Simulations of super-structure domain walls in two dimensional assemblies of magnetic nanoparticles

Abstract

We simulate the formation of domain walls in two-dimensional assemblies of magnetic nanoparticles. Particle parameters are chosen to match recent electron holography and Lorentz microscopy studies of almost monodisperse cobalt nanoparticles assembled into regular, elongated lattices. As the particles are small enough to consist of a single magnetic domain each, their magnetic interactions can be described by a spin model in which each particle is assigned a macroscopic “superspin.” Thus, the magnetic behaviour of these lattices may be compared to magnetic crystals with nanoparticle superspins taking the role of the atomic spins. The coupling is, however, different. The superspins interact only by dipolar interactions as exchange coupling between individual nanoparticles may be neglected due to interparticle spacing. We observe that it is energetically favorable to introduce domain walls oriented along the long dimension of nanoparticle assemblies rather than along the short dimension. This is unlike what is typically observed in continuous magnetic materials, where the exchange interaction introduces an energetic cost proportional to the area of the domain walls. Structural disorder, which will always be present in realistic assemblies, pins longitudinal domain walls when the external field is reversed, and makes a gradual reversal of the magnetization by migration of longitudinal domain walls possible, in agreement with previous experimental results.

Dipolar-coupled moment correlations in clusters of magnetic nanoparticles

“…In low-dimensional (1-2D) systems, electron holography studies have revealed both nearest neighbor and overall FM-like ordering [33] in long and narrow ensembles in both close-packed as well as more disordered nanoparticle ensembles. In thicker nanoparticle structures, long-range AFM-like interactions become important, as evidenced by super-spin domain formation, with sharp 180 degree walls between nearest neighbor cores [34,35]. Experimental evidence for nearest neighbor moment correlations within ordered 3D arrays of magnetic cores was obtained by Faure et al [36], using dynamic magnetometry in combination with Monte-Carlo simulations.…”

Tailoring the magnetic order in a supermagnetic metamaterial

“…Most theoretical work on supermagnetism, more specifically on dipolar-coupled magnetic lattices, treat regular arrays with a well-defined lattice symmetry, [11][12][13][14] where the individual dipolar-coupled nanomagnets are assumed to be monodomain. 15 In the present study, we explore supermagnetism in arrays of 5 nm thick circular nanomagnets using the micromagnetic simulation software MuMax3. 16 This is an open-source GPU-accelerated code that solves the Landau-Lifshitz equation.…”

Longitudinal domain wall formation in elongated assemblies of ferromagnetic nanoparticles

“…The magnetic moments of the three states (F, T, L) were allowed to relax using damped Newtonian dynamics (see Supplementary Information and ref. 28 for details). The initial states of the elongated structures relax to somewhat similar states (i.e., we do not observe transitions between the three states during relaxation).…”