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Competition between intrasite and intersite interactions in U-doped YRu2Si2
Physica B 259—261 (1999) 260—262
Competition between intrasite and intersite interactions in U-doped YRu Si M. Oc\ ko *, J.-G. Park, I. Aviani Institute of Physics, Bijenic\ ka c. 46, POB 304, 10000 Zagreb, Croatia Department of Physics, Inha University, Inchon 402-751, South Korea
Abstract We report electrical resistivity and thermopower measurements of two alloy of the (U Y )Ru Si alloy system V \V (x"0.08 and 0.30). For x"0.08, we have found evidences for impurity Kondo scattering from the lowest lying CEF levels with ¹ "10 K. The sample with x"0.3 shows an antiferromagnetic transition at 15.3 K. Thereby we conclude ) that the two energy scales, ¹ and ¹ , are close to and compete against each other in dilute U of YRu Si . 1999 ) 00)7 Elsevier Science B.V. All rights reserved. Keywords: U alloys; CEF levels; Kondo scattering; Antiferromagnetic transition
Recent magnetisation, susceptibility and specific heat investigations of U La Ru Si (x)0.15) [1] show V \V evidences for both crystalline electric field (CEF) splitting and Kondo interaction with ¹ "10 K. It is pointed, ) too, that the RKKY interaction is not important for the formation of the ground state up to x"0.15. Here we present our transport properties investigations of uranium in other nonmagnetic host, YRu Si with the same ThCr Si structure as URu Si . For this work, we used samples prepared in the same conditions as before [2]. All the samples used for this work were found to be single phase. In Fig. 1 we show magnetic resistivity for x"0.08 and 0.30: o (¹)"o(¹)!o (¹)!o ; o(¹) is the measured
resistivity, o phonon contribution to the resistivity (here represented by the resistivity of YRu Si ) and o the residual resistivity, respectively. The gross feature of o (¹) for x"0.08 is similar to
the o (¹) of U Th Ru Si (x(0.08) [3]. However,
V \V although o (¹) decreases as ¹ decreases, which is in an
accordance with the theoretical predictions of the two
* Corresponding author. Tel.: 38-51-4680211; fax: 38-514680399; e-mail: [email protected].
channel Kondo effect [4], we cannot fit our result to #ln ¹ behaviour as one can in U Th Ru Si V \V (x(0.08) case [3]. The disagreement at higher temperatures might be due to a wrong determination of the absolute values of the resistivities of the alloy as well as of the YRu Si compound that is used for the phonon subtraction. However, at the low temperatures, where the phonons are not so important, the behaviour of the o (¹) is not in accordance with #ln ¹ behaviour, too.
In a recent theoretical work [5] one discusses the role of CEF excitations on the stability of nonfermi liquid over the fermi liquid behaviour in the two channel Kondo effect [5]. Our result at high temperatures does suggest that the origin of the o (¹) are CEF excitations. How ever, in this theoretical work [5] as well as in the before mentioned one [4] the resistivity is not calculated. Therefore, in order to account the CEF contribution to the resistivity we use a standard way of calculation of this contribution [6]. We have assumed in our calculations that the excited CEF levels of U ion are at 20, 66 and 150 K: these values are taken directly from the inelastic neutron data on (U Y )Ru Si [7]. Fig. 1 does show an agreement between the theory, o (¹), and experiment, & o (¹), at the high temperatures. Although o (¹) for
x"0.3 cannot be fitted satisfactorily by the theory, it is
0921-4526/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 1 0 8 8 - 6
M. Oc\ ko et al. / Physica B 259–261 (1999) 260—262
Fig. 1. Magnetic resistivity for U Y Ru Si : circles for V \V x"0.3 and squares for x"0.08. Line is curve fitting result, o (¹). (a) Thermopower data for x"0.08 (square). Kondo-like & contribution to the resistivity, Do (¹) for x"0.08 (dots). (b) ) Derivative of resistivity: for x"0.3 (line) and x"0.08 (dots). Vertical arrows in the figure indicate antiferromagnetic transition for x"0.3.
clear that a main contribution to o (¹) comes from
scattering by excited CEF levels, too. High-temperature thermopower data for x"0.08, shown in inset (a) (open squares), can be well explained by a model [8] which is equivalent to the model used for the description of the resistivity. According to the theory [8], a maximum in thermopower due to CEF excitations appears at D/3, where D is the overall CEF level splitting. Since our thermopower results show a maximum around 50 K, the overall splitting for x"0.08 is expected to be D"150 K. This value is indeed in a good agreement with the CEF model we used for the analysis of the resistivity. At low temperatures the relative deep thermopower for x"0.08 strongly suggests the presence of the Kondo scattering. When we apply a theoretical model of Bricks et al. [9] to evaluate the Kondo temperature for x"0.08, we get ¹ of 9$1 K. This ¹ value may change when ) ) one uses a realistic model appropriate for U ion once it becomes available. However, the resistivity neither shows the usual !ln ¹ temperature dependence inherent to the ordinary Kondo scattering, nor #ln ¹ as we discussed above. Besides, we also do not observe a Fermi liquid ¹ behaviour. On the other hand, a close inspection of the results shows a disagreement between the used theory [6] and experiment at low temperatures. It is interesting that this difference, *o (¹)"o (¹)!o (¹), does show an ordi)
& nary Kondo-like upturn as ¹ tends to zero (see inset
261
(a) — closed circles). According to the theoretical work in Ref. [9], which puts ¹ at about 60% of the saturation ) value of resistivity, Kondo temperature for x"0.08 is ¹ "11$1 K. We are not able to explain why *o (¹), ) ) after reaching the saturation value, tends to zero for the lowest temperatures. We can only note that the same effect is observed for Ce La B Kondo alloy [10]. One can argue that the difference, *o (¹), is only an ) artefact of the measurements, or an effect which is not inherent to the U doped alloys. However, as the first, the inset (a) to Fig. 1 strongly suggests that the *o (T) has ) the same origin as the low-temperature thermopower as it appears in the temperature region where the thermopower has a minimum. As the second, the depth of the thermopower minimum suggests that the origin of the thermopower is inherent to U doped nonmagnetic matrix. One could also argue that this contribution is too small to be a Kondo contribution. The slope of the Kondo upturn is proportional to Jn(E ), where n(E ) is $ $ the density of states of the conduction electrons at the Fermi level. In the case of a small number of conduction electrons the Kondo slope is small. The small number of conduction electrons can, in the other hand, explain a relatively large value of the measured spin disorder resistivity [6]. We can also add that for the higher concentrations of U (0.5)x)0.66) the ordinary Kondolike upturn in the resistivity can be seen in the direct measurements. However, it is very small, too. In inset (b) we show *o/*¹ for the two alloys. As one can see, the two alloys have different temperature behaviours between 10 and 50 K. For x"0.3 there is a double-peaked structure, which is absent in the x"0.08 sample. It is very interesting to note that such a doublepeaked structure, certainly much more pronounced, was found near the antiferromagnetic (AF) transition of URu Si and of U Y Ru Si for x'0.30. Therefore, V \V we think that x"0.3 sample has an AF transition around 15 K. In summary, our study of U doped YRu Si alloys well agrees with the previous (U,La)Ru Si results [1] in that CEF excitations are necessary to explain the properties of dilute U samples and that the Kondo interaction is also present in dilute U alloys. Besides, we found that RKKY interaction stabilises AF transition at 15 K for x"0.3. Work at Inha University was supported by the Ministry of Education, Korea (BSRI-97-2430).
References [1] K. Marumoto, T. Takeuchi, Y. Miyako, Phys. Rev. B 54 (1996) 12194. [2] J.-G. Park, Ph.D. Thesis, University of London, 1993 (unpublished).
262
M. Oc\ ko et al. / Physica B 259–261 (1999) 260—262
[3] H. Amitsuka, T. Sakakibara, J. Phys. Soc. 63 (1994) 736. [4] O. Sakai, S. Suzuki, Y. Shimizu, H. Kusunose, M. Miyake, Solid. State. Commun. 99 (1996) 461. [5] M. Koga, H. Shiba, J. Phys. Soc. 66 (1997) 1485. [6] Z. Kletovski, J. Phys.: Condens. Matter 5 (1993) 8955.
[7] J.-G. Park, to be published. [8] I. Peschel, P. Fulde, Z. Physik 238 (1970) 99. [9] N.E. Bickers, D.L. Cox, J.W. Wilkins, Phys. Rev. B 36 (1987) 2036. [10] S. Nakamura, O. Suzuki, T. Goto, S. Sakatsume, T. Matsumura, S. Kunii, J. Phys. Soc. Japan 66, 552 (1997).
Competition between intrasite and intersite interactions in U-doped YRu Si M. Oc\ ko *, J.-G. Park, I. Aviani Institute of Physics, Bijenic\ ka c. 46, POB 304, 10000 Zagreb, Croatia Department of Physics, Inha University, Inchon 402-751, South Korea
Abstract We report electrical resistivity and thermopower measurements of two alloy of the (U Y )Ru Si alloy system V \V (x"0.08 and 0.30). For x"0.08, we have found evidences for impurity Kondo scattering from the lowest lying CEF levels with ¹ "10 K. The sample with x"0.3 shows an antiferromagnetic transition at 15.3 K. Thereby we conclude ) that the two energy scales, ¹ and ¹ , are close to and compete against each other in dilute U of YRu Si . 1999 ) 00)7 Elsevier Science B.V. All rights reserved. Keywords: U alloys; CEF levels; Kondo scattering; Antiferromagnetic transition
Recent magnetisation, susceptibility and specific heat investigations of U La Ru Si (x)0.15) [1] show V \V evidences for both crystalline electric field (CEF) splitting and Kondo interaction with ¹ "10 K. It is pointed, ) too, that the RKKY interaction is not important for the formation of the ground state up to x"0.15. Here we present our transport properties investigations of uranium in other nonmagnetic host, YRu Si with the same ThCr Si structure as URu Si . For this work, we used samples prepared in the same conditions as before [2]. All the samples used for this work were found to be single phase. In Fig. 1 we show magnetic resistivity for x"0.08 and 0.30: o (¹)"o(¹)!o (¹)!o ; o(¹) is the measured
resistivity, o phonon contribution to the resistivity (here represented by the resistivity of YRu Si ) and o the residual resistivity, respectively. The gross feature of o (¹) for x"0.08 is similar to
the o (¹) of U Th Ru Si (x(0.08) [3]. However,
V \V although o (¹) decreases as ¹ decreases, which is in an
accordance with the theoretical predictions of the two
* Corresponding author. Tel.: 38-51-4680211; fax: 38-514680399; e-mail: [email protected].
channel Kondo effect [4], we cannot fit our result to #ln ¹ behaviour as one can in U Th Ru Si V \V (x(0.08) case [3]. The disagreement at higher temperatures might be due to a wrong determination of the absolute values of the resistivities of the alloy as well as of the YRu Si compound that is used for the phonon subtraction. However, at the low temperatures, where the phonons are not so important, the behaviour of the o (¹) is not in accordance with #ln ¹ behaviour, too.
In a recent theoretical work [5] one discusses the role of CEF excitations on the stability of nonfermi liquid over the fermi liquid behaviour in the two channel Kondo effect [5]. Our result at high temperatures does suggest that the origin of the o (¹) are CEF excitations. How ever, in this theoretical work [5] as well as in the before mentioned one [4] the resistivity is not calculated. Therefore, in order to account the CEF contribution to the resistivity we use a standard way of calculation of this contribution [6]. We have assumed in our calculations that the excited CEF levels of U ion are at 20, 66 and 150 K: these values are taken directly from the inelastic neutron data on (U Y )Ru Si [7]. Fig. 1 does show an agreement between the theory, o (¹), and experiment, & o (¹), at the high temperatures. Although o (¹) for
x"0.3 cannot be fitted satisfactorily by the theory, it is
0921-4526/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 1 0 8 8 - 6
M. Oc\ ko et al. / Physica B 259–261 (1999) 260—262
Fig. 1. Magnetic resistivity for U Y Ru Si : circles for V \V x"0.3 and squares for x"0.08. Line is curve fitting result, o (¹). (a) Thermopower data for x"0.08 (square). Kondo-like & contribution to the resistivity, Do (¹) for x"0.08 (dots). (b) ) Derivative of resistivity: for x"0.3 (line) and x"0.08 (dots). Vertical arrows in the figure indicate antiferromagnetic transition for x"0.3.
clear that a main contribution to o (¹) comes from
scattering by excited CEF levels, too. High-temperature thermopower data for x"0.08, shown in inset (a) (open squares), can be well explained by a model [8] which is equivalent to the model used for the description of the resistivity. According to the theory [8], a maximum in thermopower due to CEF excitations appears at D/3, where D is the overall CEF level splitting. Since our thermopower results show a maximum around 50 K, the overall splitting for x"0.08 is expected to be D"150 K. This value is indeed in a good agreement with the CEF model we used for the analysis of the resistivity. At low temperatures the relative deep thermopower for x"0.08 strongly suggests the presence of the Kondo scattering. When we apply a theoretical model of Bricks et al. [9] to evaluate the Kondo temperature for x"0.08, we get ¹ of 9$1 K. This ¹ value may change when ) ) one uses a realistic model appropriate for U ion once it becomes available. However, the resistivity neither shows the usual !ln ¹ temperature dependence inherent to the ordinary Kondo scattering, nor #ln ¹ as we discussed above. Besides, we also do not observe a Fermi liquid ¹ behaviour. On the other hand, a close inspection of the results shows a disagreement between the used theory [6] and experiment at low temperatures. It is interesting that this difference, *o (¹)"o (¹)!o (¹), does show an ordi)
& nary Kondo-like upturn as ¹ tends to zero (see inset
261
(a) — closed circles). According to the theoretical work in Ref. [9], which puts ¹ at about 60% of the saturation ) value of resistivity, Kondo temperature for x"0.08 is ¹ "11$1 K. We are not able to explain why *o (¹), ) ) after reaching the saturation value, tends to zero for the lowest temperatures. We can only note that the same effect is observed for Ce La B Kondo alloy [10]. One can argue that the difference, *o (¹), is only an ) artefact of the measurements, or an effect which is not inherent to the U doped alloys. However, as the first, the inset (a) to Fig. 1 strongly suggests that the *o (T) has ) the same origin as the low-temperature thermopower as it appears in the temperature region where the thermopower has a minimum. As the second, the depth of the thermopower minimum suggests that the origin of the thermopower is inherent to U doped nonmagnetic matrix. One could also argue that this contribution is too small to be a Kondo contribution. The slope of the Kondo upturn is proportional to Jn(E ), where n(E ) is $ $ the density of states of the conduction electrons at the Fermi level. In the case of a small number of conduction electrons the Kondo slope is small. The small number of conduction electrons can, in the other hand, explain a relatively large value of the measured spin disorder resistivity [6]. We can also add that for the higher concentrations of U (0.5)x)0.66) the ordinary Kondolike upturn in the resistivity can be seen in the direct measurements. However, it is very small, too. In inset (b) we show *o/*¹ for the two alloys. As one can see, the two alloys have different temperature behaviours between 10 and 50 K. For x"0.3 there is a double-peaked structure, which is absent in the x"0.08 sample. It is very interesting to note that such a doublepeaked structure, certainly much more pronounced, was found near the antiferromagnetic (AF) transition of URu Si and of U Y Ru Si for x'0.30. Therefore, V \V we think that x"0.3 sample has an AF transition around 15 K. In summary, our study of U doped YRu Si alloys well agrees with the previous (U,La)Ru Si results [1] in that CEF excitations are necessary to explain the properties of dilute U samples and that the Kondo interaction is also present in dilute U alloys. Besides, we found that RKKY interaction stabilises AF transition at 15 K for x"0.3. Work at Inha University was supported by the Ministry of Education, Korea (BSRI-97-2430).
References [1] K. Marumoto, T. Takeuchi, Y. Miyako, Phys. Rev. B 54 (1996) 12194. [2] J.-G. Park, Ph.D. Thesis, University of London, 1993 (unpublished).
262
M. Oc\ ko et al. / Physica B 259–261 (1999) 260—262
[3] H. Amitsuka, T. Sakakibara, J. Phys. Soc. 63 (1994) 736. [4] O. Sakai, S. Suzuki, Y. Shimizu, H. Kusunose, M. Miyake, Solid. State. Commun. 99 (1996) 461. [5] M. Koga, H. Shiba, J. Phys. Soc. 66 (1997) 1485. [6] Z. Kletovski, J. Phys.: Condens. Matter 5 (1993) 8955.
[7] J.-G. Park, to be published. [8] I. Peschel, P. Fulde, Z. Physik 238 (1970) 99. [9] N.E. Bickers, D.L. Cox, J.W. Wilkins, Phys. Rev. B 36 (1987) 2036. [10] S. Nakamura, O. Suzuki, T. Goto, S. Sakatsume, T. Matsumura, S. Kunii, J. Phys. Soc. Japan 66, 552 (1997).