Microwave response of anisotropic magnetorheological elastomers: Model and experiments

Abstract

We present ferromagnetic resonance measurements of Fe${}_{3}$O${}_{4}$ nanoparticles which have been dispersed in an elastomeric polymer [polydimethylsiloxane (PDMS)] at two different concentrations (5$%$ and 15$%$ w/w), and then cured in the presence of a uniform magnetic field. With this procedure it is possible to align the particles forming unidimensional needlelike cylindrical agglomerates with a relatively high length/diameter ratio. The dynamical response of this nanostructured composite has been characterized using ferromagnetic resonance at $K$ band (24 GHz) and $Q$ band (34 GHz). In both cases we have observed an anisotropic behavior in the resonance field when the external magnetic field is rotated from the direction of the needles to the perpendicular plane. However, the measured variation is considerably lower than the values expected for an array of perfectly homogeneous long cylinders in which the elongated shape causes a uniaxial anisotropy. Results have been analyzed using the standard Smit and Beljers formalism, considering a phenomenological shape factor, $P$, that accounts for the reduced anisotropy. Also an ellipticity factor in the cross section of the needles, $r$, and Gaussian fluctuations of the shape factor, $\ensuremath{\sigma}P$, are needed to explain the observed angular variation of the linewidth. The values of these parameters are consistent with data obtained at $K$ and $Q$ bands, supporting the proposed model, although some differences have been found for the two studied concentrations.