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Fermi-liquid behavior of electrical resistivity in the dilute uranium system UxLa1−xRu2Si2
PERGAMON
Solid State Communications 117 (2001) 245±248
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Fermi-liquid behavior of electrical resistivity in the dilute uranium system UxLa12xRu2Si2 K. Marumoto a,*, T. Takeuchi b, Y. Miyako c, M. Ocio d, P. Pari d, J. Hammann d a Department of Applied Physics, Nagoya University, Nagoya 464-8603, Japan Low Temperature Center, Osaka University, Toyonaka 560-0043, Osaka, Japan c Graduate School of Science, Osaka University, Toyonaka 560-0043, Osaka, Japan d Service de Physique de l'Etat CondenseÂ, CEA Saclay, 91191 Gif sur Yvette Cedex, France b
Received 30 August 2000; received in revised form 4 October 2000; accepted 15 October 2000 by H. Akai
Abstract Electrical resistivity measurements have been performed on the dilute uranium compound UxLa12xRu2Si2 x 0:07 with the current along the a and the c axes between 300 K and 28 mK. The electrical resistivity, r , along the a and the c axes decreases as temperature is lowered below 300 K. In the low-temperature region between 7 K and 28 mK, the magnetic contribution of the 5f electron to the resistivity, r m, exhibits the Fermi-liquid behavior with a clear T 2 dependence. The Kadowaki±Woods ratio A5f/g 5f2 is estimated from r m and the speci®c heat data previously reported, and is found to be the same order as that of URu2Si2. This indicates that the enhanced density of states at the Fermi level causes the T 2 dependence of r m in the dilute uranium compound UxLa12xRu2Si2. q 2001 Elsevier Science Ltd. All rights reserved. Keywords: A. Metals; B. Crystal growth; D. Electronic transport; D. Heavy fermions; D. Kondo effects PACS: 72.15.Qm; 75.20.Hr; 71.70.Ch
URu2Si2 is one of the most anomalous heavy-fermion superconductors, because it exhibits the coexistence of a type-I antiferromagnetism TN 17:5 K with an unusual small ordered moment (0.01±0.04 mB) and non-BCS-type superconductivity Tc 1:5 K: Many experimental and theoretical studies have been done extensively to understand this system from various standing points [1±12]. As one of them, the contribution of the quadrupolar coupling between 5f electrons of the uranium atoms was suggested for the phase transition at TN by the study of the non-linear susceptibility [13±15]. A pressure effect on the tiny antiferromagnetic moment was studied by using the elastic neutron scattering [16]. The mechanism of the phase transition at TN is, however, still controversial. It seems that a complete explanation for the experimental results has not been given. Although the crystalline ®eld levels are not so clear as well as the valence state of uranium in URu2Si2, the large * Corresponding author. Tel.: 181-52-789-5165; fax: 181-52789-3712. E-mail address: [email protected] (K. Marumoto).
anisotropy of the susceptibility above 100 K seems to be well explained by the non-Kramers doublet ground state of U 41 ion as in the case for the dilute uranium system UxLa12xRu2Si2 [17±18]. In order to clarify this situation experimentally and to understand the role of crystalline electric ®eld (CEF) splitting, we have carried out the magnetic and speci®c-heat measurements on the dilute uranium system UxLa12xRu2Si2 (x 0:05; 0.07, and 0.15) (the La system) [19±21]. The magnetic and thermodynamic properties at low-temperatures were well explained by the Kondo model. The observation of the enhanced g value meant that the ground state of the 5f electrons is a Kondo singlet state that is described as the Fermi liquid [22]. In contrast with the results of the La system, another dilute uranium system UxTh12xRu2Si2 x # 0:07 (the Th system) shows a ln T dependence in the magnetic susceptibility x , speci®c heat divided by temperature, C/T, and electrical resistivity r [23±24]. These features are understood as a non-Fermi-liquid behavior. The resistivity r of the Th system exhibits a steep decrease as temperature decreases, following ,ln T (1 K , T , 10 K) and ,T 1/2 0:1 K , T , 1 K.
0038-1098/01/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved. PII: S 0038-109 8(00)00439-7
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K. Marumoto et al. / Solid State Communications 117 (2001) 245±248
Fig. 1. Temperature dependence of the electrical resistivities r of U0.07La0.93Ru2Si2 and LaRu2Si2 along the a and the c axes.
For the case of the La system, the results of r have been preliminarily reported [21]. Recently, uranium concentration dependence of r was studied by using UxLa12xRu2Si2 (x 0:03; 0.05, and 0.07) with the current along the a axis between 300 and 1.3 K [25]. However, the measurement below 1 K has not been performed, and the anisotropy of r has not yet been measured so far. In this paper, we report the results of r of UxLa12xRu2Si2 x 0:07 with the current along the a and the c axes between 300 K and 28 mK. The resistivity r of both axes show a clear T 2 dependence in the low-temperature region below 7 K. This Fermi-liquid behavior is consistent with the results of magnetic and speci®c-heat measurements on the La system, exhibiting Kondo screening [20]. The Kadowaki±Woods ratio A5f/g 5f2 is estimated from the 5felectron part of r and the speci®c heat obtained in Ref. [20], and is found to be the same order as that of URu2Si2. The results of r of the La system are also compared with that of the Th system that shows the non-Fermi-liquid behavior. The single crystals UxLa12xRu2Si2 x # 0:07 were prepared by the Czochralski method with a tri-arc furnace. The sample characterizations were performed by using the X-ray powder diffraction and Laue method. The X-ray diffraction experiments con®rmed that all samples show a single phase and crystallize in the ThCr2Si2-type bodycentered tetragonal structure. The single crystals were cut by using a spark erosion cutter. The electrical resistivities were measured in a wide temperature range from 300 K to 28 mK by a standard four-terminal dc method using a dilution refrigerator. While the error of the absolute value in r is 20%, which is mainly due to an estimation error of the dimension, the relative error in one run of measurements is less than 2%. Fig. 1 shows the electrical resistivities r of
U0.07La0.93Ru2Si2 and LaRu2Si2 single crystals along the a and the c axes. In the case of LaRu2Si2, the absolute values of r at 295 K along the a and the c axes are obtained to be 28 and 11 mV cm, and the residual values at 1.8 K along the a and the c axes are 0.64 and 0.28 mV cm, respectively. These values and the overall behavior of the temperature variation are in good agreement with those in the earlier work [26]. In the case of U0.07La0.93Ru2Si2, r along the a axis is larger than that along the c axis. The resistivity r of both axes decreases monotonically as temperature is lowered, and shows a distinct knee-like structure at low temperatures around 18 K. Below 1 K, the data along the a axis is found to be almost constant. There is neither ln T nor T 1/2 temperature dependence of r as observed in the Th system. The resistivity r along the a axis above 1.3 K is consistent with that previously reported for U0.07La0.93Ru2Si2 [25]. The magnetic contribution to the resistivity, r m, is estimated by subtracting the lattice contribution using r for LaRu2Si2. Fig. 2 shows r m for U0.07La0.93Ru2Si2 along the a axis in the logarithmic-temperature scale. The data are normalized for uranium concentration. The data for x 0:03 and 0.05 are taken from Ref. [25] for the comparison. There is a little difference in the absolute values each other, which may be caused by the error of the dimensional estimation as mentioned above, and the error of nominal uranium concentration. In spite of these errors, overall temperature dependences of r m for these compounds, especially below 30 K, are almost the same with each other. The residual resistivity seems to vary linearly as a function of x, and r m is considered to show the single impurity effect with respect to uranium ion. The magnetic resistivity r m decreases as temperature is lowered below 100 K, and is almost constant below 1 K. In Fig. 3 we show the r vs. T 2 plots of U0.07La0.93Ru2Si2 and LaRu2Si2 along the a and c axes in the low-temperature
Fig. 2. Temperature dependence of the magnetic resistivity r m of U0.07La0.93Ru2Si2 along the a axis in the logarithmic-temperature scale. The dashed lines show r m for UxLa12xRu2Si2 x 0:03 and 0.05) along the a axis, which are taken from Ref. [25] for the comparison.
K. Marumoto et al. / Solid State Communications 117 (2001) 245±248
Fig. 3. r vs. T 2 plots of the electrical resistivities of U0.07La0.93Ru2Si2 and LaRu2Si2 along the a and c axes.
region below 10 K. The resistivity r for LaRu2Si2 is almost constant below 10 K, but the resistivity r for U0.07La0.93Ru2Si2 shows a clear T 2 temperature dependence in the low-temperature region below about 7 K, which is commonly observed for r of the heavy-fermion system. Using the ®tting formula of r 0 1 AT 2 for U0.07La0.93Ru2Si2, the values of coef®cient A along the a and the c axes are obtained as 6.6 £ 10 23 and 5.0 £ 10 23 mV cm/K 2, respectively. The A value along the a axis is larger than that along the c axis. The contribution of uranium ion A5f is estimated from r m. The values of A5f along the a and the c axes are found to be 9.4 £ 10 22 and 7.1 £ 10 22 mV cm/ K 2 U, respectively. The value along the a axis is almost the same as those obtained above 1 K for x 0:03; 0.05, and 0.07 by Yokoyama et al. [25]. Below 1 K, we have con®rmed the T 2 dependence in this paper. For comparison with other Fermi-liquid systems, we estimated the Kadowaki±Woods ration A5f/g 5f2 for U0.07La0.93Ru2Si2, where A5f is the coef®cient of the T 2 term of r m and g 5f is the electronic speci®c heat coef®cient per molar uranium. In this estimation, we used g 5f 130 mJ/K 2 U mol reported in the previous papers [20±21]. The values of A5f/g 5f2 along the a and c axes are obtained as 0.56 £ 10 25 and 0.42 £ 10 25 mV cm (U mol K/mJ) 2/U, respectively. These values are the same order as the common value of 1.0 £ 10 25 mV cm (mol K/mJ) 2 for all of the heavy-fermion compounds including URu2Si2 [27]. The similarity of these values between U0.07La0.93Ru2Si2 and URu2Si2 indicates that the Kondo resonance enhances the density of states at the Fermi level and this enhancement contributes the scattering of the conduction electrons, causing the T 2 dependence for r. The T 2 dependence of r in the La system is clearly different from that in the Th system. As mentioned in the
247
preceding paragraph, the Th system shows the temperature dependence for r as ,ln T (1 K , T , 10 K) and ,T 1/2 (0.1 K , T , 1 K). This difference is understood to be caused by the difference of 5f-electron state between the La system and the Th system, and may be explained by the change of the CEF splitting of uranium ions. The La system has the CEF splitting of 60 ^ 6 K between the ground non-Kramers-doublet and the ®rst-excited singlet states [20±21]. On the other hand, the singlet ®rst-excited CEF state in the Th system was suggested to be located at about 4000 K [23]. The different magnitude of the CEF splitting between the ground doublet and the excited singlet states may cause the difference of 5f-electron states between the La system and the Th system [20,21]. The importance of contribution of the excited state for the non-Kramers doublet ground state is predicted by theoretical studies, clarifying that the singlet ®rst-excited CEF state plays an important role in stabilizing the Fermi-liquid state over the non-Fermi-liquid state in the hexagonal crystal structure although in the tetragonal structure it does not work to stabilize the Fermi-liquid state [28±32]. The effect of the CEF splitting of 60 K may be re¯ected in the temperature dependence of r at higher temperatures. As seen in Fig. 1, r of U0.07La0.93Ru2Si2 along the a and c axes show a broad rounded curvature around 200 K. Moreover, Fig. 2 shows a broad maximum in r m for x 0:03; 0.05, and 0.07. Similar behavior has been observed in r of CeRu2Si2, and is attributed to the CEF effect [26]. As also seen in Fig. 1, r of U0.07La0.93Ru2Si2 along both axes show a knee-like structure at around 18 K. This structure were also observed in r for x 0:03 and 0.05 [25]. The origin of the knee-like structures is not known so far, but this anomaly might be related with the CEF effect mentioned above, or with an anomaly associated with the phase transition at TN observed in URu2Si2. In the latter case, a single-site mechanism is important to bring about the phase transition at TN in URu2Si2. The further measurements of r in the magnetic ®eld seems to be needed to obtain more information about the transport properties observed in the La system.
Acknowledgements This work was supported in part by Grant-in-aid for Scienti®c Research of the Ministry of Education, Science and Culture and by Monbusho International Scienti®c Research Program, Joint Research.
References [1] T.T.M. Palstra, A.A. Menovsky, J. van den Berg, A.J. Dirkmaat, P.H. Kes, G.J. Nieuwenhuys, J.A. Mydosh, Phys. Rev. Lett. 55 (1985) 2727. [2] T.T.M. Palstra, A.A. Menovsky, J.A. Mydosh, Phys. Rev. B 33 (1986) 6527.
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[3] W. Schlabitz, J. Baumann, B. Pollit, U. Rauchschwalbe, H.M. Mayer, U. Ahlheim, C.D. Bredl, Z. Phys. B 62 (1986) 171. [4] K. Sugiyama, H. Fuke, K. Kindo, K. Shimohata, A.A. Menovsky, J.A. Mydosh, M. Date, J. Phys. Soc. Jpn 59 (1990) 3331. [5] C. Broholm, H. Lin, P.T. Matthews, T.E. Mason, W.J.L. Buyers, M.F. Collins, A.A. Menovsky, J.A. Mydosh, J.K. Kjems, Phys. Rev. B 43 (1991) 12809. [6] Y. Miyako, Transport and Thermal Properties of f-Electron Systems, Plenum, New York, 1993, p. 187. [7] B. Fak, C. Vettier, J. Flouquet, F. Bourdarot, S. Raymond, A. Vernier, P. Lejay, Ph. Boutrouille, N.R. Bernhoeft, S.T. Bramwell, R.A. Fisher, N.E. Phillips, J. Magn. Magn. Mater. 154 (1996) 339. [8] M.B. Maple, J.W. Chen, Y. Dalichaouch, T. Kohara, C. Rossel, M.S. Torikachvili, M.W. McElfresh, J.D. Thompson, Phys. Rev. Lett. 56 (1986) 185. [9] M.W. McElfrsh, J.D. Thompson, J.O. Willis, M.B. Maple, T. Kohara, M.S. Torikachvili, Phys. Rev. B 35 (1987) 43. [10] G.J. Nieuwenhuys, Phys. Rev. B 35 (1987) 5260. [11] R. Konno, Prog. Theor. Phys. 89 (1993) 51. [12] P. Santini, G. Amoretti, Phys. Rev. Lett. 73 (1994) 1027. [13] Y. Miyako, S. Kawarazaki, H. Amitsuka, C.C. Paulsen, K. Hasselbach, J. Appl. Phys. 70 (1991) 5791. [14] A.P. Ramirez, P. Coleman, P. Chandra, E. Bruck, A.A. Menovsky, Z. Fisk, E. Bucher, Phys. Rev. Lett. 68 (1992) 2680. [15] Y. Miyako, H. Amitsuka, S. Kuwai, T. Kasuya, Physica B 186±188 (1993) 236. [16] H. Amitsuka, M. Sato, N. Metoki, M. Yokoyama, K.
[17]
[18]
[19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32]
Kuwahara, S. Sakakibara, H. Morimoto, S. Kawarazaki, Y. Miyako, J.A. Mydosh, Phys. Rev. Lett. 83 (1999) 5114. Y. Miyako, T. Kuwai, T. Taniguchi, S. Kawarazaki, H. Amitsuka, C.C. Paulsen, T. Sakakibara, J. Magn. Magn. Mater. 108 (1992) 190. Y. Miyako, H. Amitsuka, S. Kawarazaki, T. Taniguchi, T. Shikama, Physical Properties of Actinide and Rare Earth Compounds, JJAP Series, Vol. 8, 1993, p. 230 (Jpn. J. Appl. Phys., Tokyo, 1993). K. Marumoto, T. Takeuchi, T. Taniguchi, Y. Miyako, Physica B 206±207 (1995) 519. K. Marumoto, T. Takeuchi, Y. Miyako, Phys. Rev. B 54 (1996) 12194. K. Marumoto, Ph.D. thesis, Osaka University, 1997. K. Yamada, Prog. Theor. Phys. 53 (1975) 970. H. Amitsuka, T. Sakakibara, J. Phys. Soc. Jpn 63 (1994) 736. H. Amitsuka, T. Sakakibara, A. de Visser, F.E. Kayzel, J.J.M. Franse, Physica B 230±232 (1997) 613. M. Yokoyama, H. Amitsuka, K. Kuwahara, A. Okumura, T. Tenya, T. Sakakibara, Physica B 281±282 (2000) 395. F. Lapierre, P. Haen, J. Magn. Magn. Mater. 108 (1992) 167. K. Kadowaki, S.B. Woods, Solid State Commun. 58 (1986) 507. M. Koga, H. Shiba, J. Phys. Soc. Jpn 64 (1995) 4345. M. Koga, H. Shiba, J. Phys. Soc. Jpn 65 (1996) 3007. M. Koga, H. Shiba, J. Phys. Soc. Jpn 66 (1997) 1485. H. Kusunose, J. Phys. Soc. Jpn 67 (1998) 61. Y. Shimizu, O. Sakai, S. Suzuki, J. Phys. Soc. Jpn 67 (1998) 2395.
Solid State Communications 117 (2001) 245±248
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Fermi-liquid behavior of electrical resistivity in the dilute uranium system UxLa12xRu2Si2 K. Marumoto a,*, T. Takeuchi b, Y. Miyako c, M. Ocio d, P. Pari d, J. Hammann d a Department of Applied Physics, Nagoya University, Nagoya 464-8603, Japan Low Temperature Center, Osaka University, Toyonaka 560-0043, Osaka, Japan c Graduate School of Science, Osaka University, Toyonaka 560-0043, Osaka, Japan d Service de Physique de l'Etat CondenseÂ, CEA Saclay, 91191 Gif sur Yvette Cedex, France b
Received 30 August 2000; received in revised form 4 October 2000; accepted 15 October 2000 by H. Akai
Abstract Electrical resistivity measurements have been performed on the dilute uranium compound UxLa12xRu2Si2 x 0:07 with the current along the a and the c axes between 300 K and 28 mK. The electrical resistivity, r , along the a and the c axes decreases as temperature is lowered below 300 K. In the low-temperature region between 7 K and 28 mK, the magnetic contribution of the 5f electron to the resistivity, r m, exhibits the Fermi-liquid behavior with a clear T 2 dependence. The Kadowaki±Woods ratio A5f/g 5f2 is estimated from r m and the speci®c heat data previously reported, and is found to be the same order as that of URu2Si2. This indicates that the enhanced density of states at the Fermi level causes the T 2 dependence of r m in the dilute uranium compound UxLa12xRu2Si2. q 2001 Elsevier Science Ltd. All rights reserved. Keywords: A. Metals; B. Crystal growth; D. Electronic transport; D. Heavy fermions; D. Kondo effects PACS: 72.15.Qm; 75.20.Hr; 71.70.Ch
URu2Si2 is one of the most anomalous heavy-fermion superconductors, because it exhibits the coexistence of a type-I antiferromagnetism TN 17:5 K with an unusual small ordered moment (0.01±0.04 mB) and non-BCS-type superconductivity Tc 1:5 K: Many experimental and theoretical studies have been done extensively to understand this system from various standing points [1±12]. As one of them, the contribution of the quadrupolar coupling between 5f electrons of the uranium atoms was suggested for the phase transition at TN by the study of the non-linear susceptibility [13±15]. A pressure effect on the tiny antiferromagnetic moment was studied by using the elastic neutron scattering [16]. The mechanism of the phase transition at TN is, however, still controversial. It seems that a complete explanation for the experimental results has not been given. Although the crystalline ®eld levels are not so clear as well as the valence state of uranium in URu2Si2, the large * Corresponding author. Tel.: 181-52-789-5165; fax: 181-52789-3712. E-mail address: [email protected] (K. Marumoto).
anisotropy of the susceptibility above 100 K seems to be well explained by the non-Kramers doublet ground state of U 41 ion as in the case for the dilute uranium system UxLa12xRu2Si2 [17±18]. In order to clarify this situation experimentally and to understand the role of crystalline electric ®eld (CEF) splitting, we have carried out the magnetic and speci®c-heat measurements on the dilute uranium system UxLa12xRu2Si2 (x 0:05; 0.07, and 0.15) (the La system) [19±21]. The magnetic and thermodynamic properties at low-temperatures were well explained by the Kondo model. The observation of the enhanced g value meant that the ground state of the 5f electrons is a Kondo singlet state that is described as the Fermi liquid [22]. In contrast with the results of the La system, another dilute uranium system UxTh12xRu2Si2 x # 0:07 (the Th system) shows a ln T dependence in the magnetic susceptibility x , speci®c heat divided by temperature, C/T, and electrical resistivity r [23±24]. These features are understood as a non-Fermi-liquid behavior. The resistivity r of the Th system exhibits a steep decrease as temperature decreases, following ,ln T (1 K , T , 10 K) and ,T 1/2 0:1 K , T , 1 K.
0038-1098/01/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved. PII: S 0038-109 8(00)00439-7
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K. Marumoto et al. / Solid State Communications 117 (2001) 245±248
Fig. 1. Temperature dependence of the electrical resistivities r of U0.07La0.93Ru2Si2 and LaRu2Si2 along the a and the c axes.
For the case of the La system, the results of r have been preliminarily reported [21]. Recently, uranium concentration dependence of r was studied by using UxLa12xRu2Si2 (x 0:03; 0.05, and 0.07) with the current along the a axis between 300 and 1.3 K [25]. However, the measurement below 1 K has not been performed, and the anisotropy of r has not yet been measured so far. In this paper, we report the results of r of UxLa12xRu2Si2 x 0:07 with the current along the a and the c axes between 300 K and 28 mK. The resistivity r of both axes show a clear T 2 dependence in the low-temperature region below 7 K. This Fermi-liquid behavior is consistent with the results of magnetic and speci®c-heat measurements on the La system, exhibiting Kondo screening [20]. The Kadowaki±Woods ratio A5f/g 5f2 is estimated from the 5felectron part of r and the speci®c heat obtained in Ref. [20], and is found to be the same order as that of URu2Si2. The results of r of the La system are also compared with that of the Th system that shows the non-Fermi-liquid behavior. The single crystals UxLa12xRu2Si2 x # 0:07 were prepared by the Czochralski method with a tri-arc furnace. The sample characterizations were performed by using the X-ray powder diffraction and Laue method. The X-ray diffraction experiments con®rmed that all samples show a single phase and crystallize in the ThCr2Si2-type bodycentered tetragonal structure. The single crystals were cut by using a spark erosion cutter. The electrical resistivities were measured in a wide temperature range from 300 K to 28 mK by a standard four-terminal dc method using a dilution refrigerator. While the error of the absolute value in r is 20%, which is mainly due to an estimation error of the dimension, the relative error in one run of measurements is less than 2%. Fig. 1 shows the electrical resistivities r of
U0.07La0.93Ru2Si2 and LaRu2Si2 single crystals along the a and the c axes. In the case of LaRu2Si2, the absolute values of r at 295 K along the a and the c axes are obtained to be 28 and 11 mV cm, and the residual values at 1.8 K along the a and the c axes are 0.64 and 0.28 mV cm, respectively. These values and the overall behavior of the temperature variation are in good agreement with those in the earlier work [26]. In the case of U0.07La0.93Ru2Si2, r along the a axis is larger than that along the c axis. The resistivity r of both axes decreases monotonically as temperature is lowered, and shows a distinct knee-like structure at low temperatures around 18 K. Below 1 K, the data along the a axis is found to be almost constant. There is neither ln T nor T 1/2 temperature dependence of r as observed in the Th system. The resistivity r along the a axis above 1.3 K is consistent with that previously reported for U0.07La0.93Ru2Si2 [25]. The magnetic contribution to the resistivity, r m, is estimated by subtracting the lattice contribution using r for LaRu2Si2. Fig. 2 shows r m for U0.07La0.93Ru2Si2 along the a axis in the logarithmic-temperature scale. The data are normalized for uranium concentration. The data for x 0:03 and 0.05 are taken from Ref. [25] for the comparison. There is a little difference in the absolute values each other, which may be caused by the error of the dimensional estimation as mentioned above, and the error of nominal uranium concentration. In spite of these errors, overall temperature dependences of r m for these compounds, especially below 30 K, are almost the same with each other. The residual resistivity seems to vary linearly as a function of x, and r m is considered to show the single impurity effect with respect to uranium ion. The magnetic resistivity r m decreases as temperature is lowered below 100 K, and is almost constant below 1 K. In Fig. 3 we show the r vs. T 2 plots of U0.07La0.93Ru2Si2 and LaRu2Si2 along the a and c axes in the low-temperature
Fig. 2. Temperature dependence of the magnetic resistivity r m of U0.07La0.93Ru2Si2 along the a axis in the logarithmic-temperature scale. The dashed lines show r m for UxLa12xRu2Si2 x 0:03 and 0.05) along the a axis, which are taken from Ref. [25] for the comparison.
K. Marumoto et al. / Solid State Communications 117 (2001) 245±248
Fig. 3. r vs. T 2 plots of the electrical resistivities of U0.07La0.93Ru2Si2 and LaRu2Si2 along the a and c axes.
region below 10 K. The resistivity r for LaRu2Si2 is almost constant below 10 K, but the resistivity r for U0.07La0.93Ru2Si2 shows a clear T 2 temperature dependence in the low-temperature region below about 7 K, which is commonly observed for r of the heavy-fermion system. Using the ®tting formula of r 0 1 AT 2 for U0.07La0.93Ru2Si2, the values of coef®cient A along the a and the c axes are obtained as 6.6 £ 10 23 and 5.0 £ 10 23 mV cm/K 2, respectively. The A value along the a axis is larger than that along the c axis. The contribution of uranium ion A5f is estimated from r m. The values of A5f along the a and the c axes are found to be 9.4 £ 10 22 and 7.1 £ 10 22 mV cm/ K 2 U, respectively. The value along the a axis is almost the same as those obtained above 1 K for x 0:03; 0.05, and 0.07 by Yokoyama et al. [25]. Below 1 K, we have con®rmed the T 2 dependence in this paper. For comparison with other Fermi-liquid systems, we estimated the Kadowaki±Woods ration A5f/g 5f2 for U0.07La0.93Ru2Si2, where A5f is the coef®cient of the T 2 term of r m and g 5f is the electronic speci®c heat coef®cient per molar uranium. In this estimation, we used g 5f 130 mJ/K 2 U mol reported in the previous papers [20±21]. The values of A5f/g 5f2 along the a and c axes are obtained as 0.56 £ 10 25 and 0.42 £ 10 25 mV cm (U mol K/mJ) 2/U, respectively. These values are the same order as the common value of 1.0 £ 10 25 mV cm (mol K/mJ) 2 for all of the heavy-fermion compounds including URu2Si2 [27]. The similarity of these values between U0.07La0.93Ru2Si2 and URu2Si2 indicates that the Kondo resonance enhances the density of states at the Fermi level and this enhancement contributes the scattering of the conduction electrons, causing the T 2 dependence for r. The T 2 dependence of r in the La system is clearly different from that in the Th system. As mentioned in the
247
preceding paragraph, the Th system shows the temperature dependence for r as ,ln T (1 K , T , 10 K) and ,T 1/2 (0.1 K , T , 1 K). This difference is understood to be caused by the difference of 5f-electron state between the La system and the Th system, and may be explained by the change of the CEF splitting of uranium ions. The La system has the CEF splitting of 60 ^ 6 K between the ground non-Kramers-doublet and the ®rst-excited singlet states [20±21]. On the other hand, the singlet ®rst-excited CEF state in the Th system was suggested to be located at about 4000 K [23]. The different magnitude of the CEF splitting between the ground doublet and the excited singlet states may cause the difference of 5f-electron states between the La system and the Th system [20,21]. The importance of contribution of the excited state for the non-Kramers doublet ground state is predicted by theoretical studies, clarifying that the singlet ®rst-excited CEF state plays an important role in stabilizing the Fermi-liquid state over the non-Fermi-liquid state in the hexagonal crystal structure although in the tetragonal structure it does not work to stabilize the Fermi-liquid state [28±32]. The effect of the CEF splitting of 60 K may be re¯ected in the temperature dependence of r at higher temperatures. As seen in Fig. 1, r of U0.07La0.93Ru2Si2 along the a and c axes show a broad rounded curvature around 200 K. Moreover, Fig. 2 shows a broad maximum in r m for x 0:03; 0.05, and 0.07. Similar behavior has been observed in r of CeRu2Si2, and is attributed to the CEF effect [26]. As also seen in Fig. 1, r of U0.07La0.93Ru2Si2 along both axes show a knee-like structure at around 18 K. This structure were also observed in r for x 0:03 and 0.05 [25]. The origin of the knee-like structures is not known so far, but this anomaly might be related with the CEF effect mentioned above, or with an anomaly associated with the phase transition at TN observed in URu2Si2. In the latter case, a single-site mechanism is important to bring about the phase transition at TN in URu2Si2. The further measurements of r in the magnetic ®eld seems to be needed to obtain more information about the transport properties observed in the La system.
Acknowledgements This work was supported in part by Grant-in-aid for Scienti®c Research of the Ministry of Education, Science and Culture and by Monbusho International Scienti®c Research Program, Joint Research.
References [1] T.T.M. Palstra, A.A. Menovsky, J. van den Berg, A.J. Dirkmaat, P.H. Kes, G.J. Nieuwenhuys, J.A. Mydosh, Phys. Rev. Lett. 55 (1985) 2727. [2] T.T.M. Palstra, A.A. Menovsky, J.A. Mydosh, Phys. Rev. B 33 (1986) 6527.
248
K. Marumoto et al. / Solid State Communications 117 (2001) 245±248
[3] W. Schlabitz, J. Baumann, B. Pollit, U. Rauchschwalbe, H.M. Mayer, U. Ahlheim, C.D. Bredl, Z. Phys. B 62 (1986) 171. [4] K. Sugiyama, H. Fuke, K. Kindo, K. Shimohata, A.A. Menovsky, J.A. Mydosh, M. Date, J. Phys. Soc. Jpn 59 (1990) 3331. [5] C. Broholm, H. Lin, P.T. Matthews, T.E. Mason, W.J.L. Buyers, M.F. Collins, A.A. Menovsky, J.A. Mydosh, J.K. Kjems, Phys. Rev. B 43 (1991) 12809. [6] Y. Miyako, Transport and Thermal Properties of f-Electron Systems, Plenum, New York, 1993, p. 187. [7] B. Fak, C. Vettier, J. Flouquet, F. Bourdarot, S. Raymond, A. Vernier, P. Lejay, Ph. Boutrouille, N.R. Bernhoeft, S.T. Bramwell, R.A. Fisher, N.E. Phillips, J. Magn. Magn. Mater. 154 (1996) 339. [8] M.B. Maple, J.W. Chen, Y. Dalichaouch, T. Kohara, C. Rossel, M.S. Torikachvili, M.W. McElfresh, J.D. Thompson, Phys. Rev. Lett. 56 (1986) 185. [9] M.W. McElfrsh, J.D. Thompson, J.O. Willis, M.B. Maple, T. Kohara, M.S. Torikachvili, Phys. Rev. B 35 (1987) 43. [10] G.J. Nieuwenhuys, Phys. Rev. B 35 (1987) 5260. [11] R. Konno, Prog. Theor. Phys. 89 (1993) 51. [12] P. Santini, G. Amoretti, Phys. Rev. Lett. 73 (1994) 1027. [13] Y. Miyako, S. Kawarazaki, H. Amitsuka, C.C. Paulsen, K. Hasselbach, J. Appl. Phys. 70 (1991) 5791. [14] A.P. Ramirez, P. Coleman, P. Chandra, E. Bruck, A.A. Menovsky, Z. Fisk, E. Bucher, Phys. Rev. Lett. 68 (1992) 2680. [15] Y. Miyako, H. Amitsuka, S. Kuwai, T. Kasuya, Physica B 186±188 (1993) 236. [16] H. Amitsuka, M. Sato, N. Metoki, M. Yokoyama, K.
[17]
[18]
[19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32]
Kuwahara, S. Sakakibara, H. Morimoto, S. Kawarazaki, Y. Miyako, J.A. Mydosh, Phys. Rev. Lett. 83 (1999) 5114. Y. Miyako, T. Kuwai, T. Taniguchi, S. Kawarazaki, H. Amitsuka, C.C. Paulsen, T. Sakakibara, J. Magn. Magn. Mater. 108 (1992) 190. Y. Miyako, H. Amitsuka, S. Kawarazaki, T. Taniguchi, T. Shikama, Physical Properties of Actinide and Rare Earth Compounds, JJAP Series, Vol. 8, 1993, p. 230 (Jpn. J. Appl. Phys., Tokyo, 1993). K. Marumoto, T. Takeuchi, T. Taniguchi, Y. Miyako, Physica B 206±207 (1995) 519. K. Marumoto, T. Takeuchi, Y. Miyako, Phys. Rev. B 54 (1996) 12194. K. Marumoto, Ph.D. thesis, Osaka University, 1997. K. Yamada, Prog. Theor. Phys. 53 (1975) 970. H. Amitsuka, T. Sakakibara, J. Phys. Soc. Jpn 63 (1994) 736. H. Amitsuka, T. Sakakibara, A. de Visser, F.E. Kayzel, J.J.M. Franse, Physica B 230±232 (1997) 613. M. Yokoyama, H. Amitsuka, K. Kuwahara, A. Okumura, T. Tenya, T. Sakakibara, Physica B 281±282 (2000) 395. F. Lapierre, P. Haen, J. Magn. Magn. Mater. 108 (1992) 167. K. Kadowaki, S.B. Woods, Solid State Commun. 58 (1986) 507. M. Koga, H. Shiba, J. Phys. Soc. Jpn 64 (1995) 4345. M. Koga, H. Shiba, J. Phys. Soc. Jpn 65 (1996) 3007. M. Koga, H. Shiba, J. Phys. Soc. Jpn 66 (1997) 1485. H. Kusunose, J. Phys. Soc. Jpn 67 (1998) 61. Y. Shimizu, O. Sakai, S. Suzuki, J. Phys. Soc. Jpn 67 (1998) 2395.