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Linear and nonlinear susceptibilities of amorphous Fe10Ni70B19Si1 alloy
Journal of Magnetism and Magnetic Materials 90 & 91 (1990) 343-344 North-Holland
343
Linear and nonlinear susceptibilities of amorphous FelONi70B19Sil alloy S. Chikazawa, H. Arisawa 1, T. Bitoh, T. Kikuchi, N. Hasegawa and S. Taniguchi Department of Applied Materials Science, Muroran Institute of Technology, Muroran 050, Japan
AC linear (Xo) and nonlinear (X2) susceptibilities of FelONi70Bl9Sii have been measured around the Curie temperature J;, with special emphasis on feature of X2' The results yield the following critical exponents: y = 1.32 ± 0.04, Y2 = 4.64± 0.60. These values are consistent with theoretical predictions for 3d Heisenberg systems.
In recent years much attention has been paid to critical phenomena in amorphous ferromagnetic alloys to find out the fundamental nature of disordered systems [1-5J. It has been shown that the values of the asymptotic critical exponents (exponents in the limit to 1;,) in many amorphous ferromagnets are similar to those for crystalline systems. Furthermore, the values of the critical exponents are found to be very close to those predicted for 3d Heisenberg systems [6J. These findings indicate that the Harris criterion (7J is suitable for the disordered systems [1-5J. In contrast with these results, the characteristic temperature dependence of the critical exponents, which is strongly different from those for ordered systems, has been observed in disordered systems outside the critical region [1-5J. Although it has been suggested that these characteristic behaviours are due to the inhomogeneity of the disordered system, these results are less conclusive and further investigations are required. In this paper we report our recent results of experimental investigations on paramagnetic-to-ferromagnetic phase transitions in amorphous magnetic alloys. It should be emphasized that the nonlinear susceptibility X2 represents the critical behaviour more clearly than the linear susceptibility XO [8,9J. Amorphous FelONi70B19Sil ribbons were prepared by the melt-spinning technique in vacuum. The width of the ribbons was about 1.7 mm, the thickness := 30 p rn, X-ray diffraction measurements confirmed the noncrystalline character of the alloy. In the present work as-prepared samples were used. The nonlinear susceptibility X2' as well as the linear susceptibility Xo- was measured with an ac mutual inductance bridge, by detecting third higher harmonic component [IOJ. The measurements were performed in a temperature range from 150 to 250 K and in a frequency (v) range of 10 to 320 Hz using an ac field (h o ) range of 50 to 300 mOe.
1
Present address: Fujitsu Co. Ltd., Kawasaki 211, Japan.
The earth's field along the ac-field was diminished with a Helmholtz coil. In the following we present the experimental results and discussion. First, we give the linear susceptibility Xo- Behaviour of Xo is similar to those reported by many authors [1-5J. Fig. l(a) shows the temperature dependence of Xo.· When temperature decreases from above 1;" Xo rises sharply near 1;" exhibiting a clear Hopkinson peak, and then decreases gradually at lower temperatures. The Curie temperature 1;, was determined from the Kouvel-Fisher plot of Xo(T) data of fig. l(a). Secondly, we mention the properties of the nonlinear susceptibility X2' As shown in fig. l(b), X2 is observed only in the vicinity of 1;,. With decreasing temperature, X2. decreases abruptly near 1;" showing a sharp negative
....... 30
ME ~ ::l
E
..... 0
X
.......
20
10 0 4
ME ~ ::l
E
0 (b)
2
.....
"'0
.s::
X'
0
J V
<'11'03"
-2 160 180 200 220 T(K) Fig. 1. Temperature dependence of (a) the linear susceptibility Xo; (b) the nonlinear susceptibility X2' measured at h o = 150 mOe and at ,,= 80 Hz.
0304-8853/90/$03.50
S. Chikazawa et 01. / A C susceptibilities 0/ amorphous Fe-Ni-B-Si
344
Finally, we discuss the crit ical exponent Y2' The critical exponents for 3d Heisenberg system are given in ref. [61 : Y = 1.387, fJ = 0.365. These values deduce the magnitude of the gap exponent L1( = Y + fJ) = 1.75 (12). Using these values, one can obtain the value of Y2( = Y + 2L1) = 4.89. The present result Y2 = 4.64 ± 0.60 is fairly well consistent with that of 3d Heisenberg system . It must be noted that the result is also in good agreement with the value Yz = 4.54 observed in a pure ferromagnetic CdCrzSe4 [13]. In conclusion, we obtain the critic al exponents y = 1.32 ± 0.04 and Y2 = 4.64 ± 0.60. Both values of exponents suggest that critical behaviour of the amorphous system is identical with that of the ordered ferromagnetic system.
lOt
ME
-.e u
:J
E 0
10° lO-t
X
10-2 ....... 10°
ME
-E 10u
1
:J
Cl1
10-2
~
'" 10-3
~
C")I~
10-4 10-4
103 to-2 to-I tOO
(. Fig. 2. (a) Xo- (b) X2 plotted against the reduced temperature ( (= (T - T,,)/T,,) above T" (= 201.1 K). Straight lines give values for "(and "(2 as 1.32 and 4.58, respectively.
peak just below ~. At lower temperatures X2 changes its sign and shows a positive peak. Xz is very sensitive to the amplitude of the ac magnetic field. Thirdly, we describe how to determine the values of the critical exponent y associated with Xo and of Y2 related to Xz- In fig. 2, we show a plot of the susceptibilities against the reduced temperature £( = T1;,)/1;,) on a double logarithmic scale . The result of fig. 2(a) yields as well defined value of y = 1.32. This value is in good agreement with that obtained by KouvelFisher plot mentioned above . On the contrary, it is difficult to determine the value of Y2 because of the abrupt change of Xl in a narrow temperature range of e, Fig. 2(b) shows a typical example for Xl giving a value of Y: = 4.58. The values of Yz are distributed in a range of 3.8 to 6.2 for all the measurements with various measuring conditions described above . Averaging these values, we obtained the following results : y = 1.32 ± 0.04, Yz = 4.64 ± 0.60. Next, we compare our results of the critic al exponent y with those of other Ierrornagnets and those predicted theoretically for Jd Heisenberg system . The value of y = 1.32 ± 0.04 is very close to that found · in the same component alloys by Kaul [2] and very similar to that of pure Ni [11], and also the predicted value for the 3d Heisenberg system [6].
We would like to thank Professor Y. Hamaguchi for his help in making melt-spinning samples and Dr. S. Nagata for a critical reading of the manuscript. One of the authors (S.c.) is also grateful to Professor Y. Miyako for encouragements during the work . This work was partly supported by a Gr ant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture of Japan .
References (l) S.N. Kaul, J. Magn. Magn. Mat. 53 (1985) 5. (2) S.N. Kaul, A. Hofmann and H. KronmUller, J. Phys. F 6 (1986) 365. (3) W.-U. Kellner, T. Albrecht, M. Fahnle and H. KronmUller, J. Magri. Magn, Mat. 62 (1986) 169. [4] M. Flihnle, J. Magn. Magn . Mat. 65 (1987) 1. [5) M. Haug, M. Fahne, H. KronmUller and F. Habery, J. Magri. Magn. Mat. 69 (1987) 163. [6] J.e. LeGuillou and J. Zinn-Justin, Phys. Rev. B 21 (1980) 3976. [7] A.B. Harris , J. Phys. C 7 (1974) 1671. [8) K. Wada and H. Takayama, Prog. Theor. Phys. 64 (1980) 327. [9) S. Fujiki and S. Katsura, Prog. Theor. Phys. 65 (1981) 1130. [10) S. Chikazawa, Y.G. Yuochunas and Y. Miyako, J. Phys. Soc. Jpn. 49 (1980) 1276. [11) J.S. Kouve1and M.E. Fisher, Phys. Rev. 136 (1964) A1626. [12) H.E. Stanley, Introduction to Phase Transition and Critical Phenomena (Clarendon Press, Oxford, 1971) p. 49. [13) B. Fugiel, J. Ziolo and A. Chelkowski, Solid State Commun. 40 (1981) 733.
343
Linear and nonlinear susceptibilities of amorphous FelONi70B19Sil alloy S. Chikazawa, H. Arisawa 1, T. Bitoh, T. Kikuchi, N. Hasegawa and S. Taniguchi Department of Applied Materials Science, Muroran Institute of Technology, Muroran 050, Japan
AC linear (Xo) and nonlinear (X2) susceptibilities of FelONi70Bl9Sii have been measured around the Curie temperature J;, with special emphasis on feature of X2' The results yield the following critical exponents: y = 1.32 ± 0.04, Y2 = 4.64± 0.60. These values are consistent with theoretical predictions for 3d Heisenberg systems.
In recent years much attention has been paid to critical phenomena in amorphous ferromagnetic alloys to find out the fundamental nature of disordered systems [1-5J. It has been shown that the values of the asymptotic critical exponents (exponents in the limit to 1;,) in many amorphous ferromagnets are similar to those for crystalline systems. Furthermore, the values of the critical exponents are found to be very close to those predicted for 3d Heisenberg systems [6J. These findings indicate that the Harris criterion (7J is suitable for the disordered systems [1-5J. In contrast with these results, the characteristic temperature dependence of the critical exponents, which is strongly different from those for ordered systems, has been observed in disordered systems outside the critical region [1-5J. Although it has been suggested that these characteristic behaviours are due to the inhomogeneity of the disordered system, these results are less conclusive and further investigations are required. In this paper we report our recent results of experimental investigations on paramagnetic-to-ferromagnetic phase transitions in amorphous magnetic alloys. It should be emphasized that the nonlinear susceptibility X2 represents the critical behaviour more clearly than the linear susceptibility XO [8,9J. Amorphous FelONi70B19Sil ribbons were prepared by the melt-spinning technique in vacuum. The width of the ribbons was about 1.7 mm, the thickness := 30 p rn, X-ray diffraction measurements confirmed the noncrystalline character of the alloy. In the present work as-prepared samples were used. The nonlinear susceptibility X2' as well as the linear susceptibility Xo- was measured with an ac mutual inductance bridge, by detecting third higher harmonic component [IOJ. The measurements were performed in a temperature range from 150 to 250 K and in a frequency (v) range of 10 to 320 Hz using an ac field (h o ) range of 50 to 300 mOe.
1
Present address: Fujitsu Co. Ltd., Kawasaki 211, Japan.
The earth's field along the ac-field was diminished with a Helmholtz coil. In the following we present the experimental results and discussion. First, we give the linear susceptibility Xo- Behaviour of Xo is similar to those reported by many authors [1-5J. Fig. l(a) shows the temperature dependence of Xo.· When temperature decreases from above 1;" Xo rises sharply near 1;" exhibiting a clear Hopkinson peak, and then decreases gradually at lower temperatures. The Curie temperature 1;, was determined from the Kouvel-Fisher plot of Xo(T) data of fig. l(a). Secondly, we mention the properties of the nonlinear susceptibility X2' As shown in fig. l(b), X2 is observed only in the vicinity of 1;,. With decreasing temperature, X2. decreases abruptly near 1;" showing a sharp negative
....... 30
ME ~ ::l
E
..... 0
X
.......
20
10 0 4
ME ~ ::l
E
0 (b)
2
.....
"'0
.s::
X'
0
J V
<'11'03"
-2 160 180 200 220 T(K) Fig. 1. Temperature dependence of (a) the linear susceptibility Xo; (b) the nonlinear susceptibility X2' measured at h o = 150 mOe and at ,,= 80 Hz.
0304-8853/90/$03.50
S. Chikazawa et 01. / A C susceptibilities 0/ amorphous Fe-Ni-B-Si
344
Finally, we discuss the crit ical exponent Y2' The critical exponents for 3d Heisenberg system are given in ref. [61 : Y = 1.387, fJ = 0.365. These values deduce the magnitude of the gap exponent L1( = Y + fJ) = 1.75 (12). Using these values, one can obtain the value of Y2( = Y + 2L1) = 4.89. The present result Y2 = 4.64 ± 0.60 is fairly well consistent with that of 3d Heisenberg system . It must be noted that the result is also in good agreement with the value Yz = 4.54 observed in a pure ferromagnetic CdCrzSe4 [13]. In conclusion, we obtain the critic al exponents y = 1.32 ± 0.04 and Y2 = 4.64 ± 0.60. Both values of exponents suggest that critical behaviour of the amorphous system is identical with that of the ordered ferromagnetic system.
lOt
ME
-.e u
:J
E 0
10° lO-t
X
10-2 ....... 10°
ME
-E 10u
1
:J
Cl1
10-2
~
'" 10-3
~
C")I~
10-4 10-4
103 to-2 to-I tOO
(. Fig. 2. (a) Xo- (b) X2 plotted against the reduced temperature ( (= (T - T,,)/T,,) above T" (= 201.1 K). Straight lines give values for "(and "(2 as 1.32 and 4.58, respectively.
peak just below ~. At lower temperatures X2 changes its sign and shows a positive peak. Xz is very sensitive to the amplitude of the ac magnetic field. Thirdly, we describe how to determine the values of the critical exponent y associated with Xo and of Y2 related to Xz- In fig. 2, we show a plot of the susceptibilities against the reduced temperature £( = T1;,)/1;,) on a double logarithmic scale . The result of fig. 2(a) yields as well defined value of y = 1.32. This value is in good agreement with that obtained by KouvelFisher plot mentioned above . On the contrary, it is difficult to determine the value of Y2 because of the abrupt change of Xl in a narrow temperature range of e, Fig. 2(b) shows a typical example for Xl giving a value of Y: = 4.58. The values of Yz are distributed in a range of 3.8 to 6.2 for all the measurements with various measuring conditions described above . Averaging these values, we obtained the following results : y = 1.32 ± 0.04, Yz = 4.64 ± 0.60. Next, we compare our results of the critic al exponent y with those of other Ierrornagnets and those predicted theoretically for Jd Heisenberg system . The value of y = 1.32 ± 0.04 is very close to that found · in the same component alloys by Kaul [2] and very similar to that of pure Ni [11], and also the predicted value for the 3d Heisenberg system [6].
We would like to thank Professor Y. Hamaguchi for his help in making melt-spinning samples and Dr. S. Nagata for a critical reading of the manuscript. One of the authors (S.c.) is also grateful to Professor Y. Miyako for encouragements during the work . This work was partly supported by a Gr ant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture of Japan .
References (l) S.N. Kaul, J. Magn. Magn. Mat. 53 (1985) 5. (2) S.N. Kaul, A. Hofmann and H. KronmUller, J. Phys. F 6 (1986) 365. (3) W.-U. Kellner, T. Albrecht, M. Fahnle and H. KronmUller, J. Magri. Magn, Mat. 62 (1986) 169. [4] M. Flihnle, J. Magn. Magn . Mat. 65 (1987) 1. [5) M. Haug, M. Fahne, H. KronmUller and F. Habery, J. Magri. Magn. Mat. 69 (1987) 163. [6] J.e. LeGuillou and J. Zinn-Justin, Phys. Rev. B 21 (1980) 3976. [7] A.B. Harris , J. Phys. C 7 (1974) 1671. [8) K. Wada and H. Takayama, Prog. Theor. Phys. 64 (1980) 327. [9) S. Fujiki and S. Katsura, Prog. Theor. Phys. 65 (1981) 1130. [10) S. Chikazawa, Y.G. Yuochunas and Y. Miyako, J. Phys. Soc. Jpn. 49 (1980) 1276. [11) J.S. Kouve1and M.E. Fisher, Phys. Rev. 136 (1964) A1626. [12) H.E. Stanley, Introduction to Phase Transition and Critical Phenomena (Clarendon Press, Oxford, 1971) p. 49. [13) B. Fugiel, J. Ziolo and A. Chelkowski, Solid State Commun. 40 (1981) 733.