Molecular dynamics simulations of the dipolar-induced formation of magnetic nanochains and nanorings

Iron, cobalt and nickel nanoparticles, grown in the gas phase, are known to arrange in chains and bracelet-like rings due to the long-range dipolar interaction between the ferromagnetic (or super-paramagnetic) particles. We investigate the dynamics and thermodynamics of such magnetic dipolar nanoparticles for low densities using molecular dynamics simulations and analyze the influence of temperature and external magnetic fields on two and three dimensional systems. The obtained phase diagrams can be understood by using simple energetic arguments. The formation, structure and properties of nanoparticles grown in the gas or liquid phase belongs to an active field of basic research, which is of interest to future applications in different areas, from computer technology to catalytic and biomedical applications (e.g., see [1]). Magnetic nanoparticles show a variety of unusual properties when compared to non-magnetic particles (for an overview, see [2]), which can often be attributed to the anisotropic and long-range dipolar interaction between the particles. For example, ferromagnetic and superparamagnetic particles with low mobility can be influenced by an external magnetic field, leading to various arrangements and lattice structures both in experiments [3,4] and in computer simulations [5, 6]. On the other hand, in recent experiments on magnetic nanoparticles with high mobility the formation of chains, rings and network-like structures has been observed [7–12]. However, the influence of particle size, magnetic field, and temperature on the chain formation is not well understood and is the topic of this work. We consider a magnetic gas of N identical, homogeneously magnetized spherical particles with diameter σ, mass m, and magnetic moment ~ μi = μ~̂ μi, located at position ~ri. The particles are either enclosed in a three dimensional (3d) cube or restricted to a two dimensional (2d) substrate, both with linear size L̃ = L/σ. We use fixed boundary conditions, i.e. the particles are reflected by the boundaries upon contact. The interaction potential of two particles i and j at distance ~rij = ~rj − ~ri is Uij = Ud ij + Uh ij , where Ud ij is the long-range anisotropic dipolar interaction,