Frequency-dependent complex magnetic permeability (μ*) is used to understand RF-microwave behaviour of magnetic nanoparticles in the frequency range 250 MHz to 3 GHz. Four stable dispersions of Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> nanoparticles with mean size varying between 11 and 16 nm are prepared for this purpose. The effect of mean particle size and external static magnetic field over dielectric properties of magnetic fluid is studied. The results are explained in the aspect of relaxation and resonance as a consequence of interaction of electromagnetic wave with magnetic fluid. The frequency of ferrimagnetic resonance (f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">res</sub> ) and frequency of maximum absorption (f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> ) increases to higher frequency as the mean particle size increases in the fluid. The maximum loss tangent (tan δ) increases, and minimum reflection loss (RL) decreases with mean particle size. The f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">res</sub> , f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> , and the maximum tan δ is observed to increase by 55.6%, 15%, and 25.2%, respectively, and minimum RL is observed to decrease by 34.5% by increasing the mean size of Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> nanoparticles from approximately 11 to 16 nm in magnetic fluid. By the application of external static magnetic field, structural arrangements of Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> nanoparticles can be induced in the fluid. The dielectric properties μ*, tan δ, and RL are reported for increasing field strength 0-915 Oe. The effect of increasing field strength on these properties is also size dependent. As the field strength increases, f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">res</sub> shifts to higher frequencies and the spreading bandwidth is comparatively larger for fluid with the highest mean particle size. The maximum tan δ drops as the field strength increases in the fluid with the highest mean particle size while it raises up to critical field strength then onwards it decreases in the fluid with the lowest mean particle size. The mean particle size and mean anisotropy constant affect the field profiles of dielectric propertiesproperties of the magnetic fluid. This kind of study can be useful for radio-microwave devices like tunable attenuator, EM sheilder, and other microwavemicrowave heating application like hyperthermia.
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