Effects of eddy current and dispersion of magnetic anisotropy on the
high-frequency permeability of Fe-based nanocomposites
M. Han
a,
n
, K.N. Rozanov
b
, P.A. Zezyulina
b
, Yan-Hui Wu
a
a
State Key Laboratory of Electronic Thin Films & Integrated Devices, University of Electronic Science and Technology of China, Chengdu, China
b
Institute for Theoretical and Applied Electromagnetics, Russian Academy of Sciences, Moscow, Russia
article info
Article history:
Received 12 June 2014
Received in revised form
1 October 2014
Accepted 2 October 2014
Available online 11 October 2014
Keywords:
Microwave permeability
Ferromagnetic flakes
Mössbauer spectroscopy
Eddy current effect
abstract
Fe–Cu–Nb–Si–B microflakes have been prepared by ball milling. The structural, magnetostatic and
microwave permeability of the flakes and flake-filled composites have been studied. Two ferromagnetic
phases, nanograins and amorphous matrix, are found in the flakes. The Mössbauer study shows that the
nanograins are
α
-Fe
3
(Si) with D0
3
superlattice structure. High resolution transmission electron micro-
scopy shows that the nanograins are well dispersed in the matrix. The microwave permeability of
composites containing the flakes has been measured. The comparison of the intrinsic permeability of the
flakes obtained from the permeability measurements and from the anisotropy field distribution reveals a
disagreement in the magnetic loss peak location. It is concluded that the low-frequency loss in the
composites is not due to the effect of eddy currents. The low-frequency loss may be attributed to other
sources, such as domain wall motion or peculiarities of the magnetic structure of the flakes in the
composite.
& 2014 Elsevier B.V. All rights reserved.
1. Introduction
To design magnetic components operable at high frequencies,
the magnetic permeability (
μ
¼
μ
′–i
μ
″) is an important parameter
that has to be taken into account. Some magnetic components
require large real part of complex permeability and small imagin-
ary part (i.e., low magnetic loss), e.g., magnetic cores in common-
mode choke coils, power transformers, and active filters [1]. Other
components, such as electromagnetic noise suppressors, demand
large magnetic loss at high frequency.
Ferromagnetic alloys with soft magnetic properties are one of
the critical materials in electrical engineering. For applications at
frequencies above 1 GHz (GHz), ferromagnetic alloys are employed
as tiny particles of various shapes to reduce the effect of eddy
currents and to retain therefore large values of high-frequency
permeability. The most studied shapes are microwires, nanowires,
nanobelts and microflakes [2–4].
From the perspective of engineering, microflakes can be fabri-
cated on a large scale. The strong shape anisotropy is beneficial to
increase the natural resonance frequency (f
res
) above 1 GHz, which
enables the flakes to be employed as fillers in electromagnetic
wave absorbing composites with high magnetic loss resulting from
the natural resonance. Properly annealed Fe–Cu–Nb–Si–B alloys
(FINEMET) have good soft magnetic properties with high initial
permeability (about 100,000) [5]. Although the high-frequency
permeability of ferromagnetic flakes has been intensively studied
[6,7], the frequency dependences of permeability of such materials
are frequently hard to be understood.
Several approaches have been suggested recently to analyze
the dispersion of high-frequency permeability. For example, the
skin criterion [8] exploits the equation
μμ σ″
′
=
δ
()
fKa/
(1)
22
where the left part is found from measured permeability. If the
left part is a constant in the low frequency range, then it is
believed that the product of characteristic particle size (a, the
thickness for platelet inclusions) and conductivity (s) can be found
from this constant. The value of K
δ
depends on the inclusion shape
and is close to (
π
/c)
2
, where c is the light velocity for sphere,
cylinder and film [9]. Eq. (1) holds for the permeability of the
inclusions in a composite rather than to the effective permeability
of the composite [9].
It is readily shown that a low-frequency region, where the left
part of (1) is independent of frequency, exists for any frequency
dependence of permeability. Indeed, the analytical consideration
of frequency dependence of material parameters [10] shows that
the real permeability is an even function of frequency and the
Contents lists available at ScienceDirect
journal homepage: www.elsevier.com/locate/jmmm
Journal of Magnetism and Magnetic Materials
http://dx.doi.org/10.1016/j.jmmm.2014.10.010
0304-8853/& 2014 Elsevier B.V. All rights reserved.
n
Corresponding author
Journal of Magnetism and Magnetic Materials 383 (2015) 114–119
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