ArticlePDF Available

Abstract and Figures

This article provides a summary of the basic properties and the essential phenomenology of application-oriented soft magnetic materials. Starting from an introductory section, where the magnetization process and the involved energetic aspects are highlighted, the physical rationale for the soft magnetic behavior of the materials is discussed, and a comparative illustration of their main physical, mechanical, and magnetic parameters is provided, the materials are classified according to their composition. We start from pure iron, the historical benchmark for any magnetic material, and pass through the selected alloys and compounds displaying the right combination of properties, including abundance of raw elements and costs, making them attractive for applications. We thus illustrate preparation methods, physical and magnetic properties, and applicative attributes of the following materials: (i) pure iron and low-carbon steels; (ii) nonoriented and grain-oriented Fe–Si alloys; (iii) High-Si, Fe–Al, and Fe–Al–Si alloys; (iv) soft magnetic composites; (v) amorphous alloys; (vi) nanocrystalline alloys; (vii) Ni–Fe and Co–Fe alloys; (viii) soft ferrites. For each material, we summarize (i) compositional features and intrinsic physical and magnetic properties; (ii) metallurgical aspects and preparation techniques; (iii) magnetization process and magnetic hysteresis; (iv) energy losses and their dependence on the magnetizing frequency; (v) dependence of the magnetic properties on temperature and stress; (vi) mechanical properties; (vii) applications.
Content may be subject to copyright.
W4504_PUB2 10/31/2016 10:4:36 Page 1
SOFT MAGNETIC MATERIALS
1. INTRODUCTION
A magnetic material is considered softwhen its coercive
eldstrength is of the order of or lower than the earths
magnetic eld (about 40 A/m). A soft magnetic material
(SMM) can be employed as an efcient ux multiplier in a
large variety of devices, including transformers, genera-
tors, motors, to be used in the generation, distribution, and
conversion of electrical energy, and a wide array of appa-
ratus, from household appliances to scientic equipment.
With a market around 20 billion in the year 2015 and
annual growth rate around 5%, soft magnetic materials are
today an ever-important industrial product, offering chal-
lenging issues in properties understanding, preparation,
and characterization. An overview of the whole market of
magnetic materials and the relative contributions of the
different types of soft magnets is given in Figure 1.
SMMs were at the core of the development of the early
industrial applications of electricity. The steel practice at
the turn of the nineteenth century was sufciently devel-
oped to satisfy the increasing need of mild steel for the
electrical machine cores. In 1900, Hadeld, Barrett, and
Brown proved that, by adding around 2% in weight Si to the
conventional magnetic steels, one could increase the per-
meability and decrease the energy losses (1). FeSi alloys
were more expensive and more difcult to produce and
gained slow acceptance. In addition, the poor control of the
C content was to mask the prospective performances of this
product, compared with mild steels. It took more than two
decades, characterized by a gradual improvement of the
metallurgical processes, for FeSi to become the material of
choice for transformers. An empirical attitude toward
research in magnetic materials was prevalent at the
time and applications came well before theoretical under-
standing. This is the case of the Goss process, developed in
the early 1930s, by which the rst grain-oriented FeSi
laminations could be industrially produced (2). In the years
19151923, G. W. Elmen at the Bell Telephone Laborato-
ries systematically investigated alloys made of Fe and Ni,
discovering the excellent soft magnetic properties of
the permalloys (78% Ni) (3). J. L. Snoek is credited for the
successful industrial development of ferrites inthe 1940s (4),
following attempts dating back to the rst decade of the
century. The discovery in 1967 of the soft magnetic amor-
phous alloys again occurred nearly by chance (5), but it
provided a fertile eld for technologists and theorists. It
enriched the landscape of applicative magnetic materials,
while straining existing theories on magneticordering. More
recently, the need for increasingly high frequencies of oper-
ation in miniaturized devices and the appearance of novel
phenomena of fundamental and applicative interest in low-
dimensionality systems have propelled the investigation of
the properties and the preparation techniques of soft mag-
netic thin lms (6, 7). Of special interest in this respect are
the magnetoresistive phenomena observed in multilayer
structures, where different layers can display, by combina-
tion of exchange interaction and applied eld, either parallel
or antiparallel magnetization. Spin-polarized conduction
electrons diffusing through the layers suffer a magnetiza-
tion-orientation-dependent scattering, according to their
spin-up or spin-down character, resulting in a giant magne-
toresistance effect (8).
2. GENERAL PROPERTIES OF SOFT MAGNETS
2.1. Magnetization Curve and Hysteresis
The behavior of a ferromagnetic material is summarized by
the constitutive law J(H) (i.e., M(H)), the dependence of the
polarization J(magnetization M) on the magnetic eld H.
In many instances one can usefully recur to the B(H) law,
where the magnetic induction B, the quantity involved in
the FaradayMaxwell law is related to M,J, and Hby the
relationship
Bμ0Hμ0Mμ0HJ(1)
where μ
0
=4π×10
7
N/A
2
(H/m) is the magnetic constant
(also called magnetic permeability of vacuum). The consti-
tutive law (eq. 1) is the macroscopic outcome of an
extremely complex sequence of microscopic processes,
where by combination of domain wall displacements,
domain structure rearrangements, and rotations of the
magnetic moments, the system responds to a changing
applied eld Hby moving through a succession of meta-
stable minimum energy states (9). These processes are
associated with irreversibility and losses, and a variety
of J(H) behaviors endowed with hysteresis, a property
shared with many physical phenomena. Because of hyster-
esis, any point in the (J,H) plane can be traversed by an
innite number of trajectories, depending on past history.
But the experimental investigation requires some kind of
accessible reference state. Two such states can be identi-
ed: the saturation, where all domains are swept out, and
the demagnetized state (H=0, J=0). The latter is reached
either starting from saturation (J=J
s
) and nely reducing
the amplitude of an applied alternating eld to zero value
or by cooling the sample from the Curie temperature in the
absence of any eld. The curve taken after thermal
demagnetization is called virgin curve. More frequently,
the demagnetization process is performed using the
decreasing alternating eld and the initial magnetization
curve is afterward obtained. An example of major hystere-
sis loop in a soft magnet (namely, a grain-oriented FeSi
sheet) is provided in Figure 2. It is noted that, by virtue of
the relatively low values of the applied eld, no difference
can be appreciated, according to equation 1, between the
B(H) and J(H) curves. It is also remarked in this gure that
aeld H
c
, the coercive eld, must be applied in reverse,
after having attained the peak polarization value J
p
,in
order to bring the material to the demagnetized state. H
c
provides a measure of the magnetic hardness (softness) of
the material, its value typically differing by many orders of
magnitude in soft magnetic materials and in permanent
magnets. Negligible differences between H
cJ
and H
cB
, the
elds required to bring to zero the polarization and the
induction, respectively, exist in soft magnets. By connecting
J. Webster (ed.), Wiley Encyclopedia of Electrical and Electronics Engineering. Copyright 2016 John Wiley & Sons, Inc.
DOI: 10.1002/047134608X.W4504.pub2
W4504_PUB2 10/31/2016 10:4:36 Page 2
the tip points of the nested symmetric minor loops, we
obtain the normal magnetization curve. It coincides in
practice with the initial magnetization curve. At low elds
it is in many cases described by the Rayleigh law J(H)=
aH +bH
2
, where aand bare structure-dependent con-
stants. The Rayleigh region occupies in most soft magnets
aJspan going up to some 10% of J
s
(e.g., 0.1 0.2 T in low-
carbon steels or 0.04 T in MnZn ferrites).
In the course of magnetization and demagnetization,
energy is exchanged between the sample and the external
world. In particular, the energy per unit volume to be
provided for bringing the material to a given induction
value B
p
starting from the demagnetized state is
UBpRBp
0HdB. Part of it is stored and part is dissipated
in the material. Over a complete cycle, the previous inte-
gral, the area of the hysteresis loop, provides the energy
loss per unit volume:
WHdBμ0HdHHdJHdJ(2)
It is noted that the reactive term μ0HdHaverages out to
zero. The dissipated energy increases with the frequency of
the magnetizing eld because of dynamic viscous-type
phenomena interfering with the magnetization process
(e.g., eddy currents in metallic materials). We talk in
this case of rate-dependent hysteresis, an example of which
is provided in Figure 3, showing the evolution of the
hysteresis loops versus frequency in FeCo sheets.
The hysteresis loop embodies the magnetic properties
involved in any kind of application, and by the value of its
parameters, a classication of the materials can be made.
The coercive eld H
c
, the remanent polarization J
r
, the
peak permeability μpBp=Hp, the initial permeability,
and the energy loss Ware the base parameters by which
Soft magnets
Magnetic recording
materials & devices
Hard magnets
NO Fe–Si /
low-carbon steel
GO Fe–Si
Iron/powder
cores
Soft ferrites
Amorphous/
nanocryst.
alloys
Ni–Fe, Co–Fe
Figure 1. The soft magnets cover a large proportion of the global
market of magnetic materials, with a value estimated in the year
2015 around 20 ×10
9
. A major share of the market is covered by
the grain-oriented (GO) and nonoriented (NO) electrical steels.
–300 –200 –100 0 100 200 300
–1.5
–1.0
–0.5
0.0
0.5
1.0
1.5
Non-oriented Fe–Si
J (T), B (T)
H (A/m)
Jr Br
Hc
Figure 2. Magnetic hysteresis loops in a nonoriented FeSi sheet
under quasi-static excitation. The remanent polarization J
r
(always coincident with the remanent induction B
r
) and the coer-
cive eld H
c
are put in evidence. The dashed line shows the normal
magnetization curve, obtained as the locus of the tip points of the
nested symmetric minor loops. This curve is practically coincident
with the initial magnetization curve. There are no detectable
differences between the B(H) and J(H) loops in soft magnets at
technical induction values.
–600 –400 –200 0 200 400 600
–1.0
–0.5
0.0
0.5
1.0
f = 2 Hz
f = 500 Hz
f = 1kHz
f = 2 kHz
f = 3.5 kHz
f = 5 kHz
Fe–Co alloy
J
p
= 1.2 T
J (T)
H (A/m)
Figure 3. Magnetic hysteresis loops J(H) versus magnetizing
frequency in a 0.20 mm thick Fe
49
Co
49
V
2
sheet excited with sinus-
oidal polarization J(t) of peak value J
p
=1.2 T.
2 Soft Magnetic Materials
W4504_PUB2 10/31/2016 10:4:37 Page 3
the properties of the materials can be assessed. The mate-
rial composition actually determines the values of the so-
called intrinsic magnetic parameters, like the Curie tem-
perature, the saturation magnetization, the magnetic
anisotropy constants, and the magnetostriction constants,
which, in turn, affect the magnetization process in a way
related to the material structure (e.g., crystallographic
texture, grain size, foreign phases, and lattice defects).
By proper choice of composition and suitable metallurgical
and thermal treatments, extra soft magnets can be
obtained, where the coercive eld can attain values lower
than 1 A/m, with the relative permeability in the range of a
few 10
5
. But it should be stressed that a number of addi-
tional properties, such as thermal and structural stability,
stress sensitivity of the magnetic parameters, mechanical
properties and machinability, thermal conductivity, and
exible response to thermomagnetic treatments, are to be
considered. The nal acceptance of a specic material in
applications will result from a costbenet evaluation of all
these properties.
There are cases where the DC constitutive law J(H) can
be approximated by a linear function. This occurs, for
example, in some soft magnetic alloys subjected to trans-
verse eld annealing (10) or, quite generally, at very low
inductions, inside the Rayleigh region. High-frequency
applications of soft magnets are typically limited to
such low inductions, and we can describe the material
response to a sinusoidal applied eld HtHpcos ωt
with the phase-delayed induction BtBpcos ωtδ
Bpcos δcos ωtBpsin δsin ωt. The function Btcan thus
be expressed as the sum of two 90°phase-shifted sinusoids
of peak amplitude B1Bpcos δand B2Bpsin δ. We can
equivalently write, using the complex notation, Ht
Hpejωtand BtBpejωtδ. The 90°-delayed component of
the induction is connected with the dissipation of energy.
From the denition of the energy loss per cycle Win
equation 2, we obtain the energy loss per unit volume
WZT
0
HtdBt
dtdtπHpBpsin δ(3)
On the other hand, if we apply the denition of permeabil-
ity to both in-phase and 90°out-of-phase components of
Bt, we obtain the quantities
μ´Bp
Hp
cos δμ
´´Bp
Hp
sin δ(4)
μ´and μ´´can be viewed as the components of the complex
quantity
μBpejωtδ
Hpeiωtμ´jμ´´(5)
and accordingly take the name of real and imaginary
permeability, respectively. It is immediate to obtain from
equation 3 that the energy loss per unit volume at a given
peak polarization J
p
and the complex permeability are
related by the equation
WπJ2
p
μ´´
μ´2μ´´2(6)
Going toward low frequencies, the hysteresis loss might
have a role, even at very low inductions. This is accounted
for, with good approximation, by a residual μ´´value, which
persists down to f0. An example of correlated behavior of
μ´and μ´´as a function of frequency is provided for the
specic case of a MnZn ferrite ring sample excited at
J
p
=2 mT in Figure 4. Here, we notice how μ´´takes a
negligible value at the lowest frequencies. The ratio
between the imaginary and real permeabilities provides
a measure of the departure of the behavior of an inductor
with ferromagnetic core from that of a pure inductive
reactance. Such a ratio is, according to equation 4,
μ´´=μ´tan δ. The quantity tan δ, called loss factor,
coincides with the inverse of the quality factor Qof the
inductor.
An overview of the physical and magnetic properties of
the main soft magnetic materials used in applications is
provided in the Tables 1 and 2. Figure 5 shows that the
Curie temperature, which provides a measure of the
strength of the ferromagnetic exchange interaction, pro-
gressively increases on passing from soft ferrites, where the
interaction mechanism is actually of antiferromagnetic
nature, to amorphous alloys and crystalline alloys. An
overall view of the coercive eld and maximum permeabil-
ity ranges typically attained in soft magnets is given in
Figures 6 and 7, while the behavior of the initial magneti-
zation curves is comprehensively displayed in Figure 8.
Examples of major DC hysteresis loops are nally shown in
Figure 9.
10
3
10
4
10
5
10
6
10
7
10
8
10
9
0
500
1000
1500
2000 Mn–Zn ferrite
J
p
= 2 mT
μʹμʺ
Frequency (Hz)
μʹ
μʺ
Figure 4. Broadband behavior of real μ´and imaginary μ´´ initial
permeability components in a MnZn ferrite. The measurements
are made by combination of uxmetric and transmission line
methods at the peak polarization value J
p
=2 mT.
Soft Magnetic Materials 3
W4504_PUB2 10/31/2016 10:4:42 Page 4
2.2. Anisotropy Energy and Magnetization Process
The key feature of SMMs, as of any other magnetic material,
is that they are subdivided into magnetically saturated
regions, the magnetic domains. In each domain, the magne-
tization is uniform and points along a direction changing
from domain to domain. The overall magnetization of a
macroscopic piece of SMM is thus the result of an average
over many domains, each of them being characterized by a
privileged orientation, resulting from some form of anisot-
ropy. Strength and symmetry properties of the anisotropy
play indeed a leading role in determining the magnetic
behavior of the material. The strength is measured by the
anisotropy constant, K, which has the dimensions of an
energy density (J/m
3
). The symmetry can be uniaxial, cubic,
or more complex, depending on the material.
Table 1. Physical and Mechanical Parameters of Representative Soft Magnetic Materials
Density
(kg/m
3
)
Thermal conductivity
(W/(m K))
Electrical
resistivity (Ωm)
Yield stress
(tension) (MPa)
Fracture stress
(tension) (MPa)
Vickers
hardness
Polycrystalline Fe 7867 79.6 10.5 ×10
8
70150 290 100150
NO Fe(1.0 wt%)Si 7800 40 25 ×10
8
300 400 130
NO Fe(3.5 wt%)Si 7600 20 50 ×10
8
400 530 220
GO Fe(3 wt%)Si 7650 20 45 ×10
8
320 380 200
Bonded-sintered Fe
powders
71007700 1030 50 ×10
6
1000 ×10
6
50250 50250 140
Permalloy/Mumetall
(Fe
15
Ni
80
Mo
5
)
8700 19 70 ×10
8
280 700 160
Permendur (Fe
49
Co
49
V
2
) 8200 32 40 ×10
8
200400 250650 180220
Fe
50
Ni
50
Fe
52
Ni
48
8120 13 48 ×10
8
250 520 120
Sintered ferrites (MnZn
and NiZn)
48005300 4710
2
10
5
60 60 600800
Amorphous alloys
(Fe- and Co-based)
72007900 9 120140 ×10
8
700 2800 800
Nanocrystalline alloys
(FINEMET)
7200 5 118 ×10
8
150 150 800
Table 2. Representative Soft Magnetic Materials and Typical Values of Some Basic Magnetic Parameters at Room Temperature
Composition (wt% cryst.
alloys, at% amorphous
alloys)
Max. relative
permeability
(μ
max
)
Coercive
eld H
c
(A/m)
Saturation
polarization
J
s
(T)
Curie
temperature
T
c
(°C)
Saturation
magnetostriction
λ
s
=(Δl/l)
Js
Polycrystalline Fe Fe
100
350 ×10
3
10100 2.16 770 5 ×10
6
NO FeSi Fe
96-99
-Si
14
310 ×10
3
3080 1.962.12 735765 10 ×10
6
GO FeSi Fe
97
-Si
3
1580 ×10
3
415 2.02 750 13×10
6
Fe(6.5 wt%)Si Fe
93.5
Si
6.5
530 ×10
3
1040 1.80 690 5 ×10
7
Sintered/bonded powders Fe
99.5
P
0.5
10
2
10
3
100500 1.651.95 770
Permalloy/Mumetall Fe
15
Ni
80
Mo
5
/
Fe
14
Ni
77
Mo
4
Cu
5
5×10
5
0.32 0.750.80 420 1 ×10
6
Permendur Fe
49
Co
49
V
2
2×10
3
30100 2.35 930 6010
6
Fe50Ni50 Fe
52
Ni
48
10
5
4 1.60 450 25 ×10
6
Sintered ferrites (Mn,Zn)OFe
2
O
3
10
3
10
4
520 0.40.55 130280 2×10
6
(Ni,Zn)OFe
2
O
3
10
2
10
3
20200 0.20.35 110400 20 ×10
6
Sendust Fe
85
Si
9.5
Al
5.5
50 ×10
3
510 1.70 670 1 ×10
6
Amorphous alloys
(Fe-based)
Fe
78
B
13
Si
9
10
5
25 1.56 415 37 ×10
6
Amorphous alloys
(Co-based)
Co
67
Fe
4
B
14.5
Si
14.5
5×10
5
0.51 0.62 320 5 ×10
7
Nanocrystalline alloys
(FINEMET)
Fe
73.5
Cu
1
Nb
3
Si
13.5
B
9
5×10
5
0.51 1.24 600 2 ×10
6
Nanocrystalline alloys
(NANOPERM)
Fe
86
Cu
1
Zr
7
B
6
5×10
4
3 1.52 600 1 ×10
7
μ
max
maximum DC relative permeability; H
c
coercive eld; J
s
saturation polarization; T
c
Curie temperature, λ
s
saturation magne-
tostriction. The composition is given in wt%, but for the amorphous and nanocrystalline alloys, where it is expressed in at %.
4 Soft Magnetic Materials
W4504_PUB2 10/31/2016 10:4:42 Page 5
The magnetization process in an SMM is the result of
two microscopic mechanisms: motion of the domain walls
and uniform rotation of the magnetization inside the mag-
netic domains. In conventional Fe-based crystalline alloys,
the rotations require high eld strengths, because the
interaction between eld and polarization EHH?Js,
the Zeeman energy, must balance the magnetocrystalline
anisotropy energy E
K
roughly of the order of the anisotropy
constant K
1
. Since K
1
is around some 10
4
J/m
3
,elds in the
10
3
10
4
A/m range must be applied to achieve substantial
rotations in iron and silicon steels. A soft magnetic
behavior can be achieved, in these materials, only through
easy displacements of the domain walls. Frictional
forces, inevitable in real defective materials, resist these
displacements. The coercive eld measures the typical
eld strengths at which the domain walls are unpinned
Figure 5. Curie temperature of the main applicative soft mag-
netic materials.
Figure 6. Coercive eld landscape in applicative soft magnetic
alloys.
Figure 7. As in Figure 6 for the maximum permeability value.
Figure 8. Initial magnetization curve of several types of
soft magnets: (1) FINEMET nanocrystalline alloys
Fe
73.5
Cu
1
Nb
3
B
9
Si
13.5
; (2) amorphous alloys Co
67
Fe
4
B
14.5
Si
14.5
;
(3) amorphous alloys Fe
78
B
13
Si
9
; (4) Fe
15
Ni
80
Mo
5
(Mumetall);
(5) grain-oriented Fe(3 wt%) Si sheets; (6) Fe
49
Co
49
V
2
alloys
(Permendur); (7) Nonoriented Fe(3.5 wt%)Si laminations; (8)
Low-C steels; (9) MnZn soft ferrites; (10) NiZn soft ferrites;
(11) Fe(6.5 wt%)Si; (12) Fe powder cores (Soft Magnetic
Composites).
Soft Magnetic Materials 5
W4504_PUB2 10/31/2016 10:4:43 Page 6
from defects and a substantial part of the magnetization
is reversed. Energy is lost in this process, and magnetic
hysteresis is accordingly observed. The subject of
coercivity and hysteresis is classically treated by
theorizing the motion of a domain wall, assumed either
as a rigid (11, 12) or as a exible (13) object, in a perturbed
medium. Since the energy of the domain wall γ
w
is directly
related to the anisotropy constant K
1
according to the
expression γwffiffiffiffiffiffiffiffiffi
AK1
p, where Ais the exchange stiffness
constant, denoting the strength of the ferromagnetic
exchange, any structural perturbation, inuencing the
exchange and anisotropy energies, reects in a spatially
perturbed domain wall energy. A domain wall moving in a
defective medium takes then a random energy prole,
whose spatial derivative must be overcome by the pressure
of the applied eld in order to achieve wall motion. The
coercive eld H
c
, which is the eld upon which the wall gets
loose from the hindering effect of the structural defects, is
then chiey controlled by the value of the anisotropy
constant K
1
, the larger K
1
the larger H
c
. In spite of the
relatively high values attained by K
1
, very soft magnetic
behavior can however be achieved in Fe and FeSi when
the microstructure is suitably controlled. In practice, this
means having the least content of precipitates, voids, dis-
locations, and point defects, together with large and favor-
ably oriented grains. With the applied eld directed as far
as possible alongside one of the <100>easy axes, that is in
the plane of the main 180°domain walls, an obvious
directional advantage exists for the wall displacements,
as remarkably demonstrated by the behavior of the grain-
oriented (GO) FeSi laminations. The role of the micro-
structural defects is clearly observed in Fe. Here, one can
reach coercive elds as low as a few A/m upon prolonged
purication and annealing treatments, leading to very low
dislocation densities and C and N concentrations of some
1020 parts in 10
6
(ppm) (14, 15). Coercivities of a few
hundred A/m can be found instead when these concentra-
tions are in the 100 ppm range and beyond (12). C and N are
basically insoluble in α-Fe and tend to form carbides and
nitrides, which act as strong pinning centers for the domain
walls. With much higher C content (around 1 wt%), graph-
ite precipitates and martensitic domains are additionally
formed, and H
c
can reach values typical of hard magnets
(a few 10
4
A/m).
Very low values of the magnetic anisotropy (say with K
in the range of few ten J/m
3
and less) directly lead to soft
and extra-soft magnetic properties, because both rotations
and domain wall displacements become easy processes.
This is the case, for example, of the FeNi alloys with
composition around Fe
20
Ni
80
.K
1
is positive in α-Fe (bcc
cell) and negative in Ni (f.c.c. cell), and it passes through
zero on the high Ni side in the FeNi alloys. Vanishing
anisotropy can equally be obtained in amorphous and
nanocrystalline alloys, because the structural order in
these materials is extended over limited distances, from
a few atomic spacings to a few nanometers. The character-
istic length L
ex
controlling the magnetization process, the
exchange length (of the order of the domain wall thickness),
encompasses a large number of local ordered structural
units, be them agglomerate of few atoms or nanometer-
sized crystals. The magnetic moments in such units are
constrained to alignment by the exchange interaction and
cannot follow the random directions of the local easy axes.
The local magnetocrystalline anisotropy K
1
is then aver-
aged out to a residual anisotropy K
0
across the Nstructural
units of average size δenclosed in the volume L3
ex Nδ3
according to K
0
K
1
/pN(16). Domain wall thickness and
K
0
are related by the standard equation L
ex
π(A/K
0
)
1/2
,
where Ais the stiffness constant, and we get (17)
K0K1
δ
Lex

3=2
K1
δ
L1

6
(7)
–400 –200 0 200 400
–2
–1
0
1
2
Mn–Zn ferrite
Fe–Co
NO Fe–Si
GO Fe–Si
J (T)
H (A/m)
(a)
–6 –4 –2 0 2 4 6
–1.0
–0.5
0.0
0.5
1.0
Finemet
Permalloy
Co-based
amorphous
J (T)
H (A/m)
(b)
Figure 9. DC hysteresis loops in different soft magnetic alloys. (a)
Fe
49
Co
49
V
2
(Permendur/Vacoux); Grain-oriented Fe(3 wt%)Si;
nonoriented Fe(3 wt%)Si; MnZn sintered ferrite. (b)
Fe
73.5
Cu
1
Nb
3
B
9
Si
13.5
nanocrystalline alloy (Finemet); amorphous
Co
67
Fe
4
B
14.5
Si
14.5
alloy; Fe
20
Ni
80
(Permalloy/Mumetall). All mate-
rials are heat treated for best DC response. The amorphous and
nanocrystalline ribbons are annealed under a saturating longitu-
dinal magnetic eld.
6 Soft Magnetic Materials
W4504_PUB2 10/31/2016 10:4:44 Page 7
where L
1
π(A/K
1
)
1/2
is the exchange length of the crystal-
line counterpart. By taking δ=10
9
m, K
1
=4.8 ×10
4
J/m
3
(as in Fe) and A10
11
J/m, we nd the negligible value
K
0
=5.8 ×10
6
J/m
3
.
Once the magnetocrystalline effects are made negligi-
ble, other sources of magnetic anisotropy are brought to
light. This is the case, for example, of the local anisotropies
arising in the highly magnetostrictive Fe-based amorphous
alloys, due to the magnetoelastic coupling between the
frozen-in stresses and the magnetization. In the typical
alloy of composition Fe
78
B
13
Si
9
, the saturation magneto-
striction is λ
s
3540 ×10
6
, and the long-range internal
stresses generated by the rapid solidication process are of
the order of 50100 MPa (18, 19). Induced anisotropies
K
σ
=(3/2)λ
s
σof several hundred J/m
3
can therefore
arise (20), and annealing treatments are required to
recover excellent soft magnetic behavior. Co-based
amorphous alloys (such as Co
71
Fe
4
B
15
Si
10
and
Co
66
Fe
5
Cr
4
B
15
Si
10
), FeNi alloys of the Permalloy type,
and nanocrystalline alloys (such as Fe
73.5
Cu
1
Nb
3
Si
13.5
B
9
)
have vanishing magnetostriction (λ
s
10
8
10
7
) and, lack-
ing also the anisotropy of magnetocrystalline origin, attain
the lowest coercivities and record values of permeability.
Their properties can be tailored by inducing calibrated
uniaxial anisotropies through annealing treatments under
saturating elds. In a saturated FeNi alloy, the magneti-
zation interacts with the FeFe and NiNi atomic pairs in
such a way that, if the temperature is sufciently high,
these pairs tend to diffuse and distribute preferentially
along the direction of the magnetization imposed by the
applied eld. A directional order sets in although the alloy
preserves its character of random solid solution. In the
amorphous alloys, anisotropic atomic rearrangements of
the local ordered units occur with symmetry inuenced by
the direction of the magnetization (21), while in the nano-
crystalline alloys directional pair ordering of the Si atoms
in the FeSi nanocrystals is invoked to justify the induced
anisotropy (16). In magnetostrictive alloys, stress-induced
anisotropy and anisotropy induced by eld annealing can
be suitably combined to impose a desired hysteresis loop
shape.
2.3. Magnetic Losses
SMMs are chiey employed in magnetic cores of AC
machines and devices, from 50 Hz to several MHz. The
technically relevant quantity in applications is the energy
loss. Eddy currents are generated by a time-varying mag-
netic ux, leading to both shielding of the core by the
associated counterelds (skin effect) and generation of
heat by Joule effect. Excluding ferrites, which are either
insulating or near-insulating materials, and the soft mag-
netic composites, near net-shape cores obtained by com-
pacting and bonding ferromagnetic powders, soft magnets
are generally used in sheet form in order to minimize skin
effect and losses. The theoretical assessment of these
effects is far from simple, because it is seldom possible to
treat the material as a continuum, characterized by a given
magnetic permeability, and apply to it the Maxwells equa-
tions. The magnetic structure is made of domains and
domain walls and the distribution of eddy currents can
be extraordinarily complex and nonuniform. Williams,
Shockley, and Kittel were the rst to take at face value
such a complexity, by investigating the dynamic behavior of
a 180°Bloch wall in single crystals of FeSi. They theorized
it through a balance equation involving, on the one hand,
the applied magnetic eld and, on the other hand, the
structural pinning eld and the eddy current countereld
(WSK model) (22). Pry and Bean generalized the WSK
model to a system of 180°walls, emulating the real domain
structure of a GO FeSi sheet (23). The whole problem was
eventually assessed by G. Bertotti, who showed that the
complexity of the dynamic magnetization process in real
structures can be properly described by means of statistical
methods (24, 25). Bertottis theory provides solid physical
background to the concept of loss separation, where the
total energy loss W(f) at any given magnetizing frequency f
and peak polarization J
p
can be considered as the sum of
three components, each of them depending in a different
way on frequency
WfWhWclfWexc f(8)
as illustrated in Figure 10. The meaning of these compo-
nents is the following: W
h
, called hysteresis loss, is the
residual energy dissipated in the limit f0 and, as
such, it is independent of f.W
cl
, called classical loss,is
the loss calculated applying Maxwells equations to the
material when it is ctitiously assumed as fully homoge-
neous from the magnetic viewpoint (absence of domains).
The classical loss W
cl
is a sort of background term, always
present and independent of any structural feature. For a
lamination of thickness dand conductivity σ, one nds,
under sinusoidal time dependence of the magnetic polar-
ization and complete ux penetration in the lamination
cross section (negligible skin effect), the classical loss per
unit volume
Wcl π2
6σd2B2
pfπ2
6σd2J2
pfJ=m3(9)
where, as is usual the case with soft magnets tested at
technical inductions, we neglect any difference between the
peak values of induction B
p
and polarization J
p
. As shown
in Figure 10b, by summing up W
h
and W
cl
, one falls short of
the measured energy loss value. The remainder W
exc
is
called excess loss. Figure 10b shows, in particular, that the
prediction by equation 9 grossly underestimates the meas-
ured loss in GO laminations at 5060 Hz, the frequencies at
which the largest amount of electrical energy is generated
and used, besides failing to account for the experimental
nonlinear dependence of Won f.
The three loss components are associated with different
eddy current mechanisms and different spacetime scales
of the magnetization process. Flux reversal is actually
concentrated at each instant of time inside the moving
domain walls and, even under quasi-static excitation,
eddy currents arise, because the domain wall displace-
ments, hindered by the pinning centers, occur in a jerky
fashion (Barkhausen effect). Intense local current transi-
ents, with lifetime around 10
9
s, are generated around the
jumping wall segments and energy is correspondingly
Soft Magnetic Materials 7
W4504_PUB2 10/31/2016 10:4:44 Page 8
dissipated. The hysteresis component W
h
integrates the so
generated loss over a period and the unit volume of the
material. Since the time constant of the microscopic eddy
current pulses is always many orders of magnitude smaller
than the typical magnetization period T=1/f, it is apparent
that the associated local magnetization reversal is not
affected by the rate of increase of the applied eld and
W
h
is independent of frequency. For a given value J
p
,W
h
gives a measure of the coercive eld. This is consistent with
the fact that the Barkhausen mechanism is independent,
as the coercivity should be, of the material conductivity.
The excess loss W
exc
is associated with the large-scale
motion of the domain walls. The theory shows, again in
the absence of skin effect, that the excess loss behavior in
most SMMs can be described to a good approximation by
the expression
Wexc kexc ffiffiffiffiffiffi
σf
pJ3=2
pJ=m3(10)
where k
exc
is a parameter related to the properties of the
domain structure and their relationship with the structural
properties of the material (24, 25). As such, it generally
increases to some extent with J
p
(26). Equation 10 is
actually a reduced form of a more general expression for
W
exc
. The two expressions normally coincide beyond a few
Hz (24, 26). Very broadly, it can be stated that k
exc
is the
larger the more discrete is the magnetization process. Very
large domains are therefore not desirable from this view-
point and, as discussed in the following, methods aiming at
increasing the density of the domain walls in the sheet
samples have sometimes been devised.
While Bertottis theory is solidly assessed from the
physical and experimental viewpoint and has found wide-
spread application, alternative approaches have been pro-
posed in recent times, pointing to the simultaneous
prediction of magnetic losses and shape of the hysteresis
loops versus frequency in soft magnetic sheets. In particu-
lar, Zirka et al. have developed a viscosity-based magneto-
dynamic model, where the classical Maxwells diffusion
equation is combined with a magnetic hysteresis model,
which can be either rate-independent or rate-depen-
dent (27, 28). This approach requires the implementation
of numerical methods. In the very special case of sharply
rectangular hysteresis loops, emulating ideal step-like
magnetization curves (9), it has been assumed that a
breakdown of the classically held uniformity of the distri-
bution of the magnetic ux density, implied in the deriva-
tion of equation 9, occurs even at low frequencies (29). It has
been suggested that this effect might occur, via propagation
of saturation magnetization wavefronts across the sheet
thickness, also in ordinary nonoriented (NO) steel sheets
excited at high inductions (28). However, direct experimen-
tal evidence for the occurrence of this reversal mechanism
is not available at present time.
In conclusion, if minimization of the AC energy losses is
desired, not only the lamination thickness and the material
conductivity need to be reduced, as suggested by the clas-
sical approach (eq. 9), but also the microstructure must be
controlled in order to minimize both W
h
(i.e., the coercive
eld) and W
exc
. This emphasizes the role of the metallurgi-
cal process, whose continuous renement over the years
has produced increasingly better control of the various
structural parameters (e.g., impurities, defects, grain
size, and crystallographic texture) and clear progress of
the magnetic properties of the materials.
3. IRON AND LOW-CARBON STEELS
Iron is referred to as high puritywhen the total concen-
tration of impurities (typically C, Cu, N, O, P, S, Si, Al) does
not exceed a few hundred ppm. It is otherwise called low-
carbon steel (LCS) or nonalloyed steel. When soluble ele-
ments such as Si and Al are deliberately introduced, typi-
cally in the range of a few percent, it is appropriate to speak
–150 –100 –50 0 50 100 150
–1.5
–1.0
–0.5
0.0
0.5
1.0
1.5
0.25 Hz
150 Hz
400 Hz
Grain-oriented
Fe–(3 wt%)Si
d = 0.30 mm
Jp = 1.7 T
Jp = 1.7 T
J (T)
H (A/m)
(a)
(b)
0 100 200 300 400
0
100
200
300
400
500
600 Grain-oriented
Fe–(3 wt%)Si
d = 0.30 mm
Energy loss (J/m3)
Frequenc
y
(Hz)
Wexc
Wcl
Wh
Figure 10. (a) Hysteresis loops in a grain-oriented 0.30 mm thick
FeSi steel sheet measured under sinusoidal polarization of peak
value J
p
=1.7 T at different frequencies. (b) Corresponding behav-
ior of the energy loss per cycle and unit volume W(f) (area of the
hysteresis loop) and its decomposition in the quasi-static W
h
,
classical W
cl
, and excess W
exc
components.
8 Soft Magnetic Materials
W4504_PUB2 10/31/2016 10:4:45 Page 9
of silicon steels.Very pure iron is seldom used in appli-
cations, but the study of its properties is of basic physical
interest. The main practical drawbacks of pure Fe are its
relatively high electrical conductivity, which makes it
unsuitable for AC applications, its poor mechanical prop-
erties, and its cost. Low-cost LCSs (C <0.1 wt%) are largely
applied in a multitude of small electrical machines (for
instance fractional horse power motors) and devices where
efciency is not of primary concern. Together with the
silicon steels, they cover about 70% of the world tonnage
of soft magnetic materials. More efcient LCSs are today
increasingly developed, under the pressure of rising energy
costs and environmental concerns. Higher grades are
therefore now available, where improved magnetic proper-
ties are obtained chiey by introducing a small amount of
Si (<1 wt%) and decreasing the content of impurities (espe-
cially suldes, carbides, and nitrides).
High-purity iron can be obtained starting with commer-
cially pure iron (e.g., of the ARMCO type) and rening it by
suitable methods. These include prolonged annealing in
pure H
2
at temperatures not far from the melting point (e.
g., 48 h at 1480 °C), zone melting and levitation melting. By
means of these methods, some 2030 ppm maximum total
impurity content can be reached, with C and N less than
10 ppm. Relative permeabilities μ
r
10
5
and coercivities
H
c
=12 A/m have been measured in highly puried iron
samples (30). Some common iron grades are listed in
Table 3. ARMCO-type iron is ideal for soft cores working
in a DC environment, like the electromagnets. Its high
electrical conductivity is a drawback for AC applications,
but the combination of high permeability and high conduc-
tivity can lead to efcient magnetic eld shielding at power
frequencies (31). In addition, pure iron is relatively resist-
ant to corrosion, due to the formation of a protecting
cohesive layer of rust.
Low-carbon steels used in magnetic cores are generally
produced as sheets through a sequence of hot and cold
rolling passes and thermal treatments, as schematically
showninTable4.Thespecications for these steels are
provided in the IEC Standard 60404-8-3 (32). To improve
the magnetic performance, the sheets must be decarbu-
rized. It is a nal annealing treatment in wet hydrogen
atmosphere, at temperatures around 800 °C. By this pro-
cess, the carbon concentration can be reduced to less than
50 ppm. The main detrimental effect of the residual C is
magnetic aging, that is, the increase of coercivity with
time ensuing from the precipitation of cementite particles
and the related domain wall pinning phenomena. Aging
may represent a real threat in actual magnetic cores,
where operating temperatures of 50100 °C are common.
Figure 11 shows that in LCSs with C concentrations as
low as 45 ppm (in weight) a potential for aging still
exists (33). Nitrogen can equally induce aging, but it
can be partly stabilized by the formation of AlN precipi-
tates. These, however, may adversely affect the grain
texture during recrystallization annealing, by favoring
the growth of magnetically hard {111} planes, an effect
that is contrasted by controlled addition of B (30 ppm)
and Zr (0.07 wt%) (34). Reduction of the C, N, and S
concentrations in the range of 2030 ppm can also be
obtained, in high quality steels, by vacuum degassing
of the melt, which can make the nal decarburization
anneal unnecessary, with benecial effects on the produc-
tion costs (35).
The αγtransition takes place in Fe at 911 °C and the
nal thermal treatments are thus preferably made at lower
temperatures, which may limit the range of attainable
grain sizes and crystallographic textures. LCSs are gener-
ally delivered as semiprocessed products, because they
need to be in a cold worked state before punching and
cutting. The necessary mechanical hardness is imparted by
means of temper rolling, a 35% cold reduction. Once
punched, the laminations are subjected to decarburization
and grain growth annealing, eventually followed by con-
trolled surface oxidation (bluing), to ensure acceptable
interlaminar insulation in the core. One notable conse-
quence of temper rolling is a somewhat exaggerated grain
growth upon nal annealing, which overcomes to some
Table 3. Typical Impurities and Their Concentrations (wt ppm) in Different Grades of Iron and in Low-Carbon Steel
Iron type C N O Mn P S Si Cu Ni
ARMCO 150 20 150 280 50 250 30 150
Electrolytic 40 100 100 15 20 30 30 40 10
H
2
-treated 30 10 30 280 40 <30 ——
Zone-rened 7 <10 2 0.5 <0.1 0.2 1.5 0.50
Low-carbon steel 501000 30200 2001000 5000 2001000 50300 10
3
10
4
100
Table 4. The Sequence of Thermomechanical Treatments in Low-Carbon Steel Sheet Processing
Melting, degassing, continuous casting of slabs.
Reheating (10001250 °C) and hot rolling to 22.5 mm thickness.
Pickling and cold rolling to nal thickness (0.501 mm).
Intermediate annealing for recrystallization.
Temper rolling (reduction 35%).
Punching.
Final annealing (decarburization, grain-growth, controlled surface oxidation).
Core assemblage.
Soft Magnetic Materials 9
W4504_PUB2 10/31/2016 10:4:46 Page 10
extent the limitations imposed on the upper treatment
temperatures by the αγtransition.
The performance of the LCS sheets is best described in
terms of AC magnetic properties at 5060 Hz. In the
absence of purication treatments and signicant Si con-
tent, AC losses at 60 Hz and 1.5 T can reach some 15 W/kg
in 0.65 mm thick laminations, with relative permeability
μ
r
=5001000. The addition of 0.51 wt% Si, together with
better composition control, may contribute to lowering this
loss gure to less than 68 W/kg in 0.50 mm thick sheets.
However, the introduction of Si decreases the saturation
magnetization, which may be somewhat detrimental to
permeability. Therefore, the loss performance is improved,
whenever possible, by use of very clean materials, as
obtained by extensive application of vacuum degassing.
Coated semiprocessed LCSs are thus available, which
combine improved loss and permeability behavior (P4
W/kg and μ
r
3000 at 1.5 T and 50 Hz in 0.50 mm thick
laminations) with excellent punching performance. On
increasing the magnetizing frequency, the benetof
decreasing the lamination thickness and increasing the
Si content becomes apparent, as shown in Figure 12.
Pure Fe and nonalloyed steels are employed as cores of
DC electromagnets, where one exploits their high satura-
tion magnetization to produce strong elds. Typical AC
applications are relays, lamp ballasts, fractional horse-
power motors, and small transformers, where performance
is needed at low price. It is known that in small motors
(power less than 12 kW), where the limited size imposes
high induction values in the stator teeth, copper losses tend
to predominate over iron losses. The solution offered by
nonalloyed steels, with their high values of permeability at
high inductions, high thermal conductivity, and affordable
price, represents a good compromise between the require-
ments of costs and machine efciency. Optimal product
performance is in any case obtained through proper design
considerations.
The base physical and magnetic parameters of low-
carbon steels and low-Si laminations are given in Tables
1 and 2. We list here additional properties and features of
these materials:
1. Temperature Dependence of the Magnetic
Properties. There is a moderate decrease of the
coercive eld, of the order of 10%, following the
increase of temperature from 20 to 200 °C, due to a
concurring decrease of the anisotropy energy. The
total power loss at 50 Hz decreases more rapidly, by
about 20%, in the same temperature interval because
of the concomitant increase of the electrical resistiv-
ity. The permeability is correspondingly increased,
but to somewhat lesser extent.
2. Stress Dependence of the Magnetic Properties.
Elastic tensile stresses introduce slight magnetic
softening. Compressive stresses engender instead
substantial decrease of the magnetic permeability.
This effect is consistent with sign and value of the
magnetostriction constants in iron single crystals.
Plastic deformation is conducive to increased coer-
civity and losses and decreased permeability. The
increase of coercivity roughly follows a square-root
dependence on the plastic strain (36). An example of
the effect of plastic deformation by tensile straining
on the DC hysteresis loop of polycrystalline pure iron
(grain size hsi=14 μm) is given in Figure 13.
3. Mechanical Properties. Pure Fe and low-carbon
steels are mechanically soft and can be easily
machined. However, lamination punching and cut-
ting need to be made on the cold worked materials,
before the nal annealing treatment.
103104105106107108
0.0
0.1
0.2
0.3
0.4
0.5
0.6
C =156 ppm
C = 57 ppm
C = 45 ppm
C = 21 ppm
Low-carbon steel
T = 150 °C
P(t) / P(0)
Time (s)
Figure 11. Relative increase ΔPt=P0of power losses (f=50 Hz,
J
p
=1.5 T) with aging time tat T=150 °C in low-carbon steel sheets
(Si =0.3 wt%) having C concentration (weight ppm) ranging
between 21 and 156 ppm. Adapted from Reference 33.
0 200 400 600 800 1000
0.0
0.2
0.4
0.6
0.8
1.0
1.2
NO Fe–(3.5 wt%)Si
NO Fe–(2 wt%)Si
Low-carbon steel
Jp = 1.5 T
Energy loss (J / kg)
Frequency (Hz)
Figure 12. Specic power loss versus magnetizing frequency at
peak polarization value J
p
=1.5 T in different types of commercial
soft magnetic sheets: (1) 0.65 mm thick low-carbon steel; (2)
0.50 mm thick nonoriented Fe(2 wt%) Si; (3) 0.35 mm thick non-
oriented Fe(3.5 wt%) Si.
10 Soft Magnetic Materials
W4504_PUB2 10/31/2016 10:4:46 Page 11
4. Coating. Pure iron and LCS sheets are not coated in
general. They come instead with a slight homoge-
neous surface oxidation, which is sufcient to provide
acceptable layer-to-layer electrical insulation in the
assembled cores.
5. Delivery. Pure iron is delivered either in bulk form
as billets of various diameters or thick slabs (thick-
ness daround 200 mm), hot-rolled plates (3 mm d
120 mm), or cold-rolled sheets (0.50 mm d2
mm). They are provided to the customer as semi-
nished products and need nal heat treatment after
cutting/punching, in order to attain the desired soft
magnetic properties.
6. Specications. The grades, general requirements,
magnetic properties, geometric characteristics, toler-
ances, and technological characteristics are dened
in the Standards IEC 60404-8-3 (32) and IEC 60404-
8-6 (37).
7. Applications. Low-carbon steels are chiey
employed in DC electromagnets, electromagnetic
shields at power frequencies, relays, lamp ballasts,
fractional horsepower motors, and small
transformers.
4. IRONSILICON ALLOYS
The addition of few atomic percent Si brings about notable
changes in the physical, mechanical, and magnetic proper-
ties of Fe, as summarized in Figure 14. The most notable
effect regards the electrical resistivity, which increases at a
rate around 5 ×10
8
Ωm per soluted atomic percent. This
implies a more than fourfold increase on passing from pure
Fe to the conventional Fe(3 wt%)Si alloys, a remarkable
benet in terms of decreased AC losses. But there are
further properties taking advantage of Si alloying. The
magnetocrystalline anisotropy constant K
1
decreases
with increasing Si (from 46 kJ/m
3
in pure Fe to 36 kJ/m
3
in Fe(3 wt%)Si), reecting into lower coercivity. The
yield strength increases, which favors material handling
and machining. Inspection of the FeSi phase diagram
(Figure 15) shows that above about 2 wt% Si the αγ
transition (bcc to f.c.c. structure) no longer takes place
and the previously remarked restrictions on the nal
annealing temperatures in the low-carbon steels do not
longer exist. The chief factors against substantial addition
of Si are the reduction of the saturation magnetization
(around 2.5% for any weight percentage increase of Si
concentration) and the fact that there is no practical way
of achieving laminations with more than about 4 wt% Si by
conventional rolling processes. The heterogeneous forma-
tion of FeSi and Fe
3
Si-ordered phases leads in fact to severe
material embrittlement (38). Alloying with Al in place of Si
leads to quite similar physical and structural effects, while
not causing material embrittlement. But Al is very reactive
and can easily lead to oxide formation, it brings about an
–1500 –1000 –500 0 500 1000 1500
–1.5
–1.0
–0.5
0.0
0.5
1.0
1.5
εp = 0.5%
εp = 0
εp = 5%
Iron sheet
J (T)
H (A/m)
Figure 13. Evolution of DC major hysteresis loop (J
p
=1.5 T) in cold-
rolled and recrystallized Fe sheets (average grain size hsi=14 μm)
with plastic deformation by tensile straining up to ε
p
=5%.
Figure 14. Magnetocrystalline anisotropy constant K
1
, electrical
resistivity ρ, saturation magnetic polarization J
s
, and yield stress
σ
y
versus Si concentration in the FeSi alloys. These behaviors
summarize data taken from different literature sources (39).
Soft Magnetic Materials 11
W4504_PUB2 10/31/2016 10:4:47 Page 12
increase of the magnetostriction, and is costlier. An over-
view of the behavior of the physical and intrinsic magnetic
properties of the FeSi and FeAl alloys is provided in
Reference 39.
4.1. Nonoriented FeSi Alloys
Nonoriented FeSi alloys are soft magnetic materials with
an approximately isotropic grain texture. They cover the
medium- and high-quality range of SMMs for applications
in electrical rotating machines (motors and generators),
where good isotropic magnetic properties are required.
They come in a variety of grades, the higher ones being
associated with higher Si content. The specications for NO
Si steels are provided in the Standards IEC 60404-8-4 (40),
IEC 60404-8-6 (37), and IEC 60404-8-8 (41). The materials
are typically graded by their power loss at 50 Hz and peak
polarization J
p
=1.5 T. For example, a magnetic steel sheet
with designation M250-35A has nominal thickness
0.35 mm and maximum power loss at 50 Hz and 1.5 T of
2.50 W/kg (and, typically, 1.0 W/kg at 1.0 T and magnetic
polarization J
p
=1.60 T for applied eld H=5000 A/m).
The Si concentration can vary between 1 and 3.7 wt%,
and some percentage of Al (0.20.8 wt%) and Mn
(0.10.3 wt%) is usually justi ed by metallurgical require-
ments. These impurities increase the alloy resistivity with-
out impairing the mechanical properties. Al lowers the
temperature of the primary recrystallization and prevents
aging by N precipitation and by stabilizing it through the
formation of AlN second phases. Mn can capture residual S
impurities, leading to the formation of MnS precipitates. In
order to counter the adverse effects on the soft magnetic
properties of the material brought about by these
precipitates, clean material preparation methods are
required (35). The lower grade NO laminations (less
than 2 wt% Si) are produced and delivered in the semi-
processed state and follow the same thermomechanical
history of low-carbon steels (sketched in Table 4) with nal
thickness ranging between 0.65 and 0.50 mm. The higher
grades are instead fully processed materials. They are
obtained according to the procedure outlined in Table 5.
The hot-rolled sheets (thickness 2.31.8 mm) are cold
rolled to intermediate gauge, annealed at 750900 °C,
reduced to the nal gauge of 0.650.35 mm, and subjected
to a recrystallization and decarburization anneal at
830900 °C and nal grain-growth anneal at 850
1100 °C. A single-stage cold reduction is a basic variant
of this process. A phosphate-based or chromate-based coat-
ing (thickness 0.55μm) is then applied, which not only
provides the necessary interlaminar insulation but also
ensures good sheet punchability. The latter property is
important, because of the strict tolerances required in
rotating machine cores and the need to avoid edge burrs,
a possible cause of interlaminar short-circuits in the
assembled cores. Emphasis has been given in recent times
to eco-friendly chrome-free coatings. Polymer-based lac-
quers for both semiprocessed and fully processed steels
have therefore been developed, which can be cured by
ultraviolet radiation in a fast, energy-efcient, and haz-
ard-free process (42). Contrary to the case of seminished
products, no stress relief treatment is applied in general to
the fully treated sheets after punching.
By acting on the composition and the preparation meth-
ods and relying upon improved knowledge of the role of the
structural parameters on the loss and permeability prop-
erties, industry has made available to the users a wide
range of NO steels. These materials are never isotropic and
typically exhibit some 1020% variation of the loss gure
along different directions in the lamination plane. The top
commercial grades have around 4 wt% (Si +Al) concentra-
tion and, with a gauge of 0.350.50 mm, they display a
power loss gure P
15/50
of 2.102.30 W/kg at 1.5 T and
50 Hz, reaching an induction B
25
=1.501.60 T at 2500 A/
m. Nonoriented FeSi alloys are preferentially employed in
medium- and high-power rotating machines, whereas, as
Figure 15. FeSi phase diagram: the γloop. For Si concentrations
exceeding 1.86 wt% and negligible C concentrations, the αγ
transformation does not take place and there is freedom in the
thermomechanical treatments. The width of the region where the α
(b.c.c.) and γ(f.c.c.) phases coexist increases with the C content.
Table 5. Preparation Stages of Fully Processed Nonoriented
FeSi Laminations
Composition [wt%]: Si (0.9 . . . 3.7), Al (0.2 . . . 0.8),
Mn (0.1 . . . 0.3).
Melting, degassing, continuous casting of slabs.
Reheating (10001250 °C) and hot rolling to thick-
ness 1.82.3 mm.
Pickling and cold rolling to intermediate gauge.
Intermediate annealing (750900 °C).
Cold rolling to nal gauge (0.650.35 mm).
Decarburization and recrystallization annealing
(830900 °C).
Final grain-growth annealing (8501100 °C).
Coating.
Punching.
Core assemblage.
12 Soft Magnetic Materials
W4504_PUB2 10/31/2016 10:4:49 Page 13
previously stressed, low-carbon steel laminations are pre-
ferred in small apparatus. The highest efciency (>95%) is
sought in big electrical machines not only to save energy
but also to avoid overheating and shortened machine life
span. For medium-to-high-frequency applications, like
high-speed rotating machines, thin fully processed grades
with good mechanical properties have been developed.
They span a thickness range 0.100.27 mm, as illustrated
in Table 6. The related specications are provided by the
Standard IEC 60404-8-8 (41).
The development of improved nonoriented alloys is
related to the control of a number of structural parameters,
namely, impurities, grain size, crystallographic texture,
surface state, and residual and applied stresses. A few
10 ppm concentrations of impurities such as C, N, S, and
O tend to increase coercivity and losses (43). They can do
this directly, by forming precipitates that act as pinning
centers for the domain walls, and indirectly, by adversely
affecting grain growth and texture. The role of grain size hsi
is illustrated in Figure 16, where it is observed that the
optimal hsivalue at line frequency is, depending on the
composition, around 100200 μm, where the total power
loss attains a minimum value (44, 45). This dependence is
especially important in clean materials. Figure 17 shows
that a large grain size brings about a decrease of the loss
below a few hundred Hz, while the opposite occurs at
higher frequencies. This is understood in terms of opposite
dependencies on grain size exhibited by the hysteresis loss
component W
h
, decreasing as hsi
-n
, with n=0.51, and by
the excess loss W
exc
, approximately increasing as hsi
1/2
(44).
The correlated dependence of W
h
and W
exc
on the average
grains size is theoretically predicted (46). A low-impurity
content is mandatory for achieving this optimal grain size,
because precipitates tend to hinder grain growth. In addi-
tion, some particles, such as MnS and AlN, segregating at
grain boundaries, favor the establishment of a detrimental
texture, rich of {111} planes. On the other hand, there are
soluted impurities, such as Sb and Sn, as well as Mn in very
clean steels, that can induce selective growth of those
recrystallized grains that have orientations close to the
ideal random cubic texture {100}h0vwi. A similar texture
can actually be approached, in two-stage reduced alloys, by
increasing the Al concentration up to 1.1 wt% (47) or even
1.8 wt% (48), which permits one to achieve the power loss
gure P
15/50
2 W/kg at 1.5 T and 50 Hz.
The punching operation generates localized residual
strains and, consequently, it might affect the loss gure
in fully processed materials, where, in general, stress relief
annealing is not performed. In large machines, however, an
appreciable increase of the magnetic losses could derive
from the stresses permanently introduced by stacking and
assembling the laminations in the core. The detrimental
role of such stresses, especially when they are compressive
and are applied in the plane of the lamination, is well
documented (49), as illustrated in Figure 18, and it is
empirically accounted for by the machine designers
Table 6. Industrial Nonoriented Fully Processed Electrical Steel
Sheets with Reduced Thickness (Cogent Steels)
Grade Sheet thickness
(mm)
Maximum specic loss at 1.0 T (W/kg)
f=400 Hz f=2.5 kHz
NO27 0.27 15.0 300
NO20 0.20 15.0 215
NO18 0.178 14.3 179
NO12 0.127 13.5 152
NO10 0.10 13.0 135
Figure 16. Power loss at 50 Hz versus average grain size meas-
ured in NO FeSi steel sheets. (1) Two different types of 0.35mm
thick sheets with Si 3 wt% +Al 0.4 wt% (44); (2) 0.50 mm thick
sheet with Si 3 wt% +Al 1 wt% (45).
0 200 400 600 800 1000
0
50
100
150
200
<s> = 55μm
<s> = 190μm
Jp = 1.5 T
Non-oriented Fe-(3.5 wt%)Si
d = 0.343 mm
Energy loss (mJ/kg)
Frequency (Hz)
Figure 17. Energy loss per cycle versus magnetizing frequency in
0.343 mm thick nonoriented fully processed FeSi sheets. With
increasing grain size hsi, the energy loss decreases in the lower
frequency range (up to a few hundred Hz) and increases at higher
frequencies. This behavior highlights the role of the excess loss
component W
exc
, which increases as hsi
1/2
(44).
Soft Magnetic Materials 13
W4504_PUB2 10/31/2016 10:4:49 Page 14
through the introduction of an appropriate building factor
in the estimation of the core loss gure (50).
High-Si, FeAl, and FeAlSi Alloys. Fe(6.5 wt%)Si alloys
are a prospective route to low-loss materials (51). When
compared with the conventional Fe<