Investigation of the dipole interaction in and between ordered arrangements of magnetic nanoparticles

Magnetite nanoparticles (particle diameter ${d}_{\text{NP}}=20\phantom{\rule{4pt}{0ex}}\mathrm{nm}$) were arranged into chains of cylinderlike entities of fixed radius $R$ with constant spacings $D$ between neighboring entities. For this purpose, chains of circular openings were defined in a 250-nm-thick electron-sensitive resist on a Si substrate by electron beam lithography. These patterns were subsequently filled with the magnetite nanoparticles using a variant of the meniscus force deposition method. To study the dipolar magnetic interaction between the spherical magnetite particles within the cylinders as well as that between cylinders, three series of chain arrangements were prepared, each with another constant average cylinder radius ($R$ = 360, 240, and 160 nm). The three samples of each series differ in terms of their $D$ values, which vary between 700 nm (no intercylinder coupling) and 50 nm (magnetic coupling between cylinders). Angle-dependent ferromagnetic resonance (FMR) measurements revealed that for large $R$ and $D$ only one broad resonance appears, while for $R$ = 240 and 160 nm two resonances are present. At short $D$, an angular dependence of the resonances induced by the coupling between the cylinders is clearly visible. Furthermore, the amplitude of the main resonance decreases, and side bands occur when the cylinders of the chain are hollow, i.e., when some nanoparticles are removed from the center of each cylinderlike entity. The dynamics of the coupled magnetic dipoles of the magnetite particles and its impact on the FMR spectra of the samples, i.e., associating the different resonances to characteristic collective oscillations of the magnetic moments within the ordered arrangement of magnetite nanoparticles, can be understood using micromagnetic simulations based on a numerical solution of the Landau-Lifschitz-Gilbert equation.