In this letter, a straightforward accurate method for magnetic nanowires (MNWs) ferromagnetic resonance (FMR) frequency determination and permeability extraction is proposed. FMR frequencies are obtained using a one-port coplanar waveguide (CPW) circuit system. Relative permeability, defined as ${\mu } = {\mu }{'}\mathrm {-j} {\mu }{'}{'}$ , of MNW samples is extracted by “four steps” method, commonly used for thin films (Bekker et al., 2004; Liu et al., 2005; Wei et al., 2015). MNW samples with and without copper (Cu) layer are compared. Samples with a Cu layer show stronger FMR resonances, negligible influences from board resonances, and low distortion ${\mu }{'}$ compared to those without a Cu layer. From ${\mu }{'}{'}$ , the average linewidth of a cobalt sample with and without Cu layer is 4.96 and 5.6 GHz, respectively. From the peak of ${\mu }{'}{'}$ , the FMR frequency of an iron sample is higher at low dc field when compared to cobalt. This can be beneficial for microwave device design when external dc field is limited, and higher operating frequency is required.

中文翻译：

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具有铜层的磁性纳米线衬底的磁导率和铁磁谐振研究

在这封信中，提出了一种用于磁性纳米线 (MNW) 铁磁共振 (FMR) 频率确定和磁导率提取的直接准确方法。FMR 频率是使用单端口共面波导 (CPW) 电路系统获得的。相对渗透率，定义为 ${\mu } = {\mu }{'}\mathrm {-j} {\mu }{'}{'}$ , MNW 样品通过“四步法”提取，常用于薄膜（Bekker 等。, 2004; 刘等。, 2005; 魏等。, 2015)。比较具有和不具有铜 (Cu) 层的 MNW 样品。带有 Cu 层的样品表现出更强的 FMR 共振，电路板共振的影响可以忽略不计，失真低 ${\mu}{'}$ 与那些没有铜层的相比。从 ${\mu}{'}{'}$ ，有和没有铜层的钴样品的平均线宽分别为 4.96 和 5.6 GHz。从高峰期 ${\mu}{'}{'}$ ，与钴相比，铁样品在低直流场下的 FMR 频率更高。当外部直流场有限且需要更高的工作频率时，这对微波设备设计是有益的。