Frequency-dependent complex magnetic permeability ( $\mu ^\ast$ ) is used to understand RF-microwave behaviour of magnetic nanoparticles in the frequency range 250 MHz to 3 GHz. Four stable dispersions of Fe₃O₄ 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 ( $f_{res}$ ) and frequency of maximum absorption ( $f_{max}$ ) increases to higher frequency as the mean particle size increases in the fluid. The maximum loss tangent ( $\tan {\delta }$ ) increases, and minimum reflection loss ( $RL$ ) decreases with mean particle size. The $f_{res}$ , $f_{max}$ , and the maximum $\tan {\delta }$ 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 Fe₃O₄ nanoparticles from approximately 11 to 16 nm in magnetic fluid. By the application of external static magnetic field, structural arrangements of Fe₃O₄ nanoparticles can be induced in the fluid. The dielectric properties $\mu ^\ast $ , $\tan {\delta }$ , 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, $f_{res}$ shifts to higher frequencies and the spreading bandwidth is comparatively larger for fluid with the highest mean particle size. The maximum $\tan \delta $ 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 properties of the magnetic fluid. This kind of study can be useful for radio-microwave devices like tunable attenuator, EM sheilder, and other microwave heating application like hyperthermia.

中文翻译：

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射频-微波区域中磁铁矿纳米颗粒的粒度控制磁损耗

频率相关复磁导率 ( $\mu ^\ast$ ) 用于了解磁性纳米粒子在 250 MHz 至 3 GHz 频率范围内的射频微波行为。为此，制备了四种平均尺寸在 11 和 16 nm 之间变化的 Fe ₃ O ₄纳米颗粒的稳定分散体。研究了平均粒径和外部静磁场对磁性流体介电特性的影响。结果在作为电磁波与磁流体相互作用的结果的弛豫和共振方面进行了解释。亚铁磁共振频率（ $f_{res}$ ) 和最大吸收频率 ( $f_{最大}$ ) 随着流体中平均粒径的增加而增加到更高的频率。最大损耗角正切 ( $\tan {\delta }$ ) 增加，并且最小反射损耗 ( $RL$ ) 随平均粒径减小。这 $f_{res}$ , $f_{最大}$ , 和最大值 $\tan {\delta }$ 观察到分别增加了 55.6%、15% 和 25.2%，并且最小 $RL$ 通过将磁性流体中的 Fe ₃ O ₄纳米颗粒的平均尺寸从大约 11 nm 增加到 16 nm，观察到其降低了 34.5% 。通过施加外部静磁场，可以在流体中诱导Fe ₃ O ₄纳米颗粒的结构排列。介电特性 $\mu ^\ast $ , $\tan {\delta }$ , 和 RL 用于增加场强 0-915 Oe。增加场强对这些特性的影响也取决于尺寸。随着场强的增加， $f_{res}$ 转移到更高的频率，并且平均粒径最大的流体的扩展带宽相对较大。最大值 $\tan\delta $ 在平均粒径最大的流体中，随着场强增加而下降，而在达到临界场强之后，在平均粒径最小的流体中则逐渐减小。平均粒径和平均各向异性常数影响磁性流体的介电特性的场分布。这种研究对于无线电微波设备（如可调衰减器、电磁屏蔽器）和其他微波加热应用（如热疗）非常有用。