K. GRUSZKA: ANALYSIS OF THE STRUCTURAL-DEFECT INFLUENCE ON THE MAGNETIZATION PROCESS ...
707–718
ANALYSIS OF THE STRUCTURAL-DEFECT INFLUENCE ON THE
MAGNETIZATION PROCESS IN AND ABOVE THE RAYLEIGH
REGION
ANALIZA VPLIVA STRUKTURNIH DEFEKTOV NA PROCES
MAGNETIZACIJE V IN NAD RAYLEIGH PODRO^JEM
Konrad Gruszka
Czestochowa University of Technology, Faculty of Production Engineering and Materials Technology, Institute of Physics,
Armii Krajowej Av. 19, 42-200 Czestochowa, Poland
kgruszka@wip.pcz.pl
Prejem rokopisa – received: 2015-06-30; sprejem za objavo – accepted for publication: 2015-09-16
doi:10.17222/mit.2015.154
The paper presents studies of the structural-defect influence on the magnetization process in low magnetic fields (H < 0.4 Hc)
and above the Rayleigh range. The investigated Fe62Co10Y8B20 alloy samples were obtained with the injection casting method
resulting in the amorphous-structure state, which was confirmed with XRD. The studies were conducted by analyzing the
disaccommodation of the magnetic-susceptibility process and using Kronmüller’s theory in the approach to the ferromagnetic
saturation area. On the basis of the obtained results, it was found that the main factor responsible for the processes of
magnetization in low magnetic fields are point defects, whereas in the case of high magnetic fields, the magnetization process
depends mainly on second-type pseudo-dislocation dipoles.
Keywords: metallic glasses, defects, disaccommodation, Kronmüller’s theory
^lanek predstavlja {tudij vpliva strukturnih defektov na proces magnetizacije v {ibkem magnetnem polju (H < 0,4 Hc) in nad
Rayleigh podro~jem. Vzorci preiskovane zlitine Fe62Co10Y8B20 so bili izdelani z metodo injekcijskega brizganja, kar je
povzro~ilo amorfno strukturo, ki je bila potrjena z rentgensko analizo (XRD). [tudije so bile izvedene z analizo procesa
neustreznosti magnetne ob~utljivosti in z uporabo Kronmülerjeve teorije pri pribli`evanju feromagnetno nasi~enemu podro~ju.
Na osnovi dobljenih rezultatov je bilo ugotovljeno, da so pri procesu magnetizacije glavni faktor to~kaste napake, medtem ko je
v primeru magnetizacije v mo~nem magnetnem polju proces odvisen predvsem od druge vrste psevdodislociranih dipolov.
Klju~ne besede: kovinska stekla, napake, neustreznost, Kronmüllerjeva teorija
1 INTRODUCTION
Iron-based amorphous materials are extensively stu-
died because of their excellent soft-magnetic proper-
ties.1–3 For this reason, they have been widely used in the
electrical industry, primarily as high-efficiency cores for
power transformers and chokes and also as coatings due
to their high corrosion resistance.4,5
In terms of topological structure, amorphous mate-
rials have properties similar to those of liquids. The
atoms forming the material are scattered in a chaotic
manner so that the observation of the long-range order is
not possible. When the cooling rate of a liquefied alloy is
sufficiently large, the kinetic energy of the atoms is taken
so fast that they are trapped at higher energy positions.
This results in the density and local chemical-compo-
sition fluctuations, and is the major cause of the areas
with a deficiency of atoms. This type of local voids are
called point defects (by analogy with the vacancies
occurring in a crystal structure). In the cases where
several point defects are located in a small local envi-
ronment, a concentration to two-dimensional defects
occurs and it is referred to as pseudo-dislocation dipoles.
Point defects and their conglomerates have a signifi-
cant impact on the process of magnetization in high
magnetic fields.6,7 The presence of structural defects,
which are the centers of internal stresses, causes a defor-
mation of local magnetization vectors. The presence of
structural defects in amorphous materials affects the
magnetization process in the area called the approach to
ferromagnetic saturation.8 In close proximity to a point
defect, the magnetization vectors are arranged in a
"streamline" way9,10 which is a potential cause of do-
main-wall anchors. A more complicated situation occurs
in the presence of a pseudo-dislocation dipole, where the
arrangement of individual vectors is not collinear and the
centers of the deformation of these vectors are hooked at
the dipole ends.11–13
Ferromagnetic materials, especially the ones based
on the Fe-Co-B composition are well known for their
great soft-magnetic properties, in particular a low coer-
cive field and magnetostriction while they are not expen-
sive and have a high sensitivity to alloying additives. In
the compounds of this type, iron is typically the major
part (more than a 50 % amount fraction) while Co,
which has similar properties, allows an increase in the
magnetization. Boron, due to a significant difference in
the atomic radius, improves the glass-forming ability
(GFA). In order to further increase the GFA, a small
Materiali in tehnologije / Materials and technology 50 (2016) 5, 707–718 707
UDK 620.1:67.017:621.318 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 50(5)707(2016)
amount of yttrium atoms are introduced. According to
the literature, a concentration of up to a 4 % amount
fraction has a positive effect on the GFA but exceeding
this value brakes down good soft-magnetic properties.
Using the studies on susceptibility-disaccommodation
phenomena and approach to the ferromagnetic saturation
area, it is possible to indirectly describe the structural
defects existing in a material. This paper focuses on
defects – the relations within a magnetization process
and shows that despite an yttrium addition of up to 8 %,
one can obtain reasonable results in terms of soft-mag-
netic parameters.
2 STUDIED MATERIAL AND METHODOLOGY
The investigated material comprises chemical ele-
ments of high purity (Fe – a 99.95 % amount fraction,
the remaining component elements – 99.99 % amount
fractions). A two-step preparation procedure was used.
Initially, the ingredients were melted using a plasma arc
(a working current of ~300 A) under a reduced pressure
in a protective atmosphere of argon. The samples were
melted several times to ensure a good homogeneity of
the constituent distribution. Then the resulting ingot was
melted, using an induction furnace, in a quartz tube and
injected into a copper water-cooled mold, which was also
under an argon atmosphere (at a pressure of 700 hPa). In
the radial cooling process, good-quality amorphous solid
samples with dimensions of 15 mm × 10 mm × 0.5 mm
were obtained. The structure of the obtained samples was
examined using an X-ray diffractometer (Bruker D8
Advance, Cu-K). The magnetic properties were deter-
mined with an analysis of the static hysteresis loop and
the initial magnetization curve, which were obtained
from the measurements of the magnetization as a func-
tion of the magnetic-field strength using a vibrating
sample magnetometer (model Lakeschore 7301). Measu-
rements of the initial permeability of the samples were
taken over a wide temperature range of 300–650 K. The
samples were suspended in a permalloy frame and
placed in a quartz vacuum tube with a thermocouple, and
the whole system was placed in an accumulative furnace.
The disaccommodation-aftereffect intensity defined as
Δ
1 1 1
1 0x t t
⎛
⎝
⎜ ⎞
⎠
⎟ = −
 ( ) ( )
was measured in time (t1 – t0) = 118 s
with the transformer method. The frequency of the ac
field was set to 50 Hz. The samples were demagnetized
by applying a sinusoidal decreasing magnetic field of
120 kHz.
3 RESULTS
Figure 1 shows the XRD of a sample after the solidi-
fication, measured for the 2 angle in a range from 30°
to 100°.
The diffraction pattern shows only the broad fuzzy
maximum, located in a 2 angle range from approxima-
tely 35° to 50°. This means that in a sample in the
as-quenched state, there is no long-range order and the
interactions between the atoms have a close- or me-
dium-range character. Such a shape of a diffraction
pattern is typical for the materials with an amorphous
structure. Then measurements of the static magnetic
hysteresis loop were carried out and the result is shown
in Figure 2.
The observed shape of the curve is characteristic for a
magnetic material with soft magnetic properties. Based
on the analysis of the static magnetic hysteresis loop, the
basic parameters for the magnetic sample were deter-
mined: magnetization saturation Ms = 1.27 (T), coercive
field Hc = 289 (A/m). Next, an analysis of the primary
magnetization curve in the approach to the ferromagnetic
saturation area was carried out. Figures 3 and 4 show
magnetization curves as a function of (μ0H)–2 and
(μ0H)1/2.
With respect to Kronmüller’s theory, as a result of the
analysis of the primary magnetization curve, it was
found that in a Fe62Co10Y8B20 alloy sample the magne-
tization process in the area called "Ewing’s knee" relates
to the change in magnetization vector directions caused
by the presence of free-volume conglomerates. The
linear-defect size (Ddip) must therefore be larger than the
exchange distance. Assuming that Ddip > lH, the a2/(μ0H)2
law of approach to the ferromagnetic saturation area is
K. GRUSZKA: ANALYSIS OF THE STRUCTURAL-DEFECT INFLUENCE ON THE MAGNETIZATION PROCESS ...
708 Materiali in tehnologije / Materials and technology 50 (2016) 5, 707–718
Figure 2: Static magnetic hysteresis loop for the Fe62Co10Y8B20 alloy
Slika 2: Stati~na magnetna histerezna zanka zlitine Fe62Co10Y8B20
Figure 1: X-ray diffraction pattern of Fe62Co10Y8B20 in the
as-quenched state
Slika 1: Rentgenska difrakcija Fe62Co10Y8B20 v kaljenem stanju
fulfilled. Thus, these defects are the main source of stress
in the magnetic-field strength from 0.084 (T) to 0.25 (T).
Above the (μ0H)–2 dependence, Holstein-Primakoff’s
process intensifies, indicating that the further process of
magnetization is associated with the damping of ther-
mally excited spin waves with an external magnetic field
(the b coefficient). The parameters obtained from the
analysis of the primary magnetization curve are summar-
ized in Table 1.
Table 1: Parameters obtained with the analysis of the primary mag-
netization curve
Tabela 1: Parametri, dobljeni z analizo primarne krivulje magnetiza-
cije
a2
(10–2 T2)
b
(10–2 T1/2)
Dsp
(10–2 meV nm2)
Aex
(10–12 J m–1)
lh
(nm)
0.056 6.59 40.70 1.64 3.59
The absence of the a1/2 and a1 factors indicate that the
point defects and linear defects of a smaller size had no
effect on the magnetization process in magnetic fields
greater than 0.4 Hc (above the Rayleigh region). This
does not mean, however, that those defects are not pre-
sent in the sample’s structure but only that they are insig-
nificant for the magnetization process. To investigate
their potential impact on the magnetization at low fields,
the susceptibility disaccommodation studies were con-
ducted. According to Kronmüller’s theory, it is possible
to calculate the exchange distance of pseudo-dislocation
dipoles (the lh parameter) and the exchange-constant
(Aex) parameter. The latter is responsible for transferring
magnetic interactions between the nearest neighbors (the
energy of aligned spins) and the former describes the
size of a defect’s influence zone. The Dsp parameter,
which describes the spin-wave stiffness (and, therefore,
the ability to transfer the spin torque) is more than
twelve times higher (Dsp/DFe = 12.96) than with pure Fe
(the largest percentage share in the alloy), which is found
to be between DFe = 2.8 meV nm2 at 4.2 K14 and DFe =
3.14 meV nm2 at room temperature.15 This parameter is
connected with the atomic packing density (a higher Dsp
means a higher surface density16) and it may indicate that
linear defects should rather be considered as swellings of
voids resulting in an increase in the local density around
the defects, while keeping the overall material density
low.
The thermal stability of the initial magnetic suscep-
tibility was also investigated. This parameter is very
important and often determines possible applications.
For the studied sample, the shape of the dependency is
shown in Figure 5.
Quite minor temperature-related changes in the value
of the initial magnetic susceptibility were observed. A
good stability and an almost linear growth may indicate
that, in magnetic terms, the material is homogeneous and
no other magnetic phases were formed (in accordance to
K. GRUSZKA: ANALYSIS OF THE STRUCTURAL-DEFECT INFLUENCE ON THE MAGNETIZATION PROCESS ...
Materiali in tehnologije / Materials and technology 50 (2016) 5, 707–718 709
Figure 5: Dependence of the low-field magnetic susceptibility as a
function of temperature for the Fe62Co10Y8B20 sample
Slika 5: Odvisnost magnetne ob~utljivosti v {ibkem polju od tempera-
ture vzorca Fe62Co10Y8B20
Figure 3: Magnetization as a function of (μ0H)–2 for the
Fe62Co10Y8B20 alloy
Slika 3: Magnetizacija kot funkcija (μ0H)–2 zlitine Fe62Co10Y8B20
Figure 4: Magnetization as a function of (μ0H)1/2 for the
Fe62Co10Y8B20 alloy. Holstein-Primakoff process
Slika 4: Magnetizacija kot funkcija (μ0H)1/2 zlitine Fe62Co10Y8B20.
Proces Holstein-Primakoff
the XRD). Considering the rather low temperatures
region, the conspicuous increase between 325 K and 400 K
can be elucidated mainly with the sample’s internal-
tension relaxation processes, together with a minor con-
tribution of the magnetic-anisotropy reduction. The sharp
decline observed near 600 K is associated with the
paramagnetic transition when the ferromagnetic order is
destroyed.
The time dependence of the initial susceptibility after
the demagnetization at various temperatures, or the
magnetic-susceptibility disaccommodation curve for the
investigated alloy, is presented in Figure 6.
As can be seen in Figure 6, the disaccommodation
intensity linearly rises up to the broad maximum located
at about 542 K. Above 542 K, the intensity decreases,
which is directly connected with the decrease in the
amount of the atom pairs reorienting in the point-defect
vicinity. A pair reorientation can occur in two cases: the
first one is associated with a reversible process, in which,
through energy delivery, atom pairs near the point
defects can swap their positions and return to the initial
state after the energy reduction, and in the second one,
this displacement is permanent due to the major changes
in the local space involving a minimum of three atoms.
Both processes can occur in the same time and the curve
observed in Figure 6 indicates the effect of the impo-
sition of these two phenomena. The visible kink in the
same temperature region as in the case of the stability of
the initial-susceptibility curve (Figure 5) is presumably
also caused by the relaxation processes. This phenome-
non must therefore at least partially occur through the
irreversible atomic-pair reorientation, clearly manifested
between 325 K and 400 K (Figure 6). As the relaxation
process of the material has to occur through the displace-
ment of atoms into positions that lead to a lower total
energy of the system, a part of these movements must
therefore lead to the reorientation of atomic pairs visible
as disaccommodation phenomena. Next, a numerical
analysis of the disaccommodation curve was done (Fig-
ure 7).
The isochronal magnetic-susceptibility disaccommo-
dation curve was numerically analyzed using the depen-
dence given with Equation (1):
Δ
1
3
3
1
1
x
I T
T
e
i
i
mi
i
l
pi pi
t
⎛
⎝
⎜ ⎞
⎠
⎟ = ⋅
⋅
−=
−
∫∑  

  



e
t
e
z
z
mi
z
ie e z−
⎛
⎝
⎜
⎞
⎠
⎟
− −
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟
2
2
   d
(1)
where the mean relaxation time mi is given:
 mi
mi
pi
Q
k T T
= − −
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟exp
1 1
 – the pre-exponential factor in the Arrhenius law, Ipi –
the intensity of the ith process at temperature Tpi, Qmi –
the mean activation energy,  – the distribution width
and z mi= ln /  .
The results of the analysis of the disaccommodation
curve in function of temperature, based on the above
formula done using the least squares method is presented
in Table 2.
Table 2: Results obtained from the numerical analysis of dis-
accommodation curve
Tabela 2: Rezultati, dobljeni iz numeri~ne analize neustrezne krivulje
a 1.095*10–7  (s)
b –2.230*10–5
Tp (K) 433.20 2.62×10-15
Ip 5.223*10–6
Q (eV) 1.378
 6.9368
Tp (K) 479.17 2.98×10-15
Ip 3.215*10–5
Q (eV) 1.5189
 5.0638
Tp (K) 542.87 5.26×10-15
Ip 2.52*10–5
Q (eV) 1.6942
 3.7668
The isochronal magnetic-susceptibility disaccommo-
dation curve was decomposed into three elementary
K. GRUSZKA: ANALYSIS OF THE STRUCTURAL-DEFECT INFLUENCE ON THE MAGNETIZATION PROCESS ...
710 Materiali in tehnologije / Materials and technology 50 (2016) 5, 707–718
Figure 7: Theoretical magnetic-susceptibility disaccommodation
curve (solid line) and experimental data for the Fe62Co10Y8B20 alloy
after solidification
Slika 7: Teoreti~na krivulja neprimerne magnetne ob~utljivosti (polna
linija) in eksperimentalni podatki za zlitino Fe62Co10Y8B20 po strje-
vanju
Figure 6: Magnetic-susceptibility disaccommodation curve for the
Fe62Co10Y8B20 alloy after solidification
Slika 6: Neprimerna krivulja magnetne ob~utljivosti zlitine
Fe62Co10Y8B20 po strjevanju
processes (peaks). The first peak with the maximum
localized at 433 K has the lowest activation energy (Q),
the highest width () and the highest intensity (Ip). Most
of the elementary-pair-reconfiguration processes there-
fore require a minimum activation energy of 1.38 eV. An
analysis of Table 2 reveals that the peak maximum
temperature (Tp) increases together with the activation
energy and relaxation time . At the same time, the
distribution width and process intensity decrease. This
phenomena is probably related with the atomic mass
(and also the radius) of the ingredients. Thus, atom pairs
with a higher mass or a bigger size require more energy
and time for the relaxation to occur. On this basis, it can
be concluded that the first elementary process is mostly
caused by boron (a radius of 82 pm, a weight of 10.8 u),
the second process mainly involves Fe (r. 126 pm, w.
55.9 u) and Co (r. 125 pm, w. 58.7 u) and the last pro-
cess, which requires the largest activation energy, is
caused due to an increasing involvement of yttrium (r.
180 pm, w. 88.9 u) atoms. Obviously, due to the smallest
size and weight of B, this element probably has the
largest share in each of the elementary processes, but it
should be noted that the pair reorientation involving
atoms with extreme size differences, tends to be
irreversible.
4 CONCLUSIONS
In the radial cooling process, a good-quality bulk
amorphous sample of the Fe62Co10Y8B20 composition was
prepared. Studies of its magnetic properties showed that
despite a notably large yttrium share, it is possible to
make the material to be rather soft (Hc = 289 A/m).
Susceptibility studies showed that in terms of magnetic
properties, the material is homogeneous. Simultaneously,
magnetic-susceptibility disaccommodation studies clear-
ly revealed a presence of point defects, which are res-
ponsible for the magnetization process in the Rayleigh
area. Therefore, point defects must also be distributed
uniformly across the entire volume of the material. The
decomposition of the susceptibility disaccommodation
curve in three elementary processes was sufficient to
completely describe the pair reorientation, showing the
dependence of the activation energy, intensity and rela-
xation time on the mass (and radius) of the elements
involved in the reorientation process. At H > 0.4 Hc, in
the approach to the ferromagnetic saturation area, the
initial-magnetization-curve analysis, with respect to
Kronmüller’s theory, led to the conclusion that in the
magnetization process, linear defects of the second type
play the main role.
A detailed analysis of the parameters obtained on the
basis of this theory showed that the defects of this type
can be considered as swellings of voids, leading to an
increase in the local density around them. On the other
hand, as it is known, long-term annealing below the
crystallization temperature leads to a decrease in dis-
accommodation phenomena17 associated with the stress
relaxation (due to the atom expansion) and defect diffu-
sion to the sample’s surface. There are no indications
that the linear defects are not subjected to the same
processes, leading to their decomposition into smaller
point defects. At the same time, no increase in the
intensity of disaccommodation phenomena is observed
(directly related to the amount of point defects). This
may suggest that the linear conglomerates of defects
disappear because of collapse-like processes and not due
to shredding. This is consistent with the conclusion
about an increase in the structural stresses around the
linear defects, pushing to fill the voids and, therefore,
reduce the system energy. Considering that the range of
the exchange interaction is smaller than the average size
of a linear defect, the stress relaxation due to the anneal-
ing process should lead to a reduction in the number of
defects, observed as a decrease in the Dsp parameter.
5 REFERENCES
1 M. G. Nabia³ek, P. Pietrusiewicz, M. J. Dospia³, M. Szota, K. B³och,
K. Gruszka, K. OŸga, S. Garus, Effect of manufacturing method on
the magnetic properties and formation of structural defects in
Fe61Co10Y8Zr1B20 amorphous alloy, Journal of Alloys and
Compounds, 615 (2014) S1, 51–55, doi:10.1016/j.jallcom.2013.
12.163
2 K. B³och, M. Nabia³ek, P. Pietrusiewicz, J. Gondro, M. Doœpia³, M.
Szota, K. Gruszka, Time and Thermal Stability of Magnetic
Properties in Fe61Co10Y8Nb1B20 Bulk Amorphous Alloys, Acta
Physica Polonica A, 126 (2014) 1, 108–109, doi:10.12693/
APhysPolA.126.108
3 K. B³och, Structure and magnetic properties of bulk amorphous
(Fe0.61Co0.10Zr0.025Hf0.025 W0.02Ti0.02B0.20)94Y6 alloy, Archives of
Materials Science and Engineering, 64 (2013) 2, 97–102
4 W. J. Botta, J. E. Berger, C. S. Kiminami, V. Roche, R. P. Nogueira,
C. Bolfarini, Corrosion resistance of Fe-based amorphous alloys,
Journal of Alloys and Compounds, 586 (2014) 1, 105–110,
doi:10.1016/j.jallcom.2012.12.130
5 Y. Han, C. T. Chang, S. L. Zhu, A. Inoue, D. V. Louzguine-Luzgin,
E. Shalaan, F. Al-Marzouki, Fe-based soft magnetic amorphous
alloys with high saturation magnetization above 1.5 T and high
corrosion resistance, Intermetallics, 54 (2014), 169–175,
doi:10.1016/j.intermet.2014.06.006
6 P. Pietrusiewicz, M. Nabia³ek, M. Szota, M. Doœpia³, K. Gruszka, In-
fluence of Low Temperature Annealing on the Magnetic and
Structural Properties of Fe61Co10Y8W1B20 Alloy, Acta Physica Polo-
nica A, 126 (2014) 1, 110–111, doi:10.12693/APhysPolA.126.110
7 K. Sobczyk, J. Œwierczek, J. Gondro, J. Zbroszczyk, W. Ciurzyñska,
J. Olszewski, P. Br¹giel, A. £ukiewska, J. Rz¹cki, M. Nabia³ek, Mi-
crostructure and some magnetic properties of bulk amorphous
(Fe0.61Co0.10Zr0.025Hf0.025Ti0.02W0.02B0.20)100-xYx (x = 0, 2, 3 or 4) alloys,
Journal of Magnetism and Magnetic Materials, 324 (2012), 540–549,
doi:10.1016/j.jmmm.2011.08.038
8 H. Kronmüller, Theory of magnetic after-effects in ferromagnetic
amorphous alloys, Philosophical Magazine B: Physics of Condensed
Matter, 48 (1983) 2, 127–150, doi:10.1080/13642818308226466
9 H. Kronmüller, Micromagnetism and microstructure of amorphous
alloys, Journal of Applied Physics, 52 (1981), 1859–1864,
doi:10.1063/1.329552
10 M. Hirscher, R. Reisser, R. Würschum, H. E. Schaefer, H. Kron-
müller, Magnetic after-effect and approach to ferromagnetic satura-
tion in nanocrystalline iron, Journal of Magnetism and Magnetic
Materials, 146 (1995), 117–122, doi:10.1016/0304-8853(94)01643-7
K. GRUSZKA: ANALYSIS OF THE STRUCTURAL-DEFECT INFLUENCE ON THE MAGNETIZATION PROCESS ...
Materiali in tehnologije / Materials and technology 50 (2016) 5, 707–718 711
11 H. Kronmüller, Micromagnetism in Amorphous Alloys, IEEE Tran-
sactions on Magnetics, 15 (1979) 5, 1218–1225, doi:10.1109/
TMAG.1979.1060343
12 N. Lenge, H. Kronmüller, Low temperature magnetization of
sputtered amorphous Fe-Ni-B films, Physica Status Solidi A, 95
(1986), 621–633, doi:10.1002/pssa.2210950232
13 D. Goll, Handbook of Magnetism and Advanced Magnetic Materials
2, J. Wiley & Sons, 2007, doi: 10.1002/9780470022184.hmm203
14 M. Pajda, J. Kudrnovsky, I. Turek, V. Drchal, P. Bruno, Ab initio
calculations of exchange interactions, spin-wave stiffness constants,
and Curie temperatures of Fe, Co, and Ni, Physical Review B, 64
(2001) 17, 174402: 1–9, doi:10.1103/PhysRevB.64.174402
15 R. B. Muniz, J. d’Albuquerque e Castro, E. da Silva, Spin wave
stiffness constant of iron, Journal de Physique Colloques, 49 (1988)
C8, 89–90, doi:10.1051/jphyscol:1988831
16 M. Nabia³ek, P. Pietrusiewicz, M. Doœpia³, M. Szota, J. Gondro, K.
Gruszka, A. Dobrzañska-Danikiewicz, S. Walters, A. J. Bukowska,
Influence of the cooling speed on the soft magnetic and mechanical
properties of Fe61Co10Y8W1B20 amorphous alloy, Alloys and Com-
pounds, 615 (2015), 56–60, doi:10.1016/j.jallcom.2013.12.236
17 M. Hasiak, W. H Ciurzyñska, Y. Yamashiro, Microstructure and
some magnetic properties of amorphous and nanocrystalline
Fe–Cu–Nb–Si–B alloys, Materials Science and Engineering A, 293
(2000) 1–2, 261–266, doi:10.1016/S0921-5093(00)01030-3
K. GRUSZKA: ANALYSIS OF THE STRUCTURAL-DEFECT INFLUENCE ON THE MAGNETIZATION PROCESS ...
712 Materiali in tehnologije / Materials and technology 50 (2016) 5, 707–718