- Email: [email protected]
Low-temperature magnetization of Ce(Ru0.85Rh0.15)2Si2
Journal of Magnetism and Magnetic Materials 177 181 (1998) 411-412
~
Journalof mnatneusm magnetic materials
ELSEVIER
Low-temperature magnetization of Ce(Ru0.ssRh0.15)2Si2 C. Sekine a'*, T. Tayama b, T. Sakakibara b, S. Murayama a, I. Shirotani a, Y.
Onuki c
"Department of Electrical and Electronic Engineering, Muroran Institute of Technology, 27-1 Mizumoto-cho, Muroran 050, Japan hDepartment of Physics, Hokkaido University, Sapporo 060, Japan CDepartment of Physics, Osaka University, Osaka 560, Japan
Abstract
Magnetization measurements have been performed on a single-crystallinesample of Ce(Ruo.ssRh0.~ 5)2Si2in magnetic fields along the tetragonal c-axis up to 8 T in the temperature range between 4 0 m K and 10 K. Two transitions (Bc = 3.45 T, BM = 5.5 T) are observed in the magnetization process at 40 inK. Further, at low temperatures, hysteresis is observed at Bc and this disappears above 2 K. Therefore, the transition at Bc is first order at low temperatures, but becomes second order above 2 K. © 1998 Elsevier Science B.V. All rights reserved. Keywords: Spin density waves; Heavy-fermion compounds; Magnetization low-temperature; Metamagnetism
The heavy-fermion Ce(Rul-xRhx)2Si2 system with the ThCrzSiz-type tetragonal structure shows a weak antiferromagnetic (AF) phase in the Ru-rich region (0.05 < x < 0.3) [1]. The ordering temperature TN has a maximum at around x = 0.15 (TN = 5.5 K). A neutron diffraction experiment for x = 0.15 shows that the AF phase has an incommensurate sinusoidal spin modulation with a wave vector T = (0, 0, 0.42) and that the magnetic moment is polarized along the c-axis with the amplitude of 0.65/~B/Ce [2]. Recent resistivity measurements for x = 0.15 have suggested that a partial gapping of the Fermi surface occurs associated with the development of a spin-density-wave(SDW) [3]. laSR experiments for x = 0.15 suggest that the local inhomogeneous static field occurs at TN almost along the c-axis, which is the same as the direction of ordered Ce moments [4]. The local field distribution below TN is consistent with the SDW ordering. The magnetic phase diagram of Ce(Rul xRhx)2Si2 in the B - T plane was reported in the preceding paper for x = 0.1 [1]. However, data below 1.4 K is lacking in the phase diagram. In this paper, we have studied the magnetic phase diagram of Ce(Ruo.85Rh0.15)28i2by means of various static magnetization measurements at very low temperatures. A high-quality single-crystalline sample of Ce(Ruo.85 RhoAs)2Si2 was grown by the Czochralsky technique in a tri-arc furnace. The magnetization measurements up to
8 T were done by a SQUID magnetometer and a highsensitivity Faraday force magnetometer in the temperature range between 40 mK and 10 K. The Faraday force magnetometer has been developed for the static magnetization measurements at very low temperatures. The details of the apparatus were reported previously [5]. All the magnetization measurements were done with fields applied parallel to the tetragonal c-axis, which is the magnetically easy axis. Fig. 1 shows the temperature variation of the differential susceptibility ~M/~B. The sharp peak (Bc) and the broad peak (B~) in ~M/~B correspond to the two-step magnetization jump of metamagnetic transitions. The transition fields at 4 0 m K are Bc = 3.45T and B~ = 5.5 T. While B~ is almost temperature-independent,
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* Correspondence author. Tel. + 81-143-47-3449;fax: + 81143-47-3288; e-mail: [email protected].
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Fig. 1. Differentialsusceptibility of Ce(Ruo.85Rho.ls)2Si2. The inset shows temperature dependence of the transition fields Bc plotted against T2.
0304-8853/98/$19.00 1998 Elsevier Science B.V. All rights reserved PII S 0 3 0 4 - 8 8 5 3 ( 9 7 t 0 0 4 5 4 - X
412
C. Sekine et al. /Journal o f Magnetism and Magnetic Materials 177-181 (1998) 411 412
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Bc decreases with increasing temperature and disappears at 6 K. On the other hand, BM is still visible at 6 K. These behaviors are similar to those for x = 0.1 [1] and suggest that Bc is associated with the destruction of the AF state. The second transition seems to be the same metamagnetic transition as that observed on CeRu2Si2 because the transition still exists above T N. Further, the hysteresis at Bc was observed at low temperatures (Fig. 2). The field-width of hysteresis becomes smaller rapidly with increasing temperature and disappears above 2 K (the inset of Fig. 2). Thus, at low temperatures the transition at Bc is first order, but becomes second order (2-like) above 2 K. On the first-order critical line in the B - T plane, the Clausius-Clapeyron relation d B c / d T = - A S ~ A M is expected to hold, where AS and AM denote the entropy and moment discontinuity across the transition, respectively. The temperature variation of Bc is plotted against T 2 in the inset of Fig. 1, where the data points lie on an almost straight line of the - 0.055 T/K 2 below 2 K. If we adopt the T 2 dependence of Bc(T), then it can be shown from the above relation that the entropy change AS is proportional to T at low temperature. Assuming that T-linear AS mainly comes from the difference in the 7 value between the two states, we expect a discontinuous increase in 7 by A7 = 130 mJ/molK 2 at Bc. Recently, specific heat measurements in the magnetic field on Ce(Ruo.85Rho.15)2Si2 were done at temperatures below 1.2 K [6]. A drastic increase in 7(B) of about A7 = 160 mJ/molK 2 was actually observed at Bc. The estimated value of A7 obtained by the calorimetric measurements is consistent with that deduced from the magnetization measurement given above. This increase of 7 suggests that Fermi-surface nesting in a heavy-fermion band was destroyed by the field and a heavy-fermion state was restored at Bc. In Fig. 3, we show the B - T phase diagram of Ce(Ruo.ssRho.15)2Si2 in fields parallel to the c-axis. Closed circles denote the transition temperature determined by the temperature variation of the susceptibility for various fields. Open circles and closed squares denote
,
4
6
8
10
"f(K)
Bcr)
Fig. 2. Magnetization curve of Ce(Ruo.ssRh0.15)2Si2. The inset shows temperature dependence of the field-width of hysteresis.
2
Fig. 3. B T phase diagram for Ce(Ru0.85Rh0 15)2Si2. the two metamagnetic transition fields. At low temperatures the transition at Bc is first order, but becomes second order above 2 K. The Ising antiferromagnet, dysprosium aluminum garnet (DAG), has a similar phase diagram [7]. DAG shows the AF to paramagnetic transition under fields. At low temperatures this transition is first order, but becomes second order above some temperature T,. Griffiths has explained this phase diagram by considering the three-dimensional (3D) relationship between staggered field (conjugate to the AForder parameter), temperature and applied field. Tt is called the tricritical point where critical lines join in the 3D phase diagram. Supposing this 3D phase diagram for Ce(Ru0.ssRho.15)2Si2, the tricritical point Tt is determined to be about 2 K. From the present experiments, the low-temperature magnetic phase diagram is obtained for the SDW state of Ce(Ru0.ssRho.15)2Si2. This compound appears a good candidate for understanding the nature of SDW on the heavy-fermion system. This work was partly supported by a Grant-in-Aid for Encouragement of Young Scientists from the Ministry of Education, Science, Sports and Culture of Japan.
References [1] C. Sekine,T. Sakakibara, H. Amitsuka, Y. Miyako, T. Goto, J. Phys. Soc. Japan 61 (1992) 4536. [2] S. Kawarazaki, Y. Kobashi, J.A. Fernandez-Baca, S. Murayama, Y. Onuki, Y. Miyako, Physica B 206 & 207 (1995) 298. [3] S. Murayama, C. Sekine, A. Yokoyanagi, K. Hoshi, Y. Onuki, Phys. Rev. B (1997), in press. I-4] S. Murayama, C. Sekine, A. Yokoyanagi, Y. Asakura, K. Hoshi, K. Nishiyama, K. Nagamine, Y. Onuki, Hyperfine Interactions 104 (1997) 205. [5] T. Sakakibara, H. Mitamura, T. Tayama, H. Amitsuka, Japan J. Appl. Phys. 33 (1994) 5067. [6] C. Sekine, Y. Nakazawa, K. Kanoda, T. Sakakibara, S. Murayama, I. Shirotani, Y. Onuki, Physica B 23(~232 (1997) 172. 1-7] R.B. Griffiths, Phys. Rev. Lett. 24 (1970) 715.
~
Journalof mnatneusm magnetic materials
ELSEVIER
Low-temperature magnetization of Ce(Ru0.ssRh0.15)2Si2 C. Sekine a'*, T. Tayama b, T. Sakakibara b, S. Murayama a, I. Shirotani a, Y.
Onuki c
"Department of Electrical and Electronic Engineering, Muroran Institute of Technology, 27-1 Mizumoto-cho, Muroran 050, Japan hDepartment of Physics, Hokkaido University, Sapporo 060, Japan CDepartment of Physics, Osaka University, Osaka 560, Japan
Abstract
Magnetization measurements have been performed on a single-crystallinesample of Ce(Ruo.ssRh0.~ 5)2Si2in magnetic fields along the tetragonal c-axis up to 8 T in the temperature range between 4 0 m K and 10 K. Two transitions (Bc = 3.45 T, BM = 5.5 T) are observed in the magnetization process at 40 inK. Further, at low temperatures, hysteresis is observed at Bc and this disappears above 2 K. Therefore, the transition at Bc is first order at low temperatures, but becomes second order above 2 K. © 1998 Elsevier Science B.V. All rights reserved. Keywords: Spin density waves; Heavy-fermion compounds; Magnetization low-temperature; Metamagnetism
The heavy-fermion Ce(Rul-xRhx)2Si2 system with the ThCrzSiz-type tetragonal structure shows a weak antiferromagnetic (AF) phase in the Ru-rich region (0.05 < x < 0.3) [1]. The ordering temperature TN has a maximum at around x = 0.15 (TN = 5.5 K). A neutron diffraction experiment for x = 0.15 shows that the AF phase has an incommensurate sinusoidal spin modulation with a wave vector T = (0, 0, 0.42) and that the magnetic moment is polarized along the c-axis with the amplitude of 0.65/~B/Ce [2]. Recent resistivity measurements for x = 0.15 have suggested that a partial gapping of the Fermi surface occurs associated with the development of a spin-density-wave(SDW) [3]. laSR experiments for x = 0.15 suggest that the local inhomogeneous static field occurs at TN almost along the c-axis, which is the same as the direction of ordered Ce moments [4]. The local field distribution below TN is consistent with the SDW ordering. The magnetic phase diagram of Ce(Rul xRhx)2Si2 in the B - T plane was reported in the preceding paper for x = 0.1 [1]. However, data below 1.4 K is lacking in the phase diagram. In this paper, we have studied the magnetic phase diagram of Ce(Ruo.85Rh0.15)28i2by means of various static magnetization measurements at very low temperatures. A high-quality single-crystalline sample of Ce(Ruo.85 RhoAs)2Si2 was grown by the Czochralsky technique in a tri-arc furnace. The magnetization measurements up to
8 T were done by a SQUID magnetometer and a highsensitivity Faraday force magnetometer in the temperature range between 40 mK and 10 K. The Faraday force magnetometer has been developed for the static magnetization measurements at very low temperatures. The details of the apparatus were reported previously [5]. All the magnetization measurements were done with fields applied parallel to the tetragonal c-axis, which is the magnetically easy axis. Fig. 1 shows the temperature variation of the differential susceptibility ~M/~B. The sharp peak (Bc) and the broad peak (B~) in ~M/~B correspond to the two-step magnetization jump of metamagnetic transitions. The transition fields at 4 0 m K are Bc = 3.45T and B~ = 5.5 T. While B~ is almost temperature-independent,
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q I [ , I I • 3,5 • Ce(RUo ~Rho.ls)2S=2 3 . 4 1 1 ~
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~ m
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I 4
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* Correspondence author. Tel. + 81-143-47-3449;fax: + 81143-47-3288; e-mail: [email protected].
i -
(-I-)
Fig. 1. Differentialsusceptibility of Ce(Ruo.85Rho.ls)2Si2. The inset shows temperature dependence of the transition fields Bc plotted against T2.
0304-8853/98/$19.00 1998 Elsevier Science B.V. All rights reserved PII S 0 3 0 4 - 8 8 5 3 ( 9 7 t 0 0 4 5 4 - X
412
C. Sekine et al. /Journal o f Magnetism and Magnetic Materials 177-181 (1998) 411 412
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Bc decreases with increasing temperature and disappears at 6 K. On the other hand, BM is still visible at 6 K. These behaviors are similar to those for x = 0.1 [1] and suggest that Bc is associated with the destruction of the AF state. The second transition seems to be the same metamagnetic transition as that observed on CeRu2Si2 because the transition still exists above T N. Further, the hysteresis at Bc was observed at low temperatures (Fig. 2). The field-width of hysteresis becomes smaller rapidly with increasing temperature and disappears above 2 K (the inset of Fig. 2). Thus, at low temperatures the transition at Bc is first order, but becomes second order (2-like) above 2 K. On the first-order critical line in the B - T plane, the Clausius-Clapeyron relation d B c / d T = - A S ~ A M is expected to hold, where AS and AM denote the entropy and moment discontinuity across the transition, respectively. The temperature variation of Bc is plotted against T 2 in the inset of Fig. 1, where the data points lie on an almost straight line of the - 0.055 T/K 2 below 2 K. If we adopt the T 2 dependence of Bc(T), then it can be shown from the above relation that the entropy change AS is proportional to T at low temperature. Assuming that T-linear AS mainly comes from the difference in the 7 value between the two states, we expect a discontinuous increase in 7 by A7 = 130 mJ/molK 2 at Bc. Recently, specific heat measurements in the magnetic field on Ce(Ruo.85Rho.15)2Si2 were done at temperatures below 1.2 K [6]. A drastic increase in 7(B) of about A7 = 160 mJ/molK 2 was actually observed at Bc. The estimated value of A7 obtained by the calorimetric measurements is consistent with that deduced from the magnetization measurement given above. This increase of 7 suggests that Fermi-surface nesting in a heavy-fermion band was destroyed by the field and a heavy-fermion state was restored at Bc. In Fig. 3, we show the B - T phase diagram of Ce(Ruo.ssRho.15)2Si2 in fields parallel to the c-axis. Closed circles denote the transition temperature determined by the temperature variation of the susceptibility for various fields. Open circles and closed squares denote
,
4
6
8
10
"f(K)
Bcr)
Fig. 2. Magnetization curve of Ce(Ruo.ssRh0.15)2Si2. The inset shows temperature dependence of the field-width of hysteresis.
2
Fig. 3. B T phase diagram for Ce(Ru0.85Rh0 15)2Si2. the two metamagnetic transition fields. At low temperatures the transition at Bc is first order, but becomes second order above 2 K. The Ising antiferromagnet, dysprosium aluminum garnet (DAG), has a similar phase diagram [7]. DAG shows the AF to paramagnetic transition under fields. At low temperatures this transition is first order, but becomes second order above some temperature T,. Griffiths has explained this phase diagram by considering the three-dimensional (3D) relationship between staggered field (conjugate to the AForder parameter), temperature and applied field. Tt is called the tricritical point where critical lines join in the 3D phase diagram. Supposing this 3D phase diagram for Ce(Ru0.ssRho.15)2Si2, the tricritical point Tt is determined to be about 2 K. From the present experiments, the low-temperature magnetic phase diagram is obtained for the SDW state of Ce(Ru0.ssRho.15)2Si2. This compound appears a good candidate for understanding the nature of SDW on the heavy-fermion system. This work was partly supported by a Grant-in-Aid for Encouragement of Young Scientists from the Ministry of Education, Science, Sports and Culture of Japan.
References [1] C. Sekine,T. Sakakibara, H. Amitsuka, Y. Miyako, T. Goto, J. Phys. Soc. Japan 61 (1992) 4536. [2] S. Kawarazaki, Y. Kobashi, J.A. Fernandez-Baca, S. Murayama, Y. Onuki, Y. Miyako, Physica B 206 & 207 (1995) 298. [3] S. Murayama, C. Sekine, A. Yokoyanagi, K. Hoshi, Y. Onuki, Phys. Rev. B (1997), in press. I-4] S. Murayama, C. Sekine, A. Yokoyanagi, Y. Asakura, K. Hoshi, K. Nishiyama, K. Nagamine, Y. Onuki, Hyperfine Interactions 104 (1997) 205. [5] T. Sakakibara, H. Mitamura, T. Tayama, H. Amitsuka, Japan J. Appl. Phys. 33 (1994) 5067. [6] C. Sekine, Y. Nakazawa, K. Kanoda, T. Sakakibara, S. Murayama, I. Shirotani, Y. Onuki, Physica B 23(~232 (1997) 172. 1-7] R.B. Griffiths, Phys. Rev. Lett. 24 (1970) 715.