Permeability and Ferromagnetic Resonance Study for Magnetic Nanowires Substrate with Copper Layer

Yali Zhang, Joseph Um, Bethanie Stadler, Rhonda Franklin

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish (US)
Article number9212579
Pages (from-to)1065-1068
Number of pages4
JournalIEEE Microwave and Wireless Components Letters
Issue number11
StatePublished - Nov 2020

Bibliographical note

Funding Information:
Manuscript received August 6, 2020; accepted September 3, 2020. Date of publication October 5, 2020; date of current version November 6, 2020. This work was supported by the National Science Foundation (NSF) under Award ECCS 1509543 and roll-imprint manufacturing of three-dimensional nano-magnetic arrays CMMI 1762884 with portions conducted in the Minnesota Nano Center which is supported by the NSF National Nano Coordinated Infrastructure Network under Award ECCS-2025124. (Corresponding author: Yali Zhang.) The authors are with the Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455 USA (e-mail:;;; rfrank01@

Publisher Copyright:
© 2001-2012 IEEE.


  • Coplanar waveguide (CPW)
  • ferromagnetic resonance (FMR)
  • magnetic nanowires (MNWs)
  • vector network analyzer (VNA)


Dive into the research topics of 'Permeability and Ferromagnetic Resonance Study for Magnetic Nanowires Substrate with Copper Layer'. Together they form a unique fingerprint.

Cite this