- Email: [email protected]
Low-temperature specific heat of CexLa1−xB6
Physica B 281&282 (2000) 559}560
Low-temperature speci"c heat of Ce La B x 1~x 6 S. Nakamura!,*, T. Goto", S. Kunii#, O. Suzuki" !Center for Low Temperature Science, Tohoku University, Katahira, Sendai 980-8577, Japan "Graduate School of Science and Technology, Niigata University, Niigata 950-2181, Japan #Department of physics, Tohoku University, Sendai 980-8578, Japan
Abstract We have measured low-temperature speci"c heat of Ce La B . No indication of long-range ordering was found in x 1~x 6 the speci"c heat of Ce La B (x"0.6 and 0.5) within the limits of the accuracy of the measurements. On the other x 1~x 6 hand, a clear indication of long-range ordering (phase IV) was found in the case of Ce La B . The ground state of 0.65 0.35 6 Ce La B in the low-temperature and low-"eld region would change from phase IV to a non-magnetic state at the x 1~x 6 critical Ce-concentration 0.6(x (0.65 as a result of the competition between the intersite interactions and the dense # Kondo e!ect. ( 2000 Elsevier Science B.V. All rights reserved. Keywords: Magnetic-phase transition; (Ce, La)B ; Speci"c heat 6
Recently, magnetic-phase diagrams of a cubic Kondo system Ce La B have attracted much attention. The x 1~x 6 ground multiplet J"5 of Ce3` ions splits into 2 a ! ground state and a excited ! state in a cubic crystal 8 7 electric "eld with the magnitude of splitting &540 K [1]. Regardless of the Ce-concentration the electrical resisitivity of Ce La B displays the !ln T temperature x 1~x 6 dependence at high temperatures and the Kondo temperature is believed to be 1}2 K [2]. The coexistence of the magnetic and quadrupolar moments in the ! state leads 8 to the coexistence of multipolar intersite interactions and this results in the characteristic magnetic phase diagrams of Ce La B . Pure CeB undergoes a transition from x 1~x 6 6 the paramagnetic state (phase I) to an antiferro-quadrupolar phase II at 3.3 K and a further transition to an antiferro-magnetic phase III [3]. The phase I}phase II boundary (phase I}II boundary) of CeB shifts to a high6 er temperature with increasing "elds. Various theoretical studies have been performed on this "eld-dependence of the phase I}II boundary of CeB [4,5]. One of the open 6 problems in relation to the magnetic phase diagrams of
* Corresponding author. Tel.:#81-22-215-2167; fax: #8122-215-2168. E-mail address: [email protected] (S. Nakamura)
Ce La B is whether the dense Kondo e!ect a!ects x 1~x 6 the magnetic phase diagrams or not. In the previous study the magnetic phase diagrams of Ce La B were 0.5 0.5 6 reported [6]. In this study, no indication of long-range ordering was found under low "elds (H(1.7 T), whereas a long-range ordering was evident under high "elds. This magnetic phase diagrams of Ce La B was inter0.5 0.5 6 preted as a result of the competition between the dense Kondo e!ect and intersite interactions [6]. However, as mentioned later, the ground state of Ce La B under 0.5 0.5 6 low-T, low-H conditions is still an open problem. If the competition between the dense Kondo e!ect and intersite interactions exists in the Ce La B system, it x 1~x 6 would be expected that the magnetic phase diagrams and the ground state of Ce La B are strongly dependent x 1~x 6 on the Ce-concentration, because the strength of the intersite interactions would change with changing the distance between Ce ions. In relation to the magnetic phase diagrams of Ce La B , a number of studies x 1~x 6 have been made by changing the Ce-concentration. However, the results reported in the previous studies are inconsistent with each other. An open problem is the extent of Ce-concentration to which an ordered state phase IV exists. Suzuki et al. proposed that the ground state of Ce La B for H"0 changes rapidly from x 1~x 6 phase IV to the non-magnetic state with decreasing x at the critical concentration x . They proposed that #
0921-4526/00/$ - see front matter ( 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 0 9 9 2 - 8
560
S. Nakamura et al. / Physica B 281&282 (2000) 559}560
Fig. 1. The speci"c heat of Ce La B for H"0. The open x 1~x 6 circles, solid squares and solid circles represent data for x"0.5, 0.6, and 0.65, respectively. The arrows represent the phase I}IV transition point.
x exists within the region 0.60(x (0.75 [7,8]. On the # # other hand, Tayama et al. [9] and Hiroi et al. [10] reported that phase IV may exist even in the case of Ce La B in the low-temperature (low-T), low-"eld 0.5 0.5 6 (low-H) region. In the present study, we measured the speci"c heat of Ce La B to determine the value of x . x 1~x 6 # Regardless of the kinds of phase transitions, a discontinuity would be found in the speci"c heat at the phase transition point. Although the order parameter of phase IV has not been identi"ed, clear anomalies were found in the speci"c heat at the phase I}IV transition points [7]. Therefore, the speci"c heat measurements would be useful to determine the value of x . # A single crystal of Ce La B was grown by the x 1~x 6 #oating zone method. The prepared samples were 164 mg block for x"0.5, 865 mg block for x"0.6 and 406 mg block for x"0.65. All of the samples used in Refs. [6}11] were cut from the same ingot when the same Ce-concentration is shown. We measured the speci"c heat by a semi-adiabatic method using the dilution refrigerator at the Center for Low Temperature Science, Tohoku University. The speci"c heat of Ce La B (x"0.5, 0.6 and 0.65) x 1~x 6 for H"0 are shown in Fig. 1. This "gure includes the speci"c heat of Ce La B taken from Ref. [7] for 0.75 0.25 6 comparison. The arrows in Fig. 1 represent the phase I}IV transition points. In the case of Ce La B , 0.75 0.25 6 a clear j-shaped peak is shown in the speci"c heat in association with the phase I}IV transition. The small peak in the speci"c heat of Ce La B shown at 0.75 0.25 6 1.1 K corresponds to the phase IV}III transition point [7,8]. In the case of Ce La B , as shown in Fig. 1, 0.65 0.35 6 a sharp j-shaped peak was found in the speci"c heat at around 1.2 K. Very recently, Suzuki et al. found a pronounced discontinuous change in the elastic constant C at around 1.2 K in the case of Ce La B [11]. 44 0.65 0.35 6 This feature of C is quite similar to that shown at the 44 phase I}IV transition point in the case of Ce La B 0.75 0.25 6
[7]. Therefore, the peak shown in the speci"c heat of Ce La B is an indication of the phase I}IV 0.65 0.35 6 transition. No additional phase transition was found in the speci"c heat of Ce La B down to &150 mK. 0.65 0.35 6 This suggests that, in the case of Ce La B , 0.65 0.35 6 the ground 4f electronic state has no degeneracy in phase IV. In contrast to the case of Ce La B , no indica0.65 0.35 6 tion of the phase I}IV transition was found in the speci"c heat of Ce La B and Ce La B within the limits 0.6 0.4 6 0.5 0.5 6 of the accuracy of the measurements. In these systems only a broad peak was observed at around 0.9 K. These broad peaks cannot be interpreted as the spin glass state, as a hysteresis loop shown in the low-T magnetization of Ce La B is quite small [9]. Probably, in the case of 0.5 0.5 6 Ce La B , the macroscopic non-magnetic state 0.5 0.5 6 which has no order parameter would be realized under low-T, low-H conditions as a result of the dense Kondo e!ect. This non-magnetic state would be broken when the intersite interactions are strong. The results of the present study support the view that the critical Ce-concentration x exists within the region 0.6(x (0.65. # # In conclusion, we measured the low-temperature speci"c heat of Ce La B with change in Ce-concentration. x 1~x 6 The results of the present study strongly suggest that the critical concentration x exists within the region # 0.6(x (0.65. The competition between the dense # Kondo e!ect and the intersite interactions exist in Ce La B and the dense Kondo e!ect have the strong x 1~x 6 in#uence on the magnetic phase diagrams of Ce La B . x 1~x 6 Acknowledgements This work was partly supported by a Grant-in-Aid from the Ministry of Education, Science and Culture of Japan. We thank S. Otomo, H. Miura, S. Tanno and K. Hosokura for their technical assistance. Supports of prof. T. Nojima for the present study is acknowledged.
References [1] E. Zirngibl et al., Phy. Rev. B 30 (1984) 4052. [2] N. Sato et al., J. Phys. Soc. Japan 54 (1985) 1923. [3] J.M. E!antin et al., J. Magn. Magn. Mater. 47&48 (1985) 145. [4] G. Uimin et al., Solid. State. Commun. 97 (1996) 595. [5] R. Shiina et al., J. Phys. Soc. Japan 66 (1997) 1741. [6] S. Nakamura et al., J. Phys. Soc. Japan 66 (1997) 552., and references therein. [7] O. Suzuki et al., J. Phys. Soc. Japan 67 (1998) 4243. [8] O. Suzuki et al., these Proceedings (SCES '99). [9] T. Tayama et al., J. Phys. Soc. Japan 66 (1997) 2268. [10] M. Hiroi et al., J. Phys. Soc. Japan 66 (1997) 1762. [11] O. Suzuki et al., unpublished.
Low-temperature speci"c heat of Ce La B x 1~x 6 S. Nakamura!,*, T. Goto", S. Kunii#, O. Suzuki" !Center for Low Temperature Science, Tohoku University, Katahira, Sendai 980-8577, Japan "Graduate School of Science and Technology, Niigata University, Niigata 950-2181, Japan #Department of physics, Tohoku University, Sendai 980-8578, Japan
Abstract We have measured low-temperature speci"c heat of Ce La B . No indication of long-range ordering was found in x 1~x 6 the speci"c heat of Ce La B (x"0.6 and 0.5) within the limits of the accuracy of the measurements. On the other x 1~x 6 hand, a clear indication of long-range ordering (phase IV) was found in the case of Ce La B . The ground state of 0.65 0.35 6 Ce La B in the low-temperature and low-"eld region would change from phase IV to a non-magnetic state at the x 1~x 6 critical Ce-concentration 0.6(x (0.65 as a result of the competition between the intersite interactions and the dense # Kondo e!ect. ( 2000 Elsevier Science B.V. All rights reserved. Keywords: Magnetic-phase transition; (Ce, La)B ; Speci"c heat 6
Recently, magnetic-phase diagrams of a cubic Kondo system Ce La B have attracted much attention. The x 1~x 6 ground multiplet J"5 of Ce3` ions splits into 2 a ! ground state and a excited ! state in a cubic crystal 8 7 electric "eld with the magnitude of splitting &540 K [1]. Regardless of the Ce-concentration the electrical resisitivity of Ce La B displays the !ln T temperature x 1~x 6 dependence at high temperatures and the Kondo temperature is believed to be 1}2 K [2]. The coexistence of the magnetic and quadrupolar moments in the ! state leads 8 to the coexistence of multipolar intersite interactions and this results in the characteristic magnetic phase diagrams of Ce La B . Pure CeB undergoes a transition from x 1~x 6 6 the paramagnetic state (phase I) to an antiferro-quadrupolar phase II at 3.3 K and a further transition to an antiferro-magnetic phase III [3]. The phase I}phase II boundary (phase I}II boundary) of CeB shifts to a high6 er temperature with increasing "elds. Various theoretical studies have been performed on this "eld-dependence of the phase I}II boundary of CeB [4,5]. One of the open 6 problems in relation to the magnetic phase diagrams of
* Corresponding author. Tel.:#81-22-215-2167; fax: #8122-215-2168. E-mail address: [email protected] (S. Nakamura)
Ce La B is whether the dense Kondo e!ect a!ects x 1~x 6 the magnetic phase diagrams or not. In the previous study the magnetic phase diagrams of Ce La B were 0.5 0.5 6 reported [6]. In this study, no indication of long-range ordering was found under low "elds (H(1.7 T), whereas a long-range ordering was evident under high "elds. This magnetic phase diagrams of Ce La B was inter0.5 0.5 6 preted as a result of the competition between the dense Kondo e!ect and intersite interactions [6]. However, as mentioned later, the ground state of Ce La B under 0.5 0.5 6 low-T, low-H conditions is still an open problem. If the competition between the dense Kondo e!ect and intersite interactions exists in the Ce La B system, it x 1~x 6 would be expected that the magnetic phase diagrams and the ground state of Ce La B are strongly dependent x 1~x 6 on the Ce-concentration, because the strength of the intersite interactions would change with changing the distance between Ce ions. In relation to the magnetic phase diagrams of Ce La B , a number of studies x 1~x 6 have been made by changing the Ce-concentration. However, the results reported in the previous studies are inconsistent with each other. An open problem is the extent of Ce-concentration to which an ordered state phase IV exists. Suzuki et al. proposed that the ground state of Ce La B for H"0 changes rapidly from x 1~x 6 phase IV to the non-magnetic state with decreasing x at the critical concentration x . They proposed that #
0921-4526/00/$ - see front matter ( 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 0 9 9 2 - 8
560
S. Nakamura et al. / Physica B 281&282 (2000) 559}560
Fig. 1. The speci"c heat of Ce La B for H"0. The open x 1~x 6 circles, solid squares and solid circles represent data for x"0.5, 0.6, and 0.65, respectively. The arrows represent the phase I}IV transition point.
x exists within the region 0.60(x (0.75 [7,8]. On the # # other hand, Tayama et al. [9] and Hiroi et al. [10] reported that phase IV may exist even in the case of Ce La B in the low-temperature (low-T), low-"eld 0.5 0.5 6 (low-H) region. In the present study, we measured the speci"c heat of Ce La B to determine the value of x . x 1~x 6 # Regardless of the kinds of phase transitions, a discontinuity would be found in the speci"c heat at the phase transition point. Although the order parameter of phase IV has not been identi"ed, clear anomalies were found in the speci"c heat at the phase I}IV transition points [7]. Therefore, the speci"c heat measurements would be useful to determine the value of x . # A single crystal of Ce La B was grown by the x 1~x 6 #oating zone method. The prepared samples were 164 mg block for x"0.5, 865 mg block for x"0.6 and 406 mg block for x"0.65. All of the samples used in Refs. [6}11] were cut from the same ingot when the same Ce-concentration is shown. We measured the speci"c heat by a semi-adiabatic method using the dilution refrigerator at the Center for Low Temperature Science, Tohoku University. The speci"c heat of Ce La B (x"0.5, 0.6 and 0.65) x 1~x 6 for H"0 are shown in Fig. 1. This "gure includes the speci"c heat of Ce La B taken from Ref. [7] for 0.75 0.25 6 comparison. The arrows in Fig. 1 represent the phase I}IV transition points. In the case of Ce La B , 0.75 0.25 6 a clear j-shaped peak is shown in the speci"c heat in association with the phase I}IV transition. The small peak in the speci"c heat of Ce La B shown at 0.75 0.25 6 1.1 K corresponds to the phase IV}III transition point [7,8]. In the case of Ce La B , as shown in Fig. 1, 0.65 0.35 6 a sharp j-shaped peak was found in the speci"c heat at around 1.2 K. Very recently, Suzuki et al. found a pronounced discontinuous change in the elastic constant C at around 1.2 K in the case of Ce La B [11]. 44 0.65 0.35 6 This feature of C is quite similar to that shown at the 44 phase I}IV transition point in the case of Ce La B 0.75 0.25 6
[7]. Therefore, the peak shown in the speci"c heat of Ce La B is an indication of the phase I}IV 0.65 0.35 6 transition. No additional phase transition was found in the speci"c heat of Ce La B down to &150 mK. 0.65 0.35 6 This suggests that, in the case of Ce La B , 0.65 0.35 6 the ground 4f electronic state has no degeneracy in phase IV. In contrast to the case of Ce La B , no indica0.65 0.35 6 tion of the phase I}IV transition was found in the speci"c heat of Ce La B and Ce La B within the limits 0.6 0.4 6 0.5 0.5 6 of the accuracy of the measurements. In these systems only a broad peak was observed at around 0.9 K. These broad peaks cannot be interpreted as the spin glass state, as a hysteresis loop shown in the low-T magnetization of Ce La B is quite small [9]. Probably, in the case of 0.5 0.5 6 Ce La B , the macroscopic non-magnetic state 0.5 0.5 6 which has no order parameter would be realized under low-T, low-H conditions as a result of the dense Kondo e!ect. This non-magnetic state would be broken when the intersite interactions are strong. The results of the present study support the view that the critical Ce-concentration x exists within the region 0.6(x (0.65. # # In conclusion, we measured the low-temperature speci"c heat of Ce La B with change in Ce-concentration. x 1~x 6 The results of the present study strongly suggest that the critical concentration x exists within the region # 0.6(x (0.65. The competition between the dense # Kondo e!ect and the intersite interactions exist in Ce La B and the dense Kondo e!ect have the strong x 1~x 6 in#uence on the magnetic phase diagrams of Ce La B . x 1~x 6 Acknowledgements This work was partly supported by a Grant-in-Aid from the Ministry of Education, Science and Culture of Japan. We thank S. Otomo, H. Miura, S. Tanno and K. Hosokura for their technical assistance. Supports of prof. T. Nojima for the present study is acknowledged.
References [1] E. Zirngibl et al., Phy. Rev. B 30 (1984) 4052. [2] N. Sato et al., J. Phys. Soc. Japan 54 (1985) 1923. [3] J.M. E!antin et al., J. Magn. Magn. Mater. 47&48 (1985) 145. [4] G. Uimin et al., Solid. State. Commun. 97 (1996) 595. [5] R. Shiina et al., J. Phys. Soc. Japan 66 (1997) 1741. [6] S. Nakamura et al., J. Phys. Soc. Japan 66 (1997) 552., and references therein. [7] O. Suzuki et al., J. Phys. Soc. Japan 67 (1998) 4243. [8] O. Suzuki et al., these Proceedings (SCES '99). [9] T. Tayama et al., J. Phys. Soc. Japan 66 (1997) 2268. [10] M. Hiroi et al., J. Phys. Soc. Japan 66 (1997) 1762. [11] O. Suzuki et al., unpublished.