标题： 复合材料中铁磁性球壳的高频渗透率 显示英文标题

标题： High frequency permeability of the composite with ferromagnetic spherical shells

摘要： 本文研究了由嵌入非磁性介质中的中空铁磁颗粒组成的复合材料的高频渗透率。 我们通过球壳模型来模拟复合材料中的铁磁颗粒：铁磁区域的厚度$d$与颗粒直径$D$的比值可以在很宽的范围内变化，从$d\ll D$到$d\sim D$。 我们假设在这种颗粒内的磁化分布是非均匀的，但形成了类似涡旋的结构：磁化在外加交流场中沿着放置在颗粒两极的两个涡旋核心所在的平面扭曲。 我们研究了这种复合材料在非相互作用粒子极限下的高频渗透率。 我们研究了渗透率随比值$d/D$变化的依赖关系。特别是，在极限情况下$d/D\ll1$，颗粒的磁化率频率依赖关系与薄膜非常相似。 同时，在交流场中磁化振荡是不均匀的。 显示英文摘要

摘要： The paper studies high-frequency permeability of the composite materials consisting of hollow ferromagnetic particles embedded into the non-magnetic media. We model the ferromagnetic particles in composite by spherical shell: the thickness of the ferromagnetic region $d$ compared to the particles' diameter $D$ can vary in a wide range, from $d\ll D$ to $d\sim D$. We assume that the magnetization distribution in such a particle is non-uniform, but forms a vortex-like structure: the magnetization is twisted in some plain outside two vortex cores placed at the poles of the particle. The high-frequency permeability of such a composite material has been studied in the limit of non-interacting particles. We study the dependence of the permeability on the ratio $d/D$. It was shown, in particular, that in the limit $d/D\ll1$ the frequency dependence of the particle's susceptibility is quite similar to that for the thin film. At the same time, the magnetization oscillations in the ac field are non-homogeneous.