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Low-temperature thermodynamic properties of CeNi1−xCuxSn
Physica B 291 (2000) 307}309
Low-temperature thermodynamic properties of CeNi Cu Sn \V V R. Vollmer , T. MiokovicH , A. SchroK der , H. v. LoK hneysen *, G.M. Kalvius, Y. Echizen, T. Takabatake Physikalisches Institut, Universita( t Karlsruhe, Engesserstrasse 7, D-76128 Karlsruhe, Germany Physik Department, Technische Universita( t Mu( nchen, D-85747 Garching, Germany Department of Quantum Matter, ADSM, Hiroshima University, Higashi-Hiroshima 739, Japan Received 6 December 1999
Abstract We report on measurements of the speci"c heat C and magnetization M of CeNi Cu Sn single crystals for ¹(1 K. \V V For x"0.05 an increase of C/¹ and M (measured in a magnetic "eld B"0.1 T applied parallel to the a-direction) towards low ¹ down to 0.1 K indicates absence of magnetic order while for x"0.078 a maximum in M is found at ¹ &0.39 K. The magnetization M(B) for both crystals measured at 0.3 K along the a-direction increases linearly up to + 7 T without any indication of saturation except for a small superimposed Brillouin-like feature. The critical concentration for the onset of magnetic order is estimated to x "0.065. 2000 Elsevier Science B.V. All rights reserved. Keywords: Kondo semimetal; Low carrier density Kondo system; Magnetic instability; Magnetic ordering
CeNiSn is a semimetal with a low carrier concentration of &2.5;10 cm\ at temperature ¹+1 K as determined from the Hall e!ect with current parallel to the orthorhombic a-direction and magnetic "eld B"1 T parallel to c [1]. The existence of a (pseudo) gap believed to be responsible for the semimetallic behavior is attributed to the strong hybridization between conduction electrons and Ce 4f electrons. For the purest CeNiSn samples the electrical resistivity o(¹) decreases below 20 K towards lower ¹ for all three crystallographic axes [1]. Upon doping with, e.g., Cu, the resistivity o(¹) of CeNi Cu Sn (x"0.01 and \V V * Corresponding author. Tel.: #49-721-608-3450; fax: #49721-608-6103. E-mail address: [email protected] (H. v. LoK hneysen).
0.05) increases with decreasing ¹ and levels o! below 1 K, reminiscent of the Kondo e!ect, which may arise from resonant Kondo-hole scattering. For x"0.05, this increase is much weaker than for x"0.01, indicating the onset of magnetic correlations. Indeed, previous measurements of the speci"c heat C have shown that CeNi Cu Sn \V V polycrystals order magnetically, with an ordering temperature of 0.86 K for x"0.1 and 3.53 K for x"0.2 as determined from well-de"ned maxima in C/¹ [2]. This evidence for magnetic ordering was supported by the observation of a strong increase of the muon spin relaxation (lSR) rate below these temperatures for the respective alloys [2]. Direct evidence of long-range antiferromagnetic order for x"0.13 below 1.4 K was obtained from elastic neutron scattering [3]. Additionally, an ordering temperature of 0.5 K was inferred from lSR data
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for x"0.08 [4]. Evidence for antiferromagnetic ordering for x"0.06 was obtained from the broadening of the NMR spectrum below 1.3 K [5]. Hence, a nonmagnetic}magnetic transition is expected to occur between x"0.05 and 0.08, with the possibility of non-Fermi-liquid behavior. C/¹ for a x"0.05 polycrystal showed an anomalous upturn down to 0.05 K [2]. In order to investigate this possibility more closely, we started to study systematically the thermodynamic properties of CeNi Cu Sn single crystals grown at the \V V Hiroshima University [6]. Here we report on results for x"0.05 and 0.078. Fig. 1 shows the speci"c heat for x"0.05 plotted as C/¹ versus log ¹. Our single-crystal data con"rm the upturn of C/¹ towards low ¹ previously observed for a polycrystal of the same x [2]. This upturn is well in excess of the constant C/¹ seen for a pure CeNiSn single crystal [2]. The inset of Fig. 1 shows that C/¹ between our lowest measuring temperature of 0.1 and 1 K can be well described by C/¹&¹\?, with a"0.29. Such an algebraic ¹ dependence was predicted [7] for strongly disordered systems near a magnetic instability within a Grif"ths phase scenario initially developed for spin glasses. The value of j"1!a"0.71 is within the range observed in other systems [8]. In an applied magnetic "eld B, the C/¹ upturn is increasingly suppressed. After subtraction of an appropriate hyper"ne contribution, C/¹ in B"6 T is approximately constant below &0.5 K (cf. dashed line in Fig. 1). This suggests the suppression of magnetic #uctuations close to a magnetic instability by a magnetic "eld as previously observed, e.g. for CeCu Au [9]. \V V Fig. 2 shows the temperature dependence of the magnetization M for the same x"0.05 single crystal, divided by the applied "eld B along the adirection. M/B is nearly constant above 1.5 K (note the expanded vertical scale) and rises by 15% below 1 K for ¹P0 in B"0.1 T. In B"1 T the low-¹ rise is largely suppressed. The solid line shows a "t of M/B"s #b/¹ where b is an e!ective Curie constant corresponding to 0.15 mol% of free Ce> moments with k "2.54k . The "t shows sub stantial deviations from the data below 0.5 K, possibly indicating antiferromagnetic correlations. The inset of Fig. 2 shows that M versus B at 0.3 K varies
Fig. 1. Speci"c heat C of CeNi Cu Sn plotted as C/¹ versus log ¹, for magnetic "elds B"0 and 6 T parallel to the a-direction. Inset shows zero-"eld data on a log}log plot.
Fig. 2. Magnetization M of CeNi Cu Sn divided by the applied magnetic "eld B (parallel to the a-direction) versus temperature ¹ for B"0.1 and 1 T. Inset shows M versus B for x"0.05 and 0.078 measured at 0.3 K.
roughly linearly up to 7 T, with no indication of saturation. The small Brillouin-like magnetization which saturates at &1 T is not visible in the data, but can be inferred from dM/dB versus B (not shown).
R. Vollmer et al. / Physica B 291 (2000) 307}309
Fig. 3. Magnetization M of CeNi Cu Sn divided by the applied magnetic "eld B (parallel to the a-direction) versus temperature ¹ for B"0.1 and 1 T. Inset shows magnetic ordering temperature ¹ versus Cu concentration x as inferred from + speci"c heat (x"0.1 and 0.2 [2]), neutron scattering (x"0.13 [8]) and low-"eld magnetization (x"0.078, in this work).
Fig. 3 shows M/B versus ¹ for x"0.078, again with B applied parallel to the a-direction. The maximum at 0.39 K for B"0.1 T indicates magnetic ordering while the ordering temperature is suppressed for B"1 T. The speci"c heat for x"0.078 (not shown) exhibits a kink near 0.45 K, suggesting antiferromagnetic rather than spin-glass ordering. Neutron-scattering experiments are planned to resolve this issue. Although the scatter in the M/B data above the ordering temperature is rather large, a sizeable Curie}Weiss-like contribution to M/B can be ruled out. Rather, M/B is almost independent of ¹, similar to what is observed for x"0.05 in the same ¹ range. Another similarity between
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both concentrations is that M varies again linearly with B, with only a slight larger slope than for x"0.05 (see inset of Fig. 2). This indicates that only a small fraction of Ce> moments is involved in the magnetic ordering. Finally, the inset of Fig. 3 shows the magnetic ordering temperatures ¹ (x) derived from the pre+ vious [2,3] and present studies. ¹ varies roughly + linearly with x and extrapolates to zero for x"0.065, i.e. between the concentrations of the present study. Further work on single crystals closer to the quantum critical point is planned in order to elucidate the physics of the magnetic instability in this interesting semimetallic system. Acknowledgements We thank S. Mock for participating in the initial stages of this study and T. Pietrus for valuable discussions. This work was supported by the Deutsche Forschungsgemeinschaft. References [1] T. Takabatake et al., J. Magn. Magn. Mater. 177}181 (1998) 277. [2] G.M. Kalvius et al., Physica B 230}232 (1997) 655. [3] A. SchroK der et al., Physica B 234}236 (1997) 861. [4] A. BruK ckl et al., Physica B 240 (1997) 199. [5] K. Nakamura et al., Phys. Rev. B 53 (1996) 6385. [6] G. Nakamoto et al., J. Phys. Soc. Japan 64 (1995) 4834. [7] A.H. Castro Neto et al., Phys. Rev. Lett. 81 (1998) 3531. [8] M.C. de Andrade et al., Phys. Rev. Lett. 81 (1998) 5620. [9] H. v. LoK hneysen et al., Phys. Rev. Lett. 72 (1994) 3262.
Low-temperature thermodynamic properties of CeNi Cu Sn \V V R. Vollmer , T. MiokovicH , A. SchroK der , H. v. LoK hneysen *, G.M. Kalvius, Y. Echizen, T. Takabatake Physikalisches Institut, Universita( t Karlsruhe, Engesserstrasse 7, D-76128 Karlsruhe, Germany Physik Department, Technische Universita( t Mu( nchen, D-85747 Garching, Germany Department of Quantum Matter, ADSM, Hiroshima University, Higashi-Hiroshima 739, Japan Received 6 December 1999
Abstract We report on measurements of the speci"c heat C and magnetization M of CeNi Cu Sn single crystals for ¹(1 K. \V V For x"0.05 an increase of C/¹ and M (measured in a magnetic "eld B"0.1 T applied parallel to the a-direction) towards low ¹ down to 0.1 K indicates absence of magnetic order while for x"0.078 a maximum in M is found at ¹ &0.39 K. The magnetization M(B) for both crystals measured at 0.3 K along the a-direction increases linearly up to + 7 T without any indication of saturation except for a small superimposed Brillouin-like feature. The critical concentration for the onset of magnetic order is estimated to x "0.065. 2000 Elsevier Science B.V. All rights reserved. Keywords: Kondo semimetal; Low carrier density Kondo system; Magnetic instability; Magnetic ordering
CeNiSn is a semimetal with a low carrier concentration of &2.5;10 cm\ at temperature ¹+1 K as determined from the Hall e!ect with current parallel to the orthorhombic a-direction and magnetic "eld B"1 T parallel to c [1]. The existence of a (pseudo) gap believed to be responsible for the semimetallic behavior is attributed to the strong hybridization between conduction electrons and Ce 4f electrons. For the purest CeNiSn samples the electrical resistivity o(¹) decreases below 20 K towards lower ¹ for all three crystallographic axes [1]. Upon doping with, e.g., Cu, the resistivity o(¹) of CeNi Cu Sn (x"0.01 and \V V * Corresponding author. Tel.: #49-721-608-3450; fax: #49721-608-6103. E-mail address: [email protected] (H. v. LoK hneysen).
0.05) increases with decreasing ¹ and levels o! below 1 K, reminiscent of the Kondo e!ect, which may arise from resonant Kondo-hole scattering. For x"0.05, this increase is much weaker than for x"0.01, indicating the onset of magnetic correlations. Indeed, previous measurements of the speci"c heat C have shown that CeNi Cu Sn \V V polycrystals order magnetically, with an ordering temperature of 0.86 K for x"0.1 and 3.53 K for x"0.2 as determined from well-de"ned maxima in C/¹ [2]. This evidence for magnetic ordering was supported by the observation of a strong increase of the muon spin relaxation (lSR) rate below these temperatures for the respective alloys [2]. Direct evidence of long-range antiferromagnetic order for x"0.13 below 1.4 K was obtained from elastic neutron scattering [3]. Additionally, an ordering temperature of 0.5 K was inferred from lSR data
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 2 2 8 2 - 6
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R. Vollmer et al. / Physica B 291 (2000) 307}309
for x"0.08 [4]. Evidence for antiferromagnetic ordering for x"0.06 was obtained from the broadening of the NMR spectrum below 1.3 K [5]. Hence, a nonmagnetic}magnetic transition is expected to occur between x"0.05 and 0.08, with the possibility of non-Fermi-liquid behavior. C/¹ for a x"0.05 polycrystal showed an anomalous upturn down to 0.05 K [2]. In order to investigate this possibility more closely, we started to study systematically the thermodynamic properties of CeNi Cu Sn single crystals grown at the \V V Hiroshima University [6]. Here we report on results for x"0.05 and 0.078. Fig. 1 shows the speci"c heat for x"0.05 plotted as C/¹ versus log ¹. Our single-crystal data con"rm the upturn of C/¹ towards low ¹ previously observed for a polycrystal of the same x [2]. This upturn is well in excess of the constant C/¹ seen for a pure CeNiSn single crystal [2]. The inset of Fig. 1 shows that C/¹ between our lowest measuring temperature of 0.1 and 1 K can be well described by C/¹&¹\?, with a"0.29. Such an algebraic ¹ dependence was predicted [7] for strongly disordered systems near a magnetic instability within a Grif"ths phase scenario initially developed for spin glasses. The value of j"1!a"0.71 is within the range observed in other systems [8]. In an applied magnetic "eld B, the C/¹ upturn is increasingly suppressed. After subtraction of an appropriate hyper"ne contribution, C/¹ in B"6 T is approximately constant below &0.5 K (cf. dashed line in Fig. 1). This suggests the suppression of magnetic #uctuations close to a magnetic instability by a magnetic "eld as previously observed, e.g. for CeCu Au [9]. \V V Fig. 2 shows the temperature dependence of the magnetization M for the same x"0.05 single crystal, divided by the applied "eld B along the adirection. M/B is nearly constant above 1.5 K (note the expanded vertical scale) and rises by 15% below 1 K for ¹P0 in B"0.1 T. In B"1 T the low-¹ rise is largely suppressed. The solid line shows a "t of M/B"s #b/¹ where b is an e!ective Curie constant corresponding to 0.15 mol% of free Ce> moments with k "2.54k . The "t shows sub stantial deviations from the data below 0.5 K, possibly indicating antiferromagnetic correlations. The inset of Fig. 2 shows that M versus B at 0.3 K varies
Fig. 1. Speci"c heat C of CeNi Cu Sn plotted as C/¹ versus log ¹, for magnetic "elds B"0 and 6 T parallel to the a-direction. Inset shows zero-"eld data on a log}log plot.
Fig. 2. Magnetization M of CeNi Cu Sn divided by the applied magnetic "eld B (parallel to the a-direction) versus temperature ¹ for B"0.1 and 1 T. Inset shows M versus B for x"0.05 and 0.078 measured at 0.3 K.
roughly linearly up to 7 T, with no indication of saturation. The small Brillouin-like magnetization which saturates at &1 T is not visible in the data, but can be inferred from dM/dB versus B (not shown).
R. Vollmer et al. / Physica B 291 (2000) 307}309
Fig. 3. Magnetization M of CeNi Cu Sn divided by the applied magnetic "eld B (parallel to the a-direction) versus temperature ¹ for B"0.1 and 1 T. Inset shows magnetic ordering temperature ¹ versus Cu concentration x as inferred from + speci"c heat (x"0.1 and 0.2 [2]), neutron scattering (x"0.13 [8]) and low-"eld magnetization (x"0.078, in this work).
Fig. 3 shows M/B versus ¹ for x"0.078, again with B applied parallel to the a-direction. The maximum at 0.39 K for B"0.1 T indicates magnetic ordering while the ordering temperature is suppressed for B"1 T. The speci"c heat for x"0.078 (not shown) exhibits a kink near 0.45 K, suggesting antiferromagnetic rather than spin-glass ordering. Neutron-scattering experiments are planned to resolve this issue. Although the scatter in the M/B data above the ordering temperature is rather large, a sizeable Curie}Weiss-like contribution to M/B can be ruled out. Rather, M/B is almost independent of ¹, similar to what is observed for x"0.05 in the same ¹ range. Another similarity between
309
both concentrations is that M varies again linearly with B, with only a slight larger slope than for x"0.05 (see inset of Fig. 2). This indicates that only a small fraction of Ce> moments is involved in the magnetic ordering. Finally, the inset of Fig. 3 shows the magnetic ordering temperatures ¹ (x) derived from the pre+ vious [2,3] and present studies. ¹ varies roughly + linearly with x and extrapolates to zero for x"0.065, i.e. between the concentrations of the present study. Further work on single crystals closer to the quantum critical point is planned in order to elucidate the physics of the magnetic instability in this interesting semimetallic system. Acknowledgements We thank S. Mock for participating in the initial stages of this study and T. Pietrus for valuable discussions. This work was supported by the Deutsche Forschungsgemeinschaft. References [1] T. Takabatake et al., J. Magn. Magn. Mater. 177}181 (1998) 277. [2] G.M. Kalvius et al., Physica B 230}232 (1997) 655. [3] A. SchroK der et al., Physica B 234}236 (1997) 861. [4] A. BruK ckl et al., Physica B 240 (1997) 199. [5] K. Nakamura et al., Phys. Rev. B 53 (1996) 6385. [6] G. Nakamoto et al., J. Phys. Soc. Japan 64 (1995) 4834. [7] A.H. Castro Neto et al., Phys. Rev. Lett. 81 (1998) 3531. [8] M.C. de Andrade et al., Phys. Rev. Lett. 81 (1998) 5620. [9] H. v. LoK hneysen et al., Phys. Rev. Lett. 72 (1994) 3262.