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Anomalous low-energy excitation in CeAuAl3
Physica B 281&282 (2000) 110}111
Anomalous low-energy excitation in CeAuAl Y. Aoki*, S.R. Saha, T.D. Matsuda, H. Sugawara, H. Sato Department of Physics, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji, Tokyo 192-0397, Japan
Abstract We have measured speci"c heat C on a single-crystalline sample of CeAuAl down to 0.1 K in magnetic "elds up to 8 T. In all the measured "elds, a power-law temperature dependence was observed at low temperatures expressed by C"a¹ . Above 1 T, the coe$cient a decreases approximately as B\ with increasing "eld, indicating the existence of a scaling relation of CJ(¹/B) . This "nding suggests that the anomalous low-energy excitation observed in the zero-"eld antiferromagnetically ordered state survives even in the almost perfectly polarized state of 8 T. 2000 Elsevier Science B.V. All rights reserved. Keywords: Antiferromagnetic ordering; Speci"c heat; CeAuAl
In the recent studies on the highly correlated electron systems related to non-Fermi liquid behaviors, anomalous low-energy excitations discovered around the magnetic critical points have been one of the major topics. For these investigations, low-temperature speci"c heat measurement has been well recognized as a powerful tool. Using this method, we have reported interesting "ndings on CeNi Ge and CeRu Si [1,2]. Here we report on an anomalous low-energy excitation evidenced in the speci"c heat of CeAuAl , in which the competition between Kondo e!ect and RKKY interaction has been inferred [3]. From the magnetic susceptibility and speci"c heat measurements on polycrystalline samples, it has been shown that CeAuAl undergoes an antiferromagnetic (AF) transition at ¹ "1.32 K [3]. Far below ¹ , the , , speci"c heat C contains a large linear-in-¹ term with the coe$cient c"227 mJ/K mol. The electrical resistivity o(¹) is expressed by o(¹)"o #A¹ with a large factor A"5.0 l) cm/K. According to these "ndings, there is the presence of moderately mass-enhanced electrons even in the magnetically ordered state. Recent success of single-crystal growth has clari"ed some aspects of the
* Corresponding author. Tel.: #81-426-772487; fax: 81-42677-2483. E-mail address: [email protected] (Y. Aoki)
anisotropy in the magnetic and transport properties [4]. o for the current J along c-axis of the tetragonal crystal lattice shows small increase below ¹ while o for J//a, axis decreases steeply, indicating the formation of a superzone gap along c-axis. In this paper, we report on the speci"c heat measurements on the same single crystal grown by Czochralski pulling method in a tetra-arc furnace (see Ref. [4]). The speci"c heat was measured by a quasi-adiabatic heat pulse method using a dilution refrigerator equipped with a superconducting magnet. Fig. 1 shows the temperature dependence of speci"c heat (C) on the CeAuAl single crystal for several mag netic "elds applied along the a-axis. In zero "eld, C shows a cusp structure around 1 K indicating AF transition although the shape of this anomaly is broader than the one reported for a polycrystalline sample [3]. Below the NeH el temperature (¹ ), C can be expressed as a¹L with , n"1.70$0.05. In 0.5 T, the cusp structure is no longer visible and the shape has changed to a broad peak centered around 1.1 K. In the lower-temperature region, the contribution of ¹ term remains although the value of a is suppressed slightly. With further increase in the magnetic "eld to above 1 T, the broad peak shifts to higher temperatures and its shape gradually approaches that of the Schottky peak for a doublet state. The peak height of 3.66 J/Kmol for B"6 T is very close to 3.65 J/Kmol expected for the doublet Schottky peak. This peak is attributable to the Zeeman splitting of the doublet crystalline-"eld (CF) ground state. In the CF
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 0 0 6 - 6
Y. Aoki et al. / Physica B 281&282 (2000) 110}111
Fig. 1. Temperature dependence of speci"c heat of CeAuAl for several values of the applied magnetic "eld (B//a-xis). The broken line for B"8 T represents the ¹ temperature dependence. Upturn observed below 0.5 K for B'2 T is the nuclear Zeeman contribution.
level scheme determined by the anisotropy of the magnetic susceptibility [4], the ground state of the 4f magnetic moment is J "$1/2 and the "rst excited state is X located &60 K above. Assuming that the energy splitting of the ground state can be expressed by 2g1J 2k B, V where g and k represent Lande g factor and the Bohr magneton, 1J 2 is estimated to be 1.85 from V the C(¹) curve for B"6 T. This is not far from the expected value of 1J 2"1.5 for the J "$ ground V X state. Surprisingly, the ¹ term still remains above 1 T at the lower-temperature side of the Schottky peak, although the coe$cient a decreases rapidly. This term can be seen even in 8 T, suggesting that the anomalous low-energy excitation observed in the zero-"eld AF state survives even in the almost perfectly polarized state of 8 T. The "eld dependence of a is shown in Fig. 2. a does not depend on "eld below about 0.6 T and decreases rapidly in higher "elds. Note that the "eld dependence of a in the high-"eld region can be expressed simply as aJB\ . Above 0.6 T, the power-law "eld dependence of a indicates the existence of a scaling relation expressed by
¹ C"a , B
111
Fig. 2. Magnetic "eld dependence of a de"ned by C"a¹ . The two broken lines represent the zero-"eld value of a and aJB\ .
adened Schottky peak in our sample rules out the distribution of the CF parameters among Ce ions. From the Al nuclear magnetic resonance (NMR) study [7], the Ce magnetic moments is estimated to be reduced by &25% at 50 mK, most probably due to Kondo screening. Therefore, the ¹ term in C might be related to the Kondo e!ect although the temperature dependence is unusual. Even if a distribution of the Kondo temperature among Ce ions [8] is assumed, the ¹ term cannot be explained. Since the NMR study also suggests that the magnetic structure of the ordered state is of a simple spiral type along c-axis [7], the low-energy magnon excitation should be taken into account as another factor. In high "elds, the short-range excitation originating from the same anisotropic RKKY interaction as in the AF state could play a dominant role in the ¹ term. In order to clarify this issue, inelastic neutron scattering experiment is desired paying attention to the sample dependence.
Acknowledgements We thank Dr. S. Paschen for giving us her data prior to the publication. This work was supported by a Grantin-Aid for Scienti"c Research from the Ministry of Education, Science, Sports and Culture of Japan.
(1)
where a "2.64 (JT /K mol). For a polycrystalline sample, a di!erent exponent for the power-law temperature dependence (¹ ) has been observed between ¹ and &¹ /10 in zero "eld [5]. , , This fact suggests that the low-energy excitation may be sensitive to the sample quality, although site-disorder between Au and Al ions is expected to be small in the BaNiSn -type structure [6], in which the present com pound crystallizes. In fact the observation of the unbro-
References [1] Y. Aoki et al., J. Phys. Soc. Japan 66 (1997) 2993. [2] Y. Aoki et al., J. Magn. Magn. Mater. 177}181 (1998) 271. [3] S. Paschen et al., Eur. Phys. J. B 2 (1998) 169. [4] H. Sugawara et al., Physica B 259}261 (1999) 16. [5] S. Paschen, private communication. [6] S.A.M. Mentink et al., J. Appl. Phys. 73 (1993) 6625. [7] P. Vonlanthen et al., Eur. Phys. J. B 7 (1999) 9. [8] O.O. Bernal et al., Phys. Rev. Lett. 75 (1995) 2023.
Anomalous low-energy excitation in CeAuAl Y. Aoki*, S.R. Saha, T.D. Matsuda, H. Sugawara, H. Sato Department of Physics, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji, Tokyo 192-0397, Japan
Abstract We have measured speci"c heat C on a single-crystalline sample of CeAuAl down to 0.1 K in magnetic "elds up to 8 T. In all the measured "elds, a power-law temperature dependence was observed at low temperatures expressed by C"a¹ . Above 1 T, the coe$cient a decreases approximately as B\ with increasing "eld, indicating the existence of a scaling relation of CJ(¹/B) . This "nding suggests that the anomalous low-energy excitation observed in the zero-"eld antiferromagnetically ordered state survives even in the almost perfectly polarized state of 8 T. 2000 Elsevier Science B.V. All rights reserved. Keywords: Antiferromagnetic ordering; Speci"c heat; CeAuAl
In the recent studies on the highly correlated electron systems related to non-Fermi liquid behaviors, anomalous low-energy excitations discovered around the magnetic critical points have been one of the major topics. For these investigations, low-temperature speci"c heat measurement has been well recognized as a powerful tool. Using this method, we have reported interesting "ndings on CeNi Ge and CeRu Si [1,2]. Here we report on an anomalous low-energy excitation evidenced in the speci"c heat of CeAuAl , in which the competition between Kondo e!ect and RKKY interaction has been inferred [3]. From the magnetic susceptibility and speci"c heat measurements on polycrystalline samples, it has been shown that CeAuAl undergoes an antiferromagnetic (AF) transition at ¹ "1.32 K [3]. Far below ¹ , the , , speci"c heat C contains a large linear-in-¹ term with the coe$cient c"227 mJ/K mol. The electrical resistivity o(¹) is expressed by o(¹)"o #A¹ with a large factor A"5.0 l) cm/K. According to these "ndings, there is the presence of moderately mass-enhanced electrons even in the magnetically ordered state. Recent success of single-crystal growth has clari"ed some aspects of the
* Corresponding author. Tel.: #81-426-772487; fax: 81-42677-2483. E-mail address: [email protected] (Y. Aoki)
anisotropy in the magnetic and transport properties [4]. o for the current J along c-axis of the tetragonal crystal lattice shows small increase below ¹ while o for J//a, axis decreases steeply, indicating the formation of a superzone gap along c-axis. In this paper, we report on the speci"c heat measurements on the same single crystal grown by Czochralski pulling method in a tetra-arc furnace (see Ref. [4]). The speci"c heat was measured by a quasi-adiabatic heat pulse method using a dilution refrigerator equipped with a superconducting magnet. Fig. 1 shows the temperature dependence of speci"c heat (C) on the CeAuAl single crystal for several mag netic "elds applied along the a-axis. In zero "eld, C shows a cusp structure around 1 K indicating AF transition although the shape of this anomaly is broader than the one reported for a polycrystalline sample [3]. Below the NeH el temperature (¹ ), C can be expressed as a¹L with , n"1.70$0.05. In 0.5 T, the cusp structure is no longer visible and the shape has changed to a broad peak centered around 1.1 K. In the lower-temperature region, the contribution of ¹ term remains although the value of a is suppressed slightly. With further increase in the magnetic "eld to above 1 T, the broad peak shifts to higher temperatures and its shape gradually approaches that of the Schottky peak for a doublet state. The peak height of 3.66 J/Kmol for B"6 T is very close to 3.65 J/Kmol expected for the doublet Schottky peak. This peak is attributable to the Zeeman splitting of the doublet crystalline-"eld (CF) ground state. In the CF
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 0 0 6 - 6
Y. Aoki et al. / Physica B 281&282 (2000) 110}111
Fig. 1. Temperature dependence of speci"c heat of CeAuAl for several values of the applied magnetic "eld (B//a-xis). The broken line for B"8 T represents the ¹ temperature dependence. Upturn observed below 0.5 K for B'2 T is the nuclear Zeeman contribution.
level scheme determined by the anisotropy of the magnetic susceptibility [4], the ground state of the 4f magnetic moment is J "$1/2 and the "rst excited state is X located &60 K above. Assuming that the energy splitting of the ground state can be expressed by 2g1J 2k B, V where g and k represent Lande g factor and the Bohr magneton, 1J 2 is estimated to be 1.85 from V the C(¹) curve for B"6 T. This is not far from the expected value of 1J 2"1.5 for the J "$ ground V X state. Surprisingly, the ¹ term still remains above 1 T at the lower-temperature side of the Schottky peak, although the coe$cient a decreases rapidly. This term can be seen even in 8 T, suggesting that the anomalous low-energy excitation observed in the zero-"eld AF state survives even in the almost perfectly polarized state of 8 T. The "eld dependence of a is shown in Fig. 2. a does not depend on "eld below about 0.6 T and decreases rapidly in higher "elds. Note that the "eld dependence of a in the high-"eld region can be expressed simply as aJB\ . Above 0.6 T, the power-law "eld dependence of a indicates the existence of a scaling relation expressed by
¹ C"a , B
111
Fig. 2. Magnetic "eld dependence of a de"ned by C"a¹ . The two broken lines represent the zero-"eld value of a and aJB\ .
adened Schottky peak in our sample rules out the distribution of the CF parameters among Ce ions. From the Al nuclear magnetic resonance (NMR) study [7], the Ce magnetic moments is estimated to be reduced by &25% at 50 mK, most probably due to Kondo screening. Therefore, the ¹ term in C might be related to the Kondo e!ect although the temperature dependence is unusual. Even if a distribution of the Kondo temperature among Ce ions [8] is assumed, the ¹ term cannot be explained. Since the NMR study also suggests that the magnetic structure of the ordered state is of a simple spiral type along c-axis [7], the low-energy magnon excitation should be taken into account as another factor. In high "elds, the short-range excitation originating from the same anisotropic RKKY interaction as in the AF state could play a dominant role in the ¹ term. In order to clarify this issue, inelastic neutron scattering experiment is desired paying attention to the sample dependence.
Acknowledgements We thank Dr. S. Paschen for giving us her data prior to the publication. This work was supported by a Grantin-Aid for Scienti"c Research from the Ministry of Education, Science, Sports and Culture of Japan.
(1)
where a "2.64 (JT /K mol). For a polycrystalline sample, a di!erent exponent for the power-law temperature dependence (¹ ) has been observed between ¹ and &¹ /10 in zero "eld [5]. , , This fact suggests that the low-energy excitation may be sensitive to the sample quality, although site-disorder between Au and Al ions is expected to be small in the BaNiSn -type structure [6], in which the present com pound crystallizes. In fact the observation of the unbro-
References [1] Y. Aoki et al., J. Phys. Soc. Japan 66 (1997) 2993. [2] Y. Aoki et al., J. Magn. Magn. Mater. 177}181 (1998) 271. [3] S. Paschen et al., Eur. Phys. J. B 2 (1998) 169. [4] H. Sugawara et al., Physica B 259}261 (1999) 16. [5] S. Paschen, private communication. [6] S.A.M. Mentink et al., J. Appl. Phys. 73 (1993) 6625. [7] P. Vonlanthen et al., Eur. Phys. J. B 7 (1999) 9. [8] O.O. Bernal et al., Phys. Rev. Lett. 75 (1995) 2023.