~ ~ ELSEVIER
Journalof magnetism and magnetic minrlals
Journal of Magnetism and Magnetic Materials 161 (1996) 203208
Magnetic phase transitions in FeCrBSi alloys I.M. Kyprianidis a,*, C.A. AchiUeos a, I.A. Tsoukalas b, H. Bremers c, j. Hesse c ~' 3rd Laborator3' of Physics, Department of Physics, University of Thessaloniki, Thessaloniki 54006, Greece b Department oflnformatics, University ofThessaloniki, Thessaloniki 54006, Greece lnstitut fur Metallphysik und Nukleare Festkorperphysik, Technische Universitgu, 38106 Braunschweig, Germany Received 6 June 1995; revised 23 November 1995
Abstract We have studied the magnetic phase transitions of some ironrich FeCrSiB alloys in both the amorphous and crystalline states, and have determined the critical exponents 3' *(T), 7c and /3¢. We used a vibrating sample magnetometer for the magnetization measurements, and 57Fe MiSssbauer spectroscopy to characterize the solid state of the alloys. The maximum values of 7 *(T) are higher for the crystalline than for the amorphous state. For the crystalline alloys, a decrease in the maximum Y *(T) values is observed as the Cr concentration is increased, which corresponds to a decrease in the mean hyperfine field at the Fe nuclei.
1. Introduction
is described by the effective FisherKouvel exponent [1]:
In the asymptotic critical regime (T, Tc) of a ferromagnet the temperature dependence of the saturation magnetization ~ ( T ) and the zerofield initial susceptibility x ( T ) are described by the following power laws:
(Tc T)
( T ~ Tc , T < T c, H ~ O ) , (1)
x(T)
~ Tc
( T ~ Tc, T > Tc, H>O). (2)
In the intermediate range, the temperature range between the asymptotic critical regime (T ~ Tc) and the mean field regime (T ~ zc), the temperature dependence of the zerofield initial susceptibility x ( T )
* Corresponding author. Fax: + 3031248639.
y* ( T ) = ( T  T c ) x ( d x  I / d T ) .
(3)
Y * (T) is constructed in such a way that it exhibits the asymptotic value Yc for T  ~ Tc, whereas it approaches the mean field value y = 1 for T* ~. It has been shown [211] that many amorphous ferro and ferrimagnetic alloys may be described within experimental error by the homogeneous threedimensional Heisenberg model. However, the temperature dependence of Y *(T) shows strong differences between homogeneous and disordered ferromagnetic systems in the intermediate range: it is monotonic for homogeneous isotropic ferromagnets, while it is nonmonotonic for disordered ferromagnets with a maximum at reduced temperatures:
t = ( T  Tc ) / T c = 0.1  0 . 5 . This behavior is in agreement with the predictions of the correlated molecular field theory [5,10,11], and with Monte Carlo computer simulations [5,1214].
03048853/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S 0 3 0 4  8 8 5 3 ( 9 6 ) 0 0 0 3 1  5
1.M. Kyprianidis et al. / Journal of Magnetism and Magnetic Materials 161 (1996) 203208
204 160
o Fe77Si9B14
.e. Fe73.6Cr6.SSiS.3B14.,
\\
',D
\
o
40
\
)
\
2
300
400
500
600
700
800
900
1000
11O0
T[Iq Fig. 1. Temperature dependence of the magnetization o for the studied samples at 1 T external magnetic field.
In this paper we study the magnetic phase transitions in some amorphous FeCrSiB alloys with high Fe and low Cr concentrations. These alloys show large differences between the crystallization temperature T~ and the Curie temperature Tc of the amorphous state (Fig. 1), so it is possible to try to verify the modified power law over an extended temperature range. We also study the magnetic phase transitions of the same alloys in the crystalline state in order to establish the differences in critical behavior between the amorphous and crystalline states.
2. Experimental details Amorphous ribbons about 30 /zm thick and 12 mm wide were produced by the meltspinning technique in a pure Ar atmosphere. The amorphous state of the samples was checked by Xray analysis. To measure the isothermal curves ~r(T,H) we used a vibrating sample magnetometer. The samples were investigated in the temperature range T = 3001150 K in applied fields up to 2 T. No changes in the magnetic behavior of the samples could be observed after annealing at temperatures up to 450 K. We applied transmission M~ssbauer spectroscopy on 57Fe nuclei in both the amorphous and crystalline
samples at room temperature. The spectra of the amorphous samples were collected on the asquenched alloys. To obtain the crystalline state we annealed the samples for 1 h at their crystallization t e m p e r a t u r e s , Tcr (see Table 1), observed during the magnetization measurements (see Fig. 1).
as quenched ..,
:il
.
~J annealed
~
.
•
9
.
~..
..
6
v tram/s]
..:
'~
g'
Fig. 2. Examples of transmission 57Fe M~issbauer spectra collected at room temperature for the alloy Fe76SisBi3.sCr2. 5 in the 'asquenched' state, showing a broadened sixline spectrum typical of an amorphous alloy; the annealed state shows distinguishable sharp sixline spectra indicating crystalline phases.
LM. Kyprianidis et al. / Journal of Magnetism and Magnetic Materials 161 (1996) 203208
205
12
Amorphous alloys ~o Fe77Si9B14 / e Fe76Si8B13.5Cr2.5 ~ = Fe75.5Si7.5B13Cr4 F73.6Si5.3B14.6Cr6.5
10
%0 o '~
8.
=
at "r
',
2
'
'
0
0
5
0
......
' \\ ix j
10
15
20
25
222
30
'
\
35
,
40
Hfrl Fig. 3. Hyperfine field probability density distribution function P(H) versus the hyperfine field H for the studied alloys in the amorphous state (see Table 1).
For all alloys in both states the shapes of the M6ssbauer spectra are complex. We therefore applied the method of hyperfine field distributions to evaluate them. As an example, Fig. 2 shows the
Mtissbauer spectra of the alloy Fe76SisB13.sCr2.5 in the amorphous and crystalline states. Fig. 3 and Fig. 4 show sequences of the hyperfine field distributions for the investigated alloys in the amorphous and
18Crystalline alloys o Fe77Si9B14 Fe76Si8B13.SCr2.5 Fe75.5Si7.5B13Cr4 1_o_.Fe73.6Si5.3B14.6Cr6.
16 14 12 10
E 8
0 0
5
10
15
20
25
30
35
40
HI'r]
Fig, 4. Hyperfine field probability density distribution function P(H) versus the hyperfine field H for the studied alloys in the crystalline state (see Table 1).
L M. Kyprianidis et al. / Journal of Magnetism and Magnetic Materials 161 (1996) 203208
206
Table 1 Critical temperatures of the studied samples Samples
Curie temperature, Tc (K)
Fe77Bi4Si 9 Fe76Cr2.5 B 13.5Sis Fe75.sCrnBI3Si7 5 Fe73 6Cr6.5 B 14.6Si5 3 Fe78 BI3Si 9 [15] Fe72 BioSils [16]
Crystallization temperature, T~r (K)
Amorphous state
Crystalline state
745.0 613.09 567.34 430.0 733.0 714.9
820.0 816.0 816.0 822.0
crystalline states, respectively, as evaluated from the roomtemperature MiSssbauer spectra.
975.0 970.1 970.96 1000.0
we get straight parallel lines in the critical regime ( T ~ Tc) (Fig. 5). The inverse zerofield susceptibility X J(T) was
3. Experimental analysis and results 8.0104
In Table 1 we present the critical temperatures obtained for the investigated alloys, and those determined for materials with similar compositions [15,16]. We determined the values of the exponent % and the Curie temperature Tc using the FisherKouvel method, and of /3c from modified Arrott plots. The exponent values for each sample are presented in Table 2. Analytically, we consider the ArrottNoakes equation of state [17]
( I4,/o)
= (7"
,
6.0 10401/6 4.0
104
0.0
100
,
,
,
,,.,
J
,
I
,
Fez~6Cr65B,46Si~ 3crystalline T =1000K . {3 =0.357 ~ Yc= 1.316

L
,
,
,
,
~
,
,
,
995K 998K 1002K
J
. . . .
,
1006 K
. . . .
I
0
'
'
'
'
'
'
'
'
(H i / O') 1/Y
50
' 100
Fig. 5. Modified Arrott plot for isotherms in the critical regime for Fe73.6Cr6.5Bi4.6Sis. 3 in the crystalline state.
+ ( ,,/m)
where H i is the internal field, o is the magnetization, Tc is the Curie temperature, T] and o~ are material constants, and we plot o~/¢ versus (Hi/o) 1/~'. We choose /3 and ,/ in such a way that
1600
I• Fe76Cr2.5Si813.5 B ] 0 Fe75.5Cr45i7.5B13 Fe73.6Cr6.SSi5,3B 146
o
•
0
O
O
1200 O
Table 2 Critical exponents /3c and % of the studied alloys (/3c estimated from modified Arrott plots, and % calculated using the KouvelFisher method) Samples
Fe77Si9B14 Fe36Cr25BI3 5Sis Fe75.5Cr4 B 13Si7.5 Fe73.6Cr6.sB J4.6Si5.3
Amorphous state
Crystalline state
zc
,8c
%
tic
1.38 1.286 1.365
0.398 0.366 0.358
1.322 1.318 1.381 1.316
0.332 0.372 0.369 0.357
0 := 600
[] o o
41.
#/
4,
o
400
o
[] •
[]
O
0
•
• ". oO~ 0
0.04
0.08
0.12
0,16
0.2
(TTca)/Tca
Fig. 6. Temperature dependence of X ~(T) for the amorphous samples.
207
1.M. Kyprianidis et al. / Journal of Magnetism and Magnetic Materials 161 (1996) 203208 4500
1.9
Io Fe77Si9B14 t~FFe76Cr2 5SiBB13 5 III Fe75.5Cr4Si7 5B13 e73.6Cr6.5Si5 3B14.E
4000
0
• •
• ' 2500 • 2000
•
• • •
•
1500 •
=~*
•
• I'e
•
•
~•i,l
0
O
o ooo °
[]
[]
[]
15 ). 14
o• o
o°:o
• %
 : •
•
.oo
•
•O 0
0
*
oo
o°
13 1.2
o °°°°
ooo °
, m* 1 oooO oooO° . e,,,.ql,~ ' o ~ £ o ° ° ° ° ° .
500
O [3
° o•
•
•
•
~.
O
° oo°
•
~
•
0
1.6 •
•
O 0
O
•
}Crystalline al~ys I
•
0
1.7
•11
1000
I •Fe76Cf2"5B13.5Si8 ] [~ Fe75,SCt4SiT.5B13 i Fe73.6C~.58i5.3B 14.6
0
•
3500 3000
O
0
1.8
oo
1.1
•
~'~
0.02
0.04
1 0.06
0.08
0.1
0.05
0.12
0.1
Fig. 7, Temperature dependence of XI(T) for the crystalline
samples.
determined from the intersections of the straight parallel lines with the ( H i / o ' ) 1/~ axis. The X  l ( T ) curves for the amorphous and crystalline alloys are shown in Fig. 6 and Fig. 7, respectively. From Eq. (3) we obtain
X'/[d( x')/dr]
0.15
0.2
= [l/,y *(r)l(r
re).
The quantity X  1/(d( X  l ) / d T ) was calculated from a cubic spline which was fitted to the experimental X i (T) curve. We plotted X l / ( d ( X i ) / d T ) versus T for each sample and we get a straight line in the asymptotic critical regime ( T ~ Tc). The FisherKouvel plot of one of the samples is depicted in Fig. 8. The inverse slope of this line is % and the intersection with the temperature axis yields the Curie temperature Tc [18]. The effective FisherKouvel exponent T * ( T ) was calculated from Eq. (3) using
Fig. 9. Temperaturedependence of the effective exponent 3' *(T) for the amorphous samples.
the value of Tc obtained from the FisherKouvel plot.
4. Discussion Plots of the FisherKouvel exponent y * (T) versus ( T  T c ) / T c are shown in Fig. 9 and Fig. 10 for the amorphous and crystalline states, respectively. The curves show the typical nonmonotonic behavior of disordered ferromagnets. The maximum values of y * (T) are higher for the
2.5 °o o
2.2
o
°o
oo
•
•
•
0
•
o
o
•
o
o o
•
[]DD o
1.9
0
°°°°°°°°°
o
o
o Fo77SigB14 • Fe76Cr2.5SiSB13.5 Fe75.SCr4Si75B13 • Fe73.6Cr6.5Si5.3B14.6
oo
o
o
o
[]
Q°o
o
°1 •
o
o o
60, Fe75.5Cr4Si7.5B13
~
~•4aeemmm
1.6
o
40.
•
• o
m
o
•
o
•o
o o
o
•
o
o o • o~.°"
I= ,7,
[]
o
o
o
Crystalline alloy
~"
0.25
(TTca)/Tca
(TTcc)/Tcc
,
o o °°
o
1.3 [CrystaH me all•us ]
20.
o o 0
0.02
0
970
995
1020
T[K]
1045
1070
Fig. 8. Kouve]Fisher plot for % for Fe755Cr4BI3Si75 in the crystalline state.
0.04
0.06
0.08
0.1
0.12
(TTcc)/Tcc
Fig. 10. Temperaturedependence of the effective exponent y *(T) for the crystalline samples.
208
I.M. Kvprianidis et al. / Journal of Magnetism and Magnetic Materials 161 (1996) 203208
Table 3 Maximum values of the KouvelFisher effective exponent y * (T) of the studied alloys
Acknowledgements
Samples
Amorphous Ymax *
Crystalline Ymax *
FevvSigB~4 Fe76Cr~ 5B135Si 8 Fe75.sCr4BI3SiT.5 Fe73.6Cr6.sB14.6Sis. 3
1.442 1.872 1.481
2.459 2.126 2.018 1.723
The authors wish to thank Associate Professor G. Stergioudis for providing the amorphous materials.
crystalline than the amorphous state of the alloys. For the crystalline samples, the maximum values of y ' ( T ) decrease with increasing Cr concentrations. This is perhaps connected with the decrease of the biggest probability of the mean hyperfine field as the Cr concentration is increased (Fig. 4). The crystalline samples show a maximum mean hyperfine field at 32 T, which is associated with the Fe3Si phase [19]. The probability of the hyperfine field at 32 T decreases as the concentration of Cr is increased. In the Mtissbauer spectrum of the crystalline alloy Fe77SigB14 the mean hyperfine field of 24 T has a higher probability. This may be due to an additional Fe 2B phase [2022]. We think that the state of the alloy does not affect the values of yc and /3c which are close to the Heisenberg values, but it does affect the maximum value of the effective exponent y* (T) (Table 3).
5. Summary We have studied the magnetic phase transitions of some ironrich FeCrSiB alloys in both the amorphous and crystalline states, and have determined the critical exponents 7 * (T), Yc and /3c. The values of Ye and /3e are close to the Heisenberg values for all the alloys studied. The maximum values of y * (T) are affected by the state of the alloy (amorphous or crystalline) and by the crystalline alloy concentrations.
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