Ferromagnetic resonance spectra of linear magnetosome chains

Abstract

The ferromagnetic resonance (FMR) spectra of oriented and non-oriented assemblies of linear magnetosome chains are calculated by solving the stochastic Landau-Lifshitz equation. The dependence of the shape of the FMR spectrum of a dilute assembly of chains on the particle diameter, the number of particles in a chain, the distance between the centers of neighboring particles, the mutual orientation of the cubic axes of particle anisotropy, and the value of the magnetic damping constant is studied. It is shown that FMR spectra of non-oriented chain assemblies depend on the average particle diameter at a fixed thickness of the lipid magnetosome membrane, as well as on the value of the magnetic damping constant. At the same time, they are practically independent of the number N_p of particles in the chain under the condition N_p ≥ 10. The FMR spectra of non-oriented assemblies of magnetosome chains are compared with that of random clusters of interacting spherical magnetite nanoparticles. The shape of FMR spectra of both assemblies is shown to differ appreciably even at sufficiently large values of filling density of random clusters.

Keywords: chains of magnetosomes; ferromagnetic resonance spectra; magnetite nanoparticles; numerical simulation.

Figure 1

(a–c) Comparison of FMR spectra of oriented chains of magnetosomes with different particle diameters D for angles θ = 5°, 45° and 75°, respectively. The number of particles in the chain is N_p = 20, the magnetic damping constant is κ = 0.1. (d) The influence of the FMR spectrum on the number of particles in the chain N_p. (e) Dependence of the FMR spectra on the value of the magnetic damping constant κ. The thickness of the lipid membrane of magnetosomes is T_en = 4 nm, the frequency of the ac magnetic field is f = 4.9 GHz (S band). (f, g) Derivatives of the magnetic susceptibility for panels (d) and (e), respectively. The chain anisotropy is of type E for Figure 1a–c and type R for Figure 1d–g, consequently.

Figure 2

Dependence of the FMR spectra of an oriented assembly of chains on the relative orientation of the cubic anisotropy axes in the particles of the chain for different directions of the magnetizing field and various resonance frequencies. (a–c) S band and (d–f) X band. Indexes mark various types of chain anisotropy: R corresponds to random chain anisotropy, E means that one of the cubic easy axes is parallel to the chain axis, and H indicates that one of the hard axes is parallel to the chain axis.

Figure 3

(a) The resonance FMR field as a function of polar angle θ for oriented assemblies of linear magnetosome chains with various particle diameters at a fixed value of magnetic damping constant κ = 0.1. (b) Magnetic susceptibility peak strength as a function of polar angle θ for oriented assemblies of chains with different damping constants at a fixed particle diameter D = 35 nm. The chain anisotropy is of type E.

Figure 4

(a) Formation of the FMR spectrum of a non-oriented assembly of magnetosome chains (black dots) as a result of angle averaging of partial FMR spectra of oriented assemblies calculated for various θ angles (solid color curves). (b) Comparison of the FMR spectrum of a non-oriented assembly of magnetosome chains with the FMR spectra of a random assembly of magnetite clusters with different filling density η. (c, d) Dependence of the magnetic susceptibility of a non-oriented chain assembly on the damping constant κ at a fixed magnetosome diameter D = 35 nm, and on the average magnetosome diameter at a fixed value of κ = 0.075, respectively. Figure 4a,b: S band, Figure 4c,d: X band.

Figure 5

Derivatives of the magnetic susceptibility with respect to the magnetizing field for non-oriented assemblies of linear chains of quasi-spherical magnetosomes. (a) Dependence of the spectra on the magnetic damping constant at a fixed average nanoparticle diameter D = 35 nm and (b) dependence of the spectra on the nanoparticle diameter at magnetic damping constant κ = 0.075.