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Temperature dependence of Landau coefficients in Lu(Co1−xGax)2
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 272–276 (2004) 505–506
Temperature dependence of Landau coefficients in LuðCo1xGax Þ2 F. Ishikawaa,*, T. Gotoa, K. Fukamichib, H. Yamadac b
a Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan Department of Material Science, Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan c Faculty of Science, Shinshu University, Matsumoto 390-8621, Japan
Abstract High-field magnetization was measured for typical itinerant-electron metamagnets LuðCo1x Gax Þ2 with x ¼ 0:06 and 0.07 at temperatures from 4.2 to 300 K in pulsed magnetic fields up to 45 T: Landau coefficients AðTÞ; BðTÞ and CðTÞ were determined by fitting measured M–H curves to the equation, H ¼ AðTÞM þ BðTÞM 3 þ CðTÞM 5 : The temperature dependence of the Landau coefficients was well explained by the theory of the metamagnetic transition considering the magnetovolume effect. r 2003 Elsevier B.V. All rights reserved. PACS: 75.30.Kz; 75.50.y; 75.60.Ej Keywords: Itinerant-electron metamagnetism; Metamagnetic transition; LuðCo1x Gax Þ2
The Laves phase intermetallic compounds YCo2 and LuCo2 are recognized as typical itinerant-electron metamagnets. Itinerant-electron metamagnetism occurs in both compounds from the enhanced Pauli paramagnetic to the ferromagnetic state by applying magnetic fields. The metamagnetic transition field was confirmed to be 69 T for YCo2 and 74 T for LuCo2 [1]. The occurrence of the transition has close relationships with the shape of the density of states, in which a sharp peak exists just below the Fermi level [2]. In such case, a broad maximum appears in the temperature dependence of the susceptibility at Tmax : The substitution of Al or Ga for Co in YCo2 and LuCo2 enhances the susceptibility and reduces the transition field [3]. In the pseudobinary LuðCo1x Gax Þ2 system, the transition field decreases with increasing Ga concentration and ferromagnetism appears above the critical concentration xc ¼ 0:095 [4]. In the present study, we have investigated the high-field magnetization *Corresponding author. Present address: High field Laboratory for Superconducting Materials, IMR, Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 980-8577, Japan. E-mail address: [email protected] (F. Ishikawa).
process of LuðCo1x Gax Þ2 (x ¼ 0:06 and 0.07) at various temperatures between 4.2 and 300 K in pulsed magnetic fields up to 45 T using powder samples and discuss the temperature dependence of the Landau coefficients. The specimens, LuðCo0:94 Ga0:06 Þ2 and LuðCo0:93 Ga0:07 Þ2 ; were prepared by arc-melting in an argon atmosphere [4]. Fig. 1 shows the high-field magnetization curves of both compounds at several temperatures. At low temperatures, the metamagnetic transition occurs sharply with hysteresis. In this study, the transition fields in increasing and decreasing fields were determined from the peak position of the derivative of the magnetization with respect to field dM=dH and averaged. The averaged value is considered as the transition field in the equilibrium state. The value at 4:2 K is 23:5 T for x ¼ 0:06 and 19:7 T for x ¼ 0:07: With increasing temperature T; the transition field increases. On the other hand, the hysteresis decreases and disappears around T0 B100 K for x ¼ 0:06 and B90 K for x ¼ 0:07: It is known that the metamagnetic transition field is proportional to the square of temperature T 2 in the low-temperature region [5]. We found that the transition field below T0 obeys this relation for both compounds.
0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.11.214
ARTICLE IN PRESS F. Ishikawa et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) 505–506
506
BðTÞ and CðTÞ are estimated by fitting the observed magnetization curves to the equation of states
0.8
Magnetization [B/Co]
T = 4.2 K
T = 4.2 K
50 K
90 K
60 K
100 K
0.6
150 K
H ¼ AðTÞM þ BðTÞM 3 þ CðTÞM 5 :
ð1Þ
200 K 150 K
0.4
250 K
200 K 250 K
300 K
300 K
0.2
Lu(Co0.93Ga0.07)2
Lu(Co0.94Ga0.06)2 0.0 0
10
20
30
40
50 0
Magnetic field [T]
10
20
30
40
50
Magnetic field [T]
Fig. 1. High-field magnetization curves of LuðCo0:94 Ga0:06 Þ2 and LuðCo0:93 Ga0:07 Þ2 :
A [1/(µB/Co)]
220 200
Lu(Co1-xGax)2
180 160 140 120 100
B [1/(µB/Co)3]
200 0
-200 -400 -600
AðTÞ is equal to the inverse of the susceptibility. The measured susceptibility shows a broad maximum at Tmax ¼ 170 K for x ¼ 0:06 and 150 K for x ¼ 0:07: BðTÞ increases with T and its sign changes from negative to positive at Tb ¼ 270 K for x ¼ 0:06 and 240 K for x ¼ 0:07: The value of Tb is higher than that of Tmax : Recently, Yamada et al. have proposed a spin fluctuation theory for itinerant-electron metamagnetism taking the magnetovolume effect into account [6]. If the magnetovolume effect is absent, the sign of BðTÞ changes at Tmax : In case that this effect is present, however, BðTÞ is expected to be negative even at Tmax : The behavior of BðTÞ estimated experimentally is consistent with the theory. The large difference between Tb and Tmax suggests that the magnetovolume coupling is very large in these compounds. In fact the coupling constant determined by Goto and Bartashevich is very large [7]. The estimated CðTÞ is temperature dependent. This suggests that higher order terms than M 5 are not negligible.
x = 0.06 x = 0.07
-800
-1000
References
C [1/(µB/Co)5]
1200 1000 800 600 400 200 0 0
50
100
150
200
250
300
Temperature [K]
Fig. 2. Temperature dependence of the Landau coefficients for LuðCo1x Gax Þ2 :
The temperature dependence of the Landau coefficients is shown in Fig. 2. The Landau coefficients AðTÞ;
[1] T. Goto, T. Sakakibara, K. Murata, H. Komatsu, K. Fukamichi, J. Magn. Magn. Mater. 90,91 (1990) 700. [2] H. Yamada, J. Inoue, M. Shimizu, J. Phys. F 15 (1985) 169. [3] T. Sakakibara, T. Goto, K. Yoshimura, M. Shiga, Y. Nakamura, Phys. Lett. A 117 (1986) 243. [4] T. Yokoyama, H. Saito, K. Fukamichi, K. Kamishima, T. Goto, H. Yamada, J. Phys.: Condens. Matter 13 (2001) 9281. [5] H. Yamada, Phys. Rev. B 47 (1993) 11211. [6] H. Yamada, K. Fukamichi, T. Goto, Phys. Rev. B 65 (2001) 024413. [7] T. Goto, M.I. Bartashevich, J. Phys.: Condens. Matter 10 (1998) 3625.
Journal of Magnetism and Magnetic Materials 272–276 (2004) 505–506
Temperature dependence of Landau coefficients in LuðCo1xGax Þ2 F. Ishikawaa,*, T. Gotoa, K. Fukamichib, H. Yamadac b
a Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan Department of Material Science, Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan c Faculty of Science, Shinshu University, Matsumoto 390-8621, Japan
Abstract High-field magnetization was measured for typical itinerant-electron metamagnets LuðCo1x Gax Þ2 with x ¼ 0:06 and 0.07 at temperatures from 4.2 to 300 K in pulsed magnetic fields up to 45 T: Landau coefficients AðTÞ; BðTÞ and CðTÞ were determined by fitting measured M–H curves to the equation, H ¼ AðTÞM þ BðTÞM 3 þ CðTÞM 5 : The temperature dependence of the Landau coefficients was well explained by the theory of the metamagnetic transition considering the magnetovolume effect. r 2003 Elsevier B.V. All rights reserved. PACS: 75.30.Kz; 75.50.y; 75.60.Ej Keywords: Itinerant-electron metamagnetism; Metamagnetic transition; LuðCo1x Gax Þ2
The Laves phase intermetallic compounds YCo2 and LuCo2 are recognized as typical itinerant-electron metamagnets. Itinerant-electron metamagnetism occurs in both compounds from the enhanced Pauli paramagnetic to the ferromagnetic state by applying magnetic fields. The metamagnetic transition field was confirmed to be 69 T for YCo2 and 74 T for LuCo2 [1]. The occurrence of the transition has close relationships with the shape of the density of states, in which a sharp peak exists just below the Fermi level [2]. In such case, a broad maximum appears in the temperature dependence of the susceptibility at Tmax : The substitution of Al or Ga for Co in YCo2 and LuCo2 enhances the susceptibility and reduces the transition field [3]. In the pseudobinary LuðCo1x Gax Þ2 system, the transition field decreases with increasing Ga concentration and ferromagnetism appears above the critical concentration xc ¼ 0:095 [4]. In the present study, we have investigated the high-field magnetization *Corresponding author. Present address: High field Laboratory for Superconducting Materials, IMR, Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 980-8577, Japan. E-mail address: [email protected] (F. Ishikawa).
process of LuðCo1x Gax Þ2 (x ¼ 0:06 and 0.07) at various temperatures between 4.2 and 300 K in pulsed magnetic fields up to 45 T using powder samples and discuss the temperature dependence of the Landau coefficients. The specimens, LuðCo0:94 Ga0:06 Þ2 and LuðCo0:93 Ga0:07 Þ2 ; were prepared by arc-melting in an argon atmosphere [4]. Fig. 1 shows the high-field magnetization curves of both compounds at several temperatures. At low temperatures, the metamagnetic transition occurs sharply with hysteresis. In this study, the transition fields in increasing and decreasing fields were determined from the peak position of the derivative of the magnetization with respect to field dM=dH and averaged. The averaged value is considered as the transition field in the equilibrium state. The value at 4:2 K is 23:5 T for x ¼ 0:06 and 19:7 T for x ¼ 0:07: With increasing temperature T; the transition field increases. On the other hand, the hysteresis decreases and disappears around T0 B100 K for x ¼ 0:06 and B90 K for x ¼ 0:07: It is known that the metamagnetic transition field is proportional to the square of temperature T 2 in the low-temperature region [5]. We found that the transition field below T0 obeys this relation for both compounds.
0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.11.214
ARTICLE IN PRESS F. Ishikawa et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) 505–506
506
BðTÞ and CðTÞ are estimated by fitting the observed magnetization curves to the equation of states
0.8
Magnetization [B/Co]
T = 4.2 K
T = 4.2 K
50 K
90 K
60 K
100 K
0.6
150 K
H ¼ AðTÞM þ BðTÞM 3 þ CðTÞM 5 :
ð1Þ
200 K 150 K
0.4
250 K
200 K 250 K
300 K
300 K
0.2
Lu(Co0.93Ga0.07)2
Lu(Co0.94Ga0.06)2 0.0 0
10
20
30
40
50 0
Magnetic field [T]
10
20
30
40
50
Magnetic field [T]
Fig. 1. High-field magnetization curves of LuðCo0:94 Ga0:06 Þ2 and LuðCo0:93 Ga0:07 Þ2 :
A [1/(µB/Co)]
220 200
Lu(Co1-xGax)2
180 160 140 120 100
B [1/(µB/Co)3]
200 0
-200 -400 -600
AðTÞ is equal to the inverse of the susceptibility. The measured susceptibility shows a broad maximum at Tmax ¼ 170 K for x ¼ 0:06 and 150 K for x ¼ 0:07: BðTÞ increases with T and its sign changes from negative to positive at Tb ¼ 270 K for x ¼ 0:06 and 240 K for x ¼ 0:07: The value of Tb is higher than that of Tmax : Recently, Yamada et al. have proposed a spin fluctuation theory for itinerant-electron metamagnetism taking the magnetovolume effect into account [6]. If the magnetovolume effect is absent, the sign of BðTÞ changes at Tmax : In case that this effect is present, however, BðTÞ is expected to be negative even at Tmax : The behavior of BðTÞ estimated experimentally is consistent with the theory. The large difference between Tb and Tmax suggests that the magnetovolume coupling is very large in these compounds. In fact the coupling constant determined by Goto and Bartashevich is very large [7]. The estimated CðTÞ is temperature dependent. This suggests that higher order terms than M 5 are not negligible.
x = 0.06 x = 0.07
-800
-1000
References
C [1/(µB/Co)5]
1200 1000 800 600 400 200 0 0
50
100
150
200
250
300
Temperature [K]
Fig. 2. Temperature dependence of the Landau coefficients for LuðCo1x Gax Þ2 :
The temperature dependence of the Landau coefficients is shown in Fig. 2. The Landau coefficients AðTÞ;
[1] T. Goto, T. Sakakibara, K. Murata, H. Komatsu, K. Fukamichi, J. Magn. Magn. Mater. 90,91 (1990) 700. [2] H. Yamada, J. Inoue, M. Shimizu, J. Phys. F 15 (1985) 169. [3] T. Sakakibara, T. Goto, K. Yoshimura, M. Shiga, Y. Nakamura, Phys. Lett. A 117 (1986) 243. [4] T. Yokoyama, H. Saito, K. Fukamichi, K. Kamishima, T. Goto, H. Yamada, J. Phys.: Condens. Matter 13 (2001) 9281. [5] H. Yamada, Phys. Rev. B 47 (1993) 11211. [6] H. Yamada, K. Fukamichi, T. Goto, Phys. Rev. B 65 (2001) 024413. [7] T. Goto, M.I. Bartashevich, J. Phys.: Condens. Matter 10 (1998) 3625.