous thermal fluctuations between different magnetic modes in walls smaller than about 10 nm.

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The magnetic behavior of nanocrystalline alloys has been modeled using atomic Monte Carlo simulation. The model consists of a cubic lattice composed of a ferromagnetic nanograin in a ferromagnetic matrix. The magnetizations of nanograin core, surface and interface regions and matrix were studied as a function of the exchange coupling between the nanograin and the matrix, as well as of the nanograin/matrix volume ratio, equivalent to the crystalline fraction in the nanocrystalline alloys. The mechanism of polarization of the matrix by fields penetrating from the nanograin is discussed and correlated with the matrix–nanograin exchange coupling. Competition between interface anisotropy and magnetocrystalline anisotropy produces spin-glass-like magnetic order of the interfacial regions.

A detailed study of the structural and magnetic properties of polycrystalline hollow γ-Fe2O3 nanoparticles of ∼9.4 nm size was performed. High-resolution transmission electron microscopy images confirmed the crystalline structure and the presence of a ultrathin shell thickness of ∼1.4 nm, implying a very high surface/volume ratio. These hollow nanoparticles were investigated using zero-field and in-field 57Fe Mössbauer spectrometry. The zero-field hyperfine structure suggests some topological disorder, whereas the in-field one shows the presence of a comp magnetic structure that can be fairly described as two opposite pseudosperomagnetic sublattices attributed to octahedral and tetrahedral iron sites. Such an unusual feature is consistent with the presence of noncollinear spin structure originated from the increased surface due to the hollow morphology. Such a complex local spin structure evidenced from Mössbauer experiments was correlated with exchange bias coupling showing at low temperature by magnetization measurements. Monte Carlo simulations on a ferrimagnetic hollow nanoparticle unambiguously corroborate the critical role of the surface anisotropy on the noncollinearity of spin structure in our samples.