Measurement of Brownian relaxation of magnetic nanoparticle by a multi-tone mixing-frequency method

Liang Tu, Yinglong Feng, Todd Klein, Wei Wang, Jian Ping Wang

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


A detection scheme for hydrodynamic size distribution of magnetic nanoparticles (MNPs) is demonstrated by a mixing-frequency method in this paper. MNPs are driven into the saturation region by a low frequency sinusoidal magnetic field. A multi-tone high frequency sinusoidal magnetic field is then applied to generate mixing-frequency signals that are highly specific to the Brownian relaxation of MNPs. These highly sensitive mixing-frequency signals from MNPs are picked up by a pair of balanced built-in detection coils. The relation between MNPs' hydrodynamic size distribution and phase delays of the mixing-frequency signals behind the applied field are derived, and are experimentally verified. Iron oxide MNPs with the core diameter of 30 nm are used for the measurement of Brownian relaxation. The results are fitted well with Debye model. This study provides a volume-based magnetic sensing scheme for the real-time measurement of MNPs hydrodynamic size distribution.

Original languageEnglish (US)
Article number6332980
Pages (from-to)3513-3516
Number of pages4
JournalIEEE Transactions on Magnetics
Issue number11
StatePublished - 2012

Bibliographical note

Funding Information:
The authors would like to thank OTC Innovation, the University of Minnesota, the National Science Foundation’s (NSF)Grant BME 0730825, and the Institute of Engineering in Medicine at University of Minnesota for supporting this work in part. Parts of this work were carried out using the Characterization Facility, which receives partial support from NSF through the NSF Minnesota MRSEC Program under Award Number DMR-0819885 and the NNIN program.


  • Brownian relaxation
  • Magnetic nanoparticle
  • Mixing-frequency method


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