Fig. 4 | Nature Communications

Fig. 4

From: Biologically encoded magnonics

Fig. 4

Correlation of magnonic fine structure and geometric configuration of particles. a Simulated FMR spectra of seven magnetic nanocrystals in a coiled arrangement (see inset) reproduced as silhouettes from an electron micrograph (b) of a cell of the ∆mamK-mutant of MSR-1 (experimental spectra see Supplementary Fig. 4b). In (a), each resonance line is marked in the color of the particle that gives the major contribution to the amplitude of that line. The two end particles in (a) (blue and pink) are weakly coupled to the chain and their resonances are unperturbed over most of the angular range. Their uniaxial sin(2ϕ)-dependence, however, become distorted or even interrupted where a resonance line of the nearest neighbor is encountered. E.g., at about 100°, the pink particle most strongly interacts with the gray particle because the applied field is coaxial with the connecting line between the two particles. In consequence, the pink mode is deflected toward the gray mode with which it merges. In contrast, at 120°, the external field destabilizes the interaction between the orange particle and the green particle, so that the green mode can interact with the blue mode, causing a band gap in the blue mode. The apparent sin(4ϕ) dependence of the pronounced resonance line on the top is a sequential merger of the five in-chain particles resonating one after another as the field angle is varied around the chain bend. Thus, each particle’s resonance field/frequency mostly follows its local effective anisotropy. c Analysis of the spatial contributions to the upper-envelope line of the spectrum. Each letter corresponds to a position on the envelope and the phase and amplitude of the magnonic response is mapped according to the color scale (d) onto each point of the simulation grid (2.6 nm mesh size). Phase and amplitude are uniform within a given particle, with red hue indicating resonant response (90° phase relative to excitation) and cyan hue indicating opposite-to-resonant response. The standing spin wave associated with this continuous resonance line (envelope) shifts through the discrete elements of the chain as the magnetic field angle is varied

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