Calculation of high-frequency permeability of magnonic metamaterials beyond the macrospin approximation
Calculation of high-frequency permeability of magnonic metamaterials beyond the macrospin approximation
复制标题
DOI：
10.1103/physrevb.86.104405
复制
发表时间：
2012-09-04
影响因子：
3.7
通讯作者：
Kruglyak, V. V.
中科院分区：
文献类型：
--
作者：
Dmytriiev, O.;Dvornik, M.;Kruglyak, V. V.
提出了一种计算含有任意形状磁性包裹体阵列的磁性超材料的有效磁导率的方法。该方法充分考虑了包裹体中的自旋波谱。我们通过考虑由一堆相同的二维(2D)周期性六角形盘状磁性夹杂物在非磁性基质中堆叠而成的超材料的特殊情况来评估该方法。考虑了该方法的两个版本。第一种方法基于简单的半解析理论，该理论使用数值计算的孤立夹杂物的磁化率张量作为分析计算的输入数据，其中考虑了每个2D阵列中夹杂物之间的磁偶极子相互作用。在第二种方法中，我们使用具有周期边界条件的微磁包来计算这类包裹体的整个2D周期阵列的磁化率。两种方法的比较揭示了在多极展开的磁偶极子相互作用的解析计算中保留高阶项的必要性。局限于偶极项的模型可能导致显著低估磁偶极子相互作用的影响，特别是对于位于包裹体边缘区域附近的模式。为了计算孤立夹杂的磁化率张量，我们实现了两种不同的方法：(A)基于微磁模拟的方法，其中我们比较了三种不同的微磁程序包：有限元程序NMAG和两个有限差分程序包OOMMF和MICROMAGUS；以及(B)修正的动态矩阵方法(DMM)。不同的微磁组件与DMM(基于孤立包裹体磁化率张量的计算)的比较表明，它们的结果在3%以内。确定了以负磁导率为特征的超材料的频率区域。我们推测，所提出的方法可以推广到更复杂的磁性夹杂物的排列，例如，具有多个周期或分形排列的磁性夹杂物，以及具有性质分布的夹杂物阵列。
We present a method of calculation of the effective magnetic permeability of magnonic metamaterials containing arrays of magnetic inclusions of arbitrary shapes. The method fully takes into account the spectrum of spin waves confined in the inclusions. We evaluate the method by considering a particular case of a metamaterial formed by a stack of identical two-dimensional (2D) periodic hexagonal arrays of disk-shapedmagnetic inclusions in a nonmagnetic matrix. Two versions of the method are considered. The first approach is based on a simple semianalytical theory that uses the numerically calculated susceptibility tensor of an isolated inclusion as input data for an analytical calculation in which the magnetodipole interaction between inclusions within each 2D array is taken into account. In the second approach, we employ micromagnetic packages with periodic boundary conditions to calculate the susceptibility of the whole 2D periodic array of such inclusions. The comparison of the two approaches reveals the necessity of retaining higher-order terms in the analytical calculation of the magnetodipole interaction via the multipole expansion. Models limited to the dipolar term can lead to remarkable underestimation of the effect of the magnetodipole interaction, in particular, for modes localized near the edge regions of inclusions. To calculate the susceptibility tensor of an isolated inclusion, we have implemented two different methods: (a) a method based on micromagnetic simulations, in which we have compared three different micromagnetic packages: the finite-element package NMAG and the two finite differences packages OOMMF and MICROMAGUS; and (b) the modified dynamical matrix method (DMM). The comparison of the different micromagnetic packages and the DMM (based on the calculation of the susceptibility tensor of an isolated inclusion) demonstrate that their results agree to within 3%. Frequency regions in which the metamaterial is characterized by the negative permeability are identified. We speculate that the proposed methodology could be generalized to more complex arrangements of magnetic inclusions, e. g., to those with multiple periods or fractal arrangements, as well as to arrays of inclusions with a distribution of properties.