- Email: [email protected]
Specific heat of Ce3Bi4Pt3 at 60 T
Physica B 294}295 (2001) 240}244
Speci"c heat of Ce Bi Pt at 60 T
M. Jaime *, R. Movshovich , G.R. Stewart, W.P. Beyermann, M. Gomez Berisso, P.C. Can"eld Los Alamos National Laboratory, Los Alamos, NM 87545, USA University of Florida, Gainesville, FL 32611-8440, USA University of California, Riverside, CA 980-8577, USA Centro Ato& mico Bariloche, Bariloche, 8400 RN, Argentina Iowa State University, Ames, IA 50011, USA
Abstract Kondo insulator materials such as CeRhAs, CeRhSb, YbB , Ce Bi Pt , and SmB , are 3d, 4f and 5f intermetallic compounds. At high temperatures they behave like metals but a gap in the conduction band opens at the Fermi energy as the temperature is reduced. It has been proposed that the formation of the low-temperature gap is a consequence of the hybridization between the conduction band and the f-electron levels. If this is true, Kondo metal physics should be recovered when the gap is closed at high magnetic "elds. We report here speci"c heat results of Ce Bi Pt in DC and pulsed magnetic "elds up to 60 T. We see evidence for the reduction of the gap in 18 T and a rapid increase of the Sommerfeld coe$cient C /¹ in 30 T'H'40 T. Numerical results and the analysis of the data with the Coq& 2 blin}Schrie!er model prove a "eld-induced Kondo insulator-to-Kondo metal crossover. 2001 Elsevier Science B.V. All rights reserved. Keywords: Speci"c heat; Kondo insulators; Pulsed magnetic "elds
1. Introduction Kondo insulator materials (KI) [1] have attracted considerable attention during recent years in part because the synthesis of quality single-crystal samples has allowed the measurement of the temperature dependence of the spin gap with highresolution photoemission techniques [2}4]. Another way to study the nature of the spin gap in KI is to measure the magnetic "eld dependence of their transport properties. The electrical resistivity [5,6],
* Corresponding author. E-mail address: [email protected] (M. Jaime).
Hall e!ect [6], and magnetization [7] were measured in cubic Ce Bi Pt (Fig. 1) as a function of the magnetic "eld in DC and capacitor-bank driven pulsed magnets. A rather large negative magnetoresistance was observed at low temperatures in single-crystal samples together with a recovery of the charge carrier concentration in "elds up to 60 T, evidence that strongly suggest that the spin gap can be closed in such magnetic "elds [6]. More recent low-temperature/high-"eld magnetization measurements in powder samples showed no indication of insulator-to-metal crossover [7], in apparent contradiction with transport results. Measurements of the speci"c heat in magnetic "eld directly probe the evolution of the excitation
0921-4526/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 0 ) 0 0 6 5 0 - 5
M. Jaime et al. / Physica B 294}295 (2001) 240}244
241
Fig. 2. Speci"c heat measured in zero "eld (䢇) and 18 T (䉭) in a superconducting magnet. Top-left inset: band diagram described in the text. Bottom-right inset: "eld dependent contribution to the heat capacity in 18 T, versus temperature.
2. Low magnetic 5elds
Fig. 1. The crystal structure of Ce Bi Pt is cubic (bcc, Y Sb Au structure), each unit cell is composed of four formula units.
spectrum, and Kondo gap in particular, and can therefore provide the key to understanding the physical origins of the very distinctive ground-state properties of KI. The 60 T long pulse (60 TLP) magnet, at the National High Magnetic Field Laboratory-Los Alamos Pulsed Field Laboratory, is driven by a 1.4 GW synchronous power generator and produces a #at top "eld for a period of 100# ms at 60 T and for longer time at lower "elds. We have built a calorimeter out of plastic materials that enables us to perform heat capacity measurements at temperatures between 1.4 and 20 K in this magnet. We have also used the relaxation technique to measure the heat capacity of our sample at higher temperatures in a 20 T superconducting magnet, in a standard calorimeter.
The presence of the spin gap in Ce Bi Pt should be evident in the temperature dependence of the speci"c heat at temperatures comparable to the gap as the conduction band is depopulated, if the phonon contribution is not too large and the sensitivity of the experiment is high. For magnetic "elds available in DC superconducting (SC) magnets, we expect the value of the gap to remain high, and therefore, the experimental temperature range must be extended to values comparable with the zero"eld gap, i.e. 50 K. A thermal relaxation technique was chosen to measure the speci"c heat of Ce Bi Pt in a SC magnet at temperatures be tween 4 and 60 K. The results of this experiment, C/¹ versus ¹, in zero "eld and 18 T, are displayed in Fig. 2 where, we see that C/¹ increases and peaks as the temperature is risen. We have subtracted the zero "eld speci"c heat (C ) from the speci"c heat in 18 T (C ) to remove the non-"eld-dependent com ponents, such as the phonon contribution, and divided the di!erence by the temperature. In this way, we obtain the di!erential Sommerfeld coe$cient (¹) and display it in the inset (bottom right) of Fig. 2. is rapidly suppressed below 30 K, and remains "nite at lower temperatures. This indicates reduction in the magnitude of the
242
M. Jaime et al. / Physica B 294}295 (2001) 240}244
gap due to the applied magnetic "eld, and a concomitant loss of charge carriers as the temperature is reduced. Clearly 18 T is not enough to completely close the gap. We performed a computation for the speci"c heat of a system with narrow valence and conduction bands of equal width BW"600 K, separated by a gap , and a narrower impurity band of width w"100 K centered at the chemical potential , see inset in Fig. 2. In this model it was assumed that valence and conduction bands accommodate 2N electrons each and the impurity band accommodates 0.01N, where N is the number of Ce atoms in the sample. We performed the computation in two cases, with a fully open gap and with a reduced gap. The di!erence between calculated speci"c heat in each case (with "155 K and 220 K simulating 18 T and zero "eld, respectively) is the solid line in the inset of Fig. 2. The quantitative agreement with the data is very good. The value obtained in our "t for the zero "eld gap is an excellent agreement with the spin gap "250 K observed in optical experi ments [8]. The gap value that we use to "t the speci"c heat results is larger than the gap observed in transport experiments. This discrepancy can be reconciled if one takes into account the impurity band centered at the chemical potential. Indeed, if the states in this band are localized or have small mobility at low temperatures, the conductivity of the material is very poor, as observed [5,6]. As the temperature is increased the relevant energy scale is the di!erence between the top of the impurity band and the bottom of the conduction band, which is 60 K in our "t and in a very good agreement with the transport experiments.
3. High magnetic 5elds For high enough magnetic "elds the spin gap should be totally suppressed and as the sample changes from insulator to metal, the low-temperature speci"c heat should change accordingly. During the magnetic "eld pulse produced by the 60 TLP magnet, which lasts for about 2 s, our plastic calorimeter can be regarded as thermally isolated, i.e. in an adiabatic condition. We used a heat pulse method, where a known amount of heat is
Fig. 3. (A) Temperature of the sample, magnetic "eld and heater voltage as a function of time during a speci"c heat measurement at 40 T. (B) Four temperature traces, corresponding to four magnetic "eld pulses required to measure at 60 T the same amount of speci"c heat data obtained at 40 T (A).
delivered to the calorimeter using a chip resistor, to measure the heat capacity of #ux-grown singlecrystal samples of Ce Bi Pt . The data collected during a typical experiment on Ce Bi Pt is dis played in Fig. 3, which shows that the calorimeter comes to thermal equilibrium both before and after the heat pulse is delivered within the magnetic "eld plateau. The temperature is measured during the entire "eld pulse with a Cernox威 bare chip resistance thermometer, provided by Lakeshore Inc., previously calibrated in DC "eld up to 30 T and in pulsed "elds up to 60 T. The heat capacity of the sample is determined as the ratio of the heat delivered to the sample to the change in its temperature due to the heat pulse.
M. Jaime et al. / Physica B 294}295 (2001) 240}244
Fig. 4. Speci"c heat divided by the temperature versus ¹ for magnetic di!erent "elds obtained in the 60 TLP magnet.
The results of the direct measurements of the speci"c heat C(¹) of a 44.85 mg single-crystal sample of Ce Bi Pt , performed in magnetic "elds up to 60 T, are displayed in Fig. 4. C(¹)/¹ is linear in ¹ and the zero temperature extrapolation in& creases from about 18 mJ/mol K in zero "eld to close to 60 mJ/mol K in 60 T. All molar heat capacities reported here are per formula unit. The observed increase in the heat capacity in "elds equal to or larger than 40 T is in very good agreement with the reversible temperature change (due to magnetocaloric e!ect) observed during the ramp portions of the magnetic "eld pulse, con"rming that entropy is conserved during the magnetic "eld pulse. Indeed, the temperature of every magnetic system in adiabatic conditions changes, when the magnetic "eld changes. The temperature change is given by Maxwell's equation [R¹/RH] "!(¹/C )[RM/R¹] , 1 & & which predicts [R¹/RH] (0 for Ce Bi Pt Both 1 the sign and magnitude of the experimentally observed temperature change are in agreement with the behavior predicted by this equation. In order to verify the calibration of our thermometry and correct operation of the calorimeter we have also measured the speci"c heat of a 303 mg Si single crystal, where we do not expect any variation of speci"c heat with magnetic "eld. The magnetic "eld e!ect observed for this sample (Fig. 5) is no larger than 0.1% per Tesla, in accord with expectation.
243
Fig. 5. Speci"c heat divided by the temperature versus ¹ in a Si single crystal. No change is observed in 60 T.
4. Discussion In order to tell, whether our results indicate the recovery of the metallic Kondo state in high "elds, the increase in observed in Ce Bi Pt needs to & be put in perspective. Magnetic susceptibility and the high temperature neutron quasielastic line width measurements can be used to estimate a zero-"eld Kondo temperature of ¹ " ) 240}320 K. In turn, the Sommerfeld coe$cient for a metal with such ¹ can be estimated using the ) expression for a single-impurity Kondo system [9] "3;1.29 R/6¹ "53}70 mJ/mol K. Taking ) into account the e!ect of the applied magnetic "elds our estimate is slightly reduced to "51}66 mJ/mol K. Hundley et al. [10] have measured the compound La Bi Pt in zero "eld and obtained "27 mJ/mol K. This value in * La Bi Pt , an isostructural metal where electronic correlations are absent, should be our lower bound limit in the high "eld metallized state of Ce Bi Pt . Fig. 6 shows , for Ce Bi Pt sample C2, in & magnetic "elds up to 60 T. The values for were & obtained from a single parameter "t of the form C(¹)" ¹# ¹ (where ¹ and ¹ are the & & & & electronic and phononic contributions respectively), with the coe$cient of the lattice term "xed & to its zero-"eld value. We see a monotonous increase in as the magnetic "eld increases. The & result of the "t suggests a saturation at a value of
244
M. Jaime et al. / Physica B 294}295 (2001) 240}244
know about Kondo insulators from transport measurements in high "elds, and will aid in the construction of a theoretical model for this important class of strongly correlated compounds. Additionally, in the course of these studies we have demonstrated the feasibility of direct speci"c heat measurements in the extreme conditions of the pulsed magnetic "elds produced by the 60 TLP magnet at the NHMFL-LANL [11,12]. Acknowledgements
Fig. 6. Sommerfeld coe$cient versus magnetic "eld. &
"62$3 mJ/mol K above 40 T. The strong en& hancement of from its zero-"eld value and the & quantitative agreement with the estimate based on ¹ for a metallic ground state of Ce Bi Pt prove ) that we indeed crossed the Kondo insulator-toKondo metal phase boundary. Our results support the conclusions arrived from the analysis of magnetoresistance and Hall e!ect data [6]. The observed increase in the Sommerfeld coe$cient, re#ecting a substantial increase in the density of states at the Fermi energy E at high $ "elds, should be detected with magnetization measurements. The magnetization data [7] is not understood at present. New magnetization measurements in single-crystal samples have con"rmed previous results in powder samples. 5. Conclusions These results of thermodynamic measurements add new and essential information to what we
We thank Z. Fisk, J.D. Thompson and P. Schlottmann for discussions; J. Kim for his assistance with the thermometry calibration in the 30 T d.c. magnet at the NHMFL/Tallahassee; D. Rickel, C. Mielke, J. Betts, J. Schillig, M. Gordon, J. Sims and M. Pacheco for technical assistance and operation of the 60 TLP magnet. References [1] G. Aeppli, Z. Fisk, Comment. Cond. Matt. Phys. 16 (1992) 155. [2] H. Kumigashira et al., Phys. Rev. Lett. 82 (1999) 1943. [3] T. Susaki et al., Phys. Rev. Lett. 82 (1999) 992. [4] K. Breuer et al., Euro. Phys. Lett. 41 (1998) 565. [5] M.F. Hundley et al., Physica B 186}188 (1993) 425. [6] G.S. Boebinger et al., Physica B 211 (1995) 227. [7] R. Modler et al., in: Z. Fisk, L. Gor'kov, R. Schrie!er (Eds.), Physical Phenomena at High Magnetic Fields } III, World Scienti"c, Singapore, 1999, p. 154. [8] L. Degiorgi, Rev. Mod. Phys. 71 (1999) 687. [9] V.T. Rajan, Phys. Rev. Lett. 51 (1983) 308. [10] M.F. Hundley et al., Phys. Rev. B 42 (1990) 6842. [11] M. Jaime et al., in: Z. Fisk, L. Gor'kov, R. Schrie!er (Eds.), Physical Phenomena at High Magnetic Fields } III, World Scienti"c, Singapore, 1999, p. 148. [12] M. Jaime et al., Nature 405 (2000) 160.
Speci"c heat of Ce Bi Pt at 60 T
M. Jaime *, R. Movshovich , G.R. Stewart, W.P. Beyermann, M. Gomez Berisso, P.C. Can"eld Los Alamos National Laboratory, Los Alamos, NM 87545, USA University of Florida, Gainesville, FL 32611-8440, USA University of California, Riverside, CA 980-8577, USA Centro Ato& mico Bariloche, Bariloche, 8400 RN, Argentina Iowa State University, Ames, IA 50011, USA
Abstract Kondo insulator materials such as CeRhAs, CeRhSb, YbB , Ce Bi Pt , and SmB , are 3d, 4f and 5f intermetallic compounds. At high temperatures they behave like metals but a gap in the conduction band opens at the Fermi energy as the temperature is reduced. It has been proposed that the formation of the low-temperature gap is a consequence of the hybridization between the conduction band and the f-electron levels. If this is true, Kondo metal physics should be recovered when the gap is closed at high magnetic "elds. We report here speci"c heat results of Ce Bi Pt in DC and pulsed magnetic "elds up to 60 T. We see evidence for the reduction of the gap in 18 T and a rapid increase of the Sommerfeld coe$cient C /¹ in 30 T'H'40 T. Numerical results and the analysis of the data with the Coq& 2 blin}Schrie!er model prove a "eld-induced Kondo insulator-to-Kondo metal crossover. 2001 Elsevier Science B.V. All rights reserved. Keywords: Speci"c heat; Kondo insulators; Pulsed magnetic "elds
1. Introduction Kondo insulator materials (KI) [1] have attracted considerable attention during recent years in part because the synthesis of quality single-crystal samples has allowed the measurement of the temperature dependence of the spin gap with highresolution photoemission techniques [2}4]. Another way to study the nature of the spin gap in KI is to measure the magnetic "eld dependence of their transport properties. The electrical resistivity [5,6],
* Corresponding author. E-mail address: [email protected] (M. Jaime).
Hall e!ect [6], and magnetization [7] were measured in cubic Ce Bi Pt (Fig. 1) as a function of the magnetic "eld in DC and capacitor-bank driven pulsed magnets. A rather large negative magnetoresistance was observed at low temperatures in single-crystal samples together with a recovery of the charge carrier concentration in "elds up to 60 T, evidence that strongly suggest that the spin gap can be closed in such magnetic "elds [6]. More recent low-temperature/high-"eld magnetization measurements in powder samples showed no indication of insulator-to-metal crossover [7], in apparent contradiction with transport results. Measurements of the speci"c heat in magnetic "eld directly probe the evolution of the excitation
0921-4526/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 0 ) 0 0 6 5 0 - 5
M. Jaime et al. / Physica B 294}295 (2001) 240}244
241
Fig. 2. Speci"c heat measured in zero "eld (䢇) and 18 T (䉭) in a superconducting magnet. Top-left inset: band diagram described in the text. Bottom-right inset: "eld dependent contribution to the heat capacity in 18 T, versus temperature.
2. Low magnetic 5elds
Fig. 1. The crystal structure of Ce Bi Pt is cubic (bcc, Y Sb Au structure), each unit cell is composed of four formula units.
spectrum, and Kondo gap in particular, and can therefore provide the key to understanding the physical origins of the very distinctive ground-state properties of KI. The 60 T long pulse (60 TLP) magnet, at the National High Magnetic Field Laboratory-Los Alamos Pulsed Field Laboratory, is driven by a 1.4 GW synchronous power generator and produces a #at top "eld for a period of 100# ms at 60 T and for longer time at lower "elds. We have built a calorimeter out of plastic materials that enables us to perform heat capacity measurements at temperatures between 1.4 and 20 K in this magnet. We have also used the relaxation technique to measure the heat capacity of our sample at higher temperatures in a 20 T superconducting magnet, in a standard calorimeter.
The presence of the spin gap in Ce Bi Pt should be evident in the temperature dependence of the speci"c heat at temperatures comparable to the gap as the conduction band is depopulated, if the phonon contribution is not too large and the sensitivity of the experiment is high. For magnetic "elds available in DC superconducting (SC) magnets, we expect the value of the gap to remain high, and therefore, the experimental temperature range must be extended to values comparable with the zero"eld gap, i.e. 50 K. A thermal relaxation technique was chosen to measure the speci"c heat of Ce Bi Pt in a SC magnet at temperatures be tween 4 and 60 K. The results of this experiment, C/¹ versus ¹, in zero "eld and 18 T, are displayed in Fig. 2 where, we see that C/¹ increases and peaks as the temperature is risen. We have subtracted the zero "eld speci"c heat (C ) from the speci"c heat in 18 T (C ) to remove the non-"eld-dependent com ponents, such as the phonon contribution, and divided the di!erence by the temperature. In this way, we obtain the di!erential Sommerfeld coe$cient (¹) and display it in the inset (bottom right) of Fig. 2. is rapidly suppressed below 30 K, and remains "nite at lower temperatures. This indicates reduction in the magnitude of the
242
M. Jaime et al. / Physica B 294}295 (2001) 240}244
gap due to the applied magnetic "eld, and a concomitant loss of charge carriers as the temperature is reduced. Clearly 18 T is not enough to completely close the gap. We performed a computation for the speci"c heat of a system with narrow valence and conduction bands of equal width BW"600 K, separated by a gap , and a narrower impurity band of width w"100 K centered at the chemical potential , see inset in Fig. 2. In this model it was assumed that valence and conduction bands accommodate 2N electrons each and the impurity band accommodates 0.01N, where N is the number of Ce atoms in the sample. We performed the computation in two cases, with a fully open gap and with a reduced gap. The di!erence between calculated speci"c heat in each case (with "155 K and 220 K simulating 18 T and zero "eld, respectively) is the solid line in the inset of Fig. 2. The quantitative agreement with the data is very good. The value obtained in our "t for the zero "eld gap is an excellent agreement with the spin gap "250 K observed in optical experi ments [8]. The gap value that we use to "t the speci"c heat results is larger than the gap observed in transport experiments. This discrepancy can be reconciled if one takes into account the impurity band centered at the chemical potential. Indeed, if the states in this band are localized or have small mobility at low temperatures, the conductivity of the material is very poor, as observed [5,6]. As the temperature is increased the relevant energy scale is the di!erence between the top of the impurity band and the bottom of the conduction band, which is 60 K in our "t and in a very good agreement with the transport experiments.
3. High magnetic 5elds For high enough magnetic "elds the spin gap should be totally suppressed and as the sample changes from insulator to metal, the low-temperature speci"c heat should change accordingly. During the magnetic "eld pulse produced by the 60 TLP magnet, which lasts for about 2 s, our plastic calorimeter can be regarded as thermally isolated, i.e. in an adiabatic condition. We used a heat pulse method, where a known amount of heat is
Fig. 3. (A) Temperature of the sample, magnetic "eld and heater voltage as a function of time during a speci"c heat measurement at 40 T. (B) Four temperature traces, corresponding to four magnetic "eld pulses required to measure at 60 T the same amount of speci"c heat data obtained at 40 T (A).
delivered to the calorimeter using a chip resistor, to measure the heat capacity of #ux-grown singlecrystal samples of Ce Bi Pt . The data collected during a typical experiment on Ce Bi Pt is dis played in Fig. 3, which shows that the calorimeter comes to thermal equilibrium both before and after the heat pulse is delivered within the magnetic "eld plateau. The temperature is measured during the entire "eld pulse with a Cernox威 bare chip resistance thermometer, provided by Lakeshore Inc., previously calibrated in DC "eld up to 30 T and in pulsed "elds up to 60 T. The heat capacity of the sample is determined as the ratio of the heat delivered to the sample to the change in its temperature due to the heat pulse.
M. Jaime et al. / Physica B 294}295 (2001) 240}244
Fig. 4. Speci"c heat divided by the temperature versus ¹ for magnetic di!erent "elds obtained in the 60 TLP magnet.
The results of the direct measurements of the speci"c heat C(¹) of a 44.85 mg single-crystal sample of Ce Bi Pt , performed in magnetic "elds up to 60 T, are displayed in Fig. 4. C(¹)/¹ is linear in ¹ and the zero temperature extrapolation in& creases from about 18 mJ/mol K in zero "eld to close to 60 mJ/mol K in 60 T. All molar heat capacities reported here are per formula unit. The observed increase in the heat capacity in "elds equal to or larger than 40 T is in very good agreement with the reversible temperature change (due to magnetocaloric e!ect) observed during the ramp portions of the magnetic "eld pulse, con"rming that entropy is conserved during the magnetic "eld pulse. Indeed, the temperature of every magnetic system in adiabatic conditions changes, when the magnetic "eld changes. The temperature change is given by Maxwell's equation [R¹/RH] "!(¹/C )[RM/R¹] , 1 & & which predicts [R¹/RH] (0 for Ce Bi Pt Both 1 the sign and magnitude of the experimentally observed temperature change are in agreement with the behavior predicted by this equation. In order to verify the calibration of our thermometry and correct operation of the calorimeter we have also measured the speci"c heat of a 303 mg Si single crystal, where we do not expect any variation of speci"c heat with magnetic "eld. The magnetic "eld e!ect observed for this sample (Fig. 5) is no larger than 0.1% per Tesla, in accord with expectation.
243
Fig. 5. Speci"c heat divided by the temperature versus ¹ in a Si single crystal. No change is observed in 60 T.
4. Discussion In order to tell, whether our results indicate the recovery of the metallic Kondo state in high "elds, the increase in observed in Ce Bi Pt needs to & be put in perspective. Magnetic susceptibility and the high temperature neutron quasielastic line width measurements can be used to estimate a zero-"eld Kondo temperature of ¹ " ) 240}320 K. In turn, the Sommerfeld coe$cient for a metal with such ¹ can be estimated using the ) expression for a single-impurity Kondo system [9] "3;1.29 R/6¹ "53}70 mJ/mol K. Taking ) into account the e!ect of the applied magnetic "elds our estimate is slightly reduced to "51}66 mJ/mol K. Hundley et al. [10] have measured the compound La Bi Pt in zero "eld and obtained "27 mJ/mol K. This value in * La Bi Pt , an isostructural metal where electronic correlations are absent, should be our lower bound limit in the high "eld metallized state of Ce Bi Pt . Fig. 6 shows , for Ce Bi Pt sample C2, in & magnetic "elds up to 60 T. The values for were & obtained from a single parameter "t of the form C(¹)" ¹# ¹ (where ¹ and ¹ are the & & & & electronic and phononic contributions respectively), with the coe$cient of the lattice term "xed & to its zero-"eld value. We see a monotonous increase in as the magnetic "eld increases. The & result of the "t suggests a saturation at a value of
244
M. Jaime et al. / Physica B 294}295 (2001) 240}244
know about Kondo insulators from transport measurements in high "elds, and will aid in the construction of a theoretical model for this important class of strongly correlated compounds. Additionally, in the course of these studies we have demonstrated the feasibility of direct speci"c heat measurements in the extreme conditions of the pulsed magnetic "elds produced by the 60 TLP magnet at the NHMFL-LANL [11,12]. Acknowledgements
Fig. 6. Sommerfeld coe$cient versus magnetic "eld. &
"62$3 mJ/mol K above 40 T. The strong en& hancement of from its zero-"eld value and the & quantitative agreement with the estimate based on ¹ for a metallic ground state of Ce Bi Pt prove ) that we indeed crossed the Kondo insulator-toKondo metal phase boundary. Our results support the conclusions arrived from the analysis of magnetoresistance and Hall e!ect data [6]. The observed increase in the Sommerfeld coe$cient, re#ecting a substantial increase in the density of states at the Fermi energy E at high $ "elds, should be detected with magnetization measurements. The magnetization data [7] is not understood at present. New magnetization measurements in single-crystal samples have con"rmed previous results in powder samples. 5. Conclusions These results of thermodynamic measurements add new and essential information to what we
We thank Z. Fisk, J.D. Thompson and P. Schlottmann for discussions; J. Kim for his assistance with the thermometry calibration in the 30 T d.c. magnet at the NHMFL/Tallahassee; D. Rickel, C. Mielke, J. Betts, J. Schillig, M. Gordon, J. Sims and M. Pacheco for technical assistance and operation of the 60 TLP magnet. References [1] G. Aeppli, Z. Fisk, Comment. Cond. Matt. Phys. 16 (1992) 155. [2] H. Kumigashira et al., Phys. Rev. Lett. 82 (1999) 1943. [3] T. Susaki et al., Phys. Rev. Lett. 82 (1999) 992. [4] K. Breuer et al., Euro. Phys. Lett. 41 (1998) 565. [5] M.F. Hundley et al., Physica B 186}188 (1993) 425. [6] G.S. Boebinger et al., Physica B 211 (1995) 227. [7] R. Modler et al., in: Z. Fisk, L. Gor'kov, R. Schrie!er (Eds.), Physical Phenomena at High Magnetic Fields } III, World Scienti"c, Singapore, 1999, p. 154. [8] L. Degiorgi, Rev. Mod. Phys. 71 (1999) 687. [9] V.T. Rajan, Phys. Rev. Lett. 51 (1983) 308. [10] M.F. Hundley et al., Phys. Rev. B 42 (1990) 6842. [11] M. Jaime et al., in: Z. Fisk, L. Gor'kov, R. Schrie!er (Eds.), Physical Phenomena at High Magnetic Fields } III, World Scienti"c, Singapore, 1999, p. 148. [12] M. Jaime et al., Nature 405 (2000) 160.