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Evolution of calorimetric, magnetic and transport properties of UxTh1−xBe13 (0.64 ≤ x ≤ 1) solid solutions
ELSEVIER
Physica B 223&224 (1996) 464 466
Evolution of calorimetric, magnetic and transport properties of UxThl-xBe13 (0.64 < x <_ 1) solid solutions F.G. Aliev 1, H. E1 Mfarrej, S. Vieira, R. Villar* Dpto Fisica de la Materia Condensada, C-Ill, Universidad Autonoma de Madrid, 28049, Madrid, Spain
Abstract We have recently found that Uo.9Tho.lBel3 displays a non-Fermi liquid ground state which is consistent with predictions of the quadrupolar Kondo effect (QKE). We report the evolution of transport, calorimetric and magnetic properties of U~Thl xBe13 (0.64 ___x < 1) solid solutions. The magnetoresistance of Uo.9Tho.lBe13 is compared with those of UBei3 and Uo.64Tho.36Bei3. We present the first experimental study of the Hall effect in the heavy fermion compound with a non-Fermi liquid ground state, with a drastic reduction of the small field Hall resistivity in the QKE state. The field dependence is opposite to those found previously for Kondo lattices.
The search for the theoretical and experimental realization of a non-Fermi liquid (NFL) ground state in strongly correlated electron systems has attracted much attention since the discovery of marginal Fermi liquid behaviour in the new oxide superconductors I-l]. After Nozieres and Blandin predicted [2] the existence of a non-Fermi liquid fixed point in the "overscreened" multichannel Kondo model, the realization of the ground state corresponding to a specific case (two-channel, spiniz Kondo) was proposed [-3] and recently observed [-4] for electron-assisted tunnelling between two-level systems. Another important possibility of experimental observation of two-channel (electric quadrupolar) Kondo effect was predicted by Cox [5] to clarify the origin of heavy fermions in the U-based compounds. Experimental support of this suggestion found recently in U~Y 1 ~Pd3(x _< 0.2) [6] and in some other compounds [-7] is not completely evident because the temperature dependences of the resistivity disagrees with the predicted x f T behaviour
[-8]. * Corresponding author. Also at: Department of Physics, Moscow State University, 119899 Moscow, Russian Federation.
We review here the low-temperature properties of Uo.9Tho.lBel3 where a non-Fermi liquid ground state observed in the specific heat and the magnetic susceptibility, is complemented for the first time by the predicted temperature dependence of the electrical resistivity. In Uo.9Tho.lBe~3 we have previously reported a nonanalytic (logarithmic versus T ) increase of the molar electronic heat capacity Ce/T in the temperature range 0.8 6 K [10]. This behaviour reflects the formation of a N F L ground state. A magnetic field of 8 T produces a small (about 10%) decrease of CU T for T < 0.8 K. The UBe13 sample shows a sharp superconducting transition with an onset of 0.89 K and a width of about 0.05 K. The magnetic susceptibility of the Uo.gTho.xBex3 compound in the temperature interval (1.7 < T < 10K) displays a temperature dependence Z = Z0(1 - A~-T) [11] corresponding to Q K E [12]. The temperature dependence of the electrical resistivity in the range 0.45 < T < 6 K is described by the asymptotic behaviour: p ~po + BxfT with B~40(2) ×10 6QcmK-1/2 and po~17(l) × 10 6 ~ c m [17]. The x / T law of p(T) and z ( T ) is suppressed in Uo.64Tho.36Be13. According to current theories, the logarithmic divergence of the linear term in the specific heat may be
0921-4526/96/$15.00 ~( 1996 Elsevier Science B.V. All rights reserved PII S092 1 - 4 5 2 6 ( 9 6 ) 0 0 1 4 9 - 4
465
F.G. Aliev et al. / Physica B 223&224 (1996) 464 466
understood in one of three ways: (i) a manifestation of the magnetic two-channel Kondo effect (TCKE) [-2, 15], (ii) as a possible realization of the quadrupolar TCKE with U atoms in the nonmagnetic ground state, the so-called quadrupolar Kondo effect (QKE) [-5] or (iii) as being due to the presence of a second-order magnetic phase transition at T = 0 K [13]. Substitution of Th for U in UxThl xBel3 has been shown to depress the superconducting critical temperature Tc which vanishes near x ~ 0.93, with some type of magnetic order below T~ for 0.96 < x < 0.98 [14]. This magnetic region of the T - x phase diagram lies relatively far from x = 0.9 in which we observe NFL behaviour. For the magnetic TCKE (i), theoretical calculations of the heat capacity in a magnetic field show a dramatic evolution toward the normal Fermi liquid behaviour [15]. The QKE, originally developed [-5] to describe the low-temperature properties of UBe13 is, in our opinion, the most suitable to describe our results. The important aspect of this approach is the realization of the nonmagnetic doublet F3 in the ground state of U-atom while local quadrupolar moments create an effective "spin-½". For this reason a weak magnetic field dependence of the low-temperature heat capacity is expected. A large negative magnet•resistance observed in UBet3 at low temperatures [16] was mentioned by Cox [5] as one of the most important inconsistencies with QKE model. We find a very small positive magnet•resistance (about 1% in H < 6T) for Uo.9Tho.lBe]3 at T < 2K, which qualitatively agrees with the calculations [18] for the QKE with strong coupling. Fig. 1 compares Ap(6 T)/p for three U~Th] ~Be~3 solid solutions. Fig. 2(a) shows the magnetic field dependences of the Hall resistivity of Uo.9Tho.~Bex3. Between 4 and 10 K the Hall coefficient gradually decreases when temperature falls down and is field independent in the whole interval of magnetic fields. Below 3 K the situation changes qualitatively. For fields higher above 2T we still observe a linear dependence of the Hall resistivity on the field, but for H < 2 T it apparently shows nonlinearity. To insure this transformation of the small field Hall effect, we carried out studies of its temperature (1.9 < T < 9K) dependence in fixed magnetic fields at 2 T and 6 T. The curves separate below 3 K (Fig. 2(b)). The Hall effect in Uo.gTho.lBet3 strongly deviates from that of UBe13 [19], supporting strongly the nonmagnetic nature of the ground state of U0.gTho. 1Bet 3. According to Affteck et al. [18], the QKE fixed point should exactly lie half way between zero and infinity Kondo coupling 2k. If a small magnetic field, not affecting the channels symmetry, is applied, then the resulting phase shifts will be 6~) = + ¼~ and - ¼~ for a spin-up (i = 1) and spin-down (i = 2) channel indexes correspondingly. As long as both electrons are coupled and free
1.021 U0.9Th0.1Be13 1.02 U0.64Th0.36Be13 b
° o~
a
•
~=jt
I[ i ~0198"-]1
+-
Ii6Ill 3K I I
ItI ,,i
o
I~ ~! ~
_
Ill==
D
I
•
5 lO H(m) 5
9K I 151(] I
I
5
lO
H(T)
I
10
15
I
I
20 I
T(K) g~
0.0t ~"
-0.1
n
H=6T
UBe13 U0.64Th0.36Be13 U0.9Th0.1Be13
Fig. 1. Magnetic field dependences of the normalized resistivity of Uo.9ThojBe13 (a) and Uo.6+Tho.36Be13(b). Temperature dependence of the normalized magnetoresistivity in the field H = 6 T for UBe13 (from Ref. 1-17]), Uo.9ThojBet3 and Uo.6+Tho.36Bel3.
electron channels are absent, the ordinary Hall effect part is absent: R ° = 0. The anomalous Hall effect part R~ part may be obtained by summing the skew scattering contributions [20], corresponding to each of the scattering channels R~ = R~/1 + R ~ 2 = ~sin 62{sin( - 4n - 3 2 ) + s i n ( ¼ n - 62)} = 0. Therefore, in the limit of small magnetic fields for the non-Fermi liquid QKE ground state one may expect to observe no Hall effect contribution. If we consider the formation of the NFL ground state as a "bosonization" of the spectrum due to a gradual disappearance of the fermi•n-type excitation modes in favour of the prevailing boson-type ones, then the QKE ground state may possibly be physically analogous to those found when approaching, from a higher temperature, the superconducting transition in the interval where the fluctuations of the superconducting order parameter become dominating. The principal difference with superconductors may be that in QKE the Bose condensation does not occur down to T = 0. In conclusion, thermodynamic, magnetic and transport characteristic of Uo.9Tho.1 Bex3 were observed to be consistent with the predictions of the QKE.
466
F.G. Aliev et al. /Physica B 223&224 (1996) 464-466
,,--, 2E-7
_ (a)
10 K / o
4K
•
E E ..E O
-,...- 1E-7
°°
A D []
OE+O 0
2
[] 2 . 5 K 4
H(T) @!
0 o3 E
(b) 4E-10
"lrY
@
2T
6T 0E+0
I
2'w
4
T(K) Fig. 2. (a) The magnetic field dependence of the Hall resistivity of Uo.9Tho.lBel 3 at different fixed temperatures. The solid lines are fits to a linear versus field dependence. (b) Temperature dependences of the Hall coefficient of Uo.gTh0.1Be13 measured in two fixed magnetic fields. We would Andreev for discussions. Grant MAT
like to acknowledge J.L. M a r t i n e z and A.V. help in the experiment and F. G u i n e a for The work in M a d r i d was s u p p o r t e d by 92-0170 from Plan Nacional de Materiales.
References [1] C.M. Varma, P.B. Littewood, S. Schmitt-Rink, E. Abrahams and A.E. Ruckenstein, Phys. Rev. Lett. 63 (1989) 1996.
[2] P. Nozieres and A. Blandin, J. Phys. (Paris) 41 (1989) 193. [3] A. Muramatsu and F. Guinea, Phys. Rev. Lett. 86 (1986) 2337. [4] D.C. Ralph, A.W.W. Ludwig, J. von Delft and R.A. Buhrman, Phys. Rev. Lett. 72 (1994) 1064. [5] D.L. Cox, Phys. Rev. Lett. 59 (1987) 1240. [6] C.L. Seamen, M.B. Malple, B.W. Lee, S. Ghamaty, M.S. Torikachvili, J.S. Kang, L.Z. Liu, J.W. Allen and D.L. Cox, Phys. Rev. Lett. 67 (1991) 2882. [7] M.B. Maple, C.L. Seaman, D.A. Gajewski, Y. Dalichaouch, V.B. Barbetta, M.C. de Andrade, H.A. Mook, D.E. MacLaughlin, H.G. Lukefahr and O.O. Bernal, J. Low Temp. Phys. 95 (1994) 225. [8] A.W.W. Ludwig and I. Affleck, Phys. Rev. Lett. 67 (1991) 3160. [9] H.R. Ott, H. Rudiger, Z. Fisk and J.L. Smith, Phys. Rev. B 31 (1985) 1651. [10] F.G. Aliev, S. Vieira, R. Villar, H.P. van der Meulen, K. Bakker and A.V. Andreev, JETP Lett. 58 (1993) 762. [11] F.G. Aliev, S. Vieira, R. Villar, J.L. Martinez, C.L. Seaman and M.B. Maple, Physica B 206&207 (1995) 454. [12] M. McElfresh, M.B. Maple, J.O Willis, D. Schiferl, J.L. Smith, Z. Fisk and D.L. Cox, Phys. Rev. B 48 (1993) 10395. [13] B. Andraka and A.M. Tsvelik, Phys. Rev. Lett. 67 (1991) 2886. [14] R.H. Heffner, D.W. Cooke, Z. Fisk, R.L. Hutson, M.E. Schillaci, J.L. Smith, J.O. Willis, D.E. MacLaughlin, C. Boekema. R.L. Lichti, A.B. Denison and J. Oostens, Phys. Rev. Lett. 57 (1986) 1255. [15] P.D. Sacramento and P. Schlottmann, Phys. Lett. A 142 (1989) 245. [16] B. Batlogg, D.J. Bishop, E. Bucher, B. Golding, A. Ramires, Z. Fisk, J.L. Smith and H.R. Ott, J. Magn. Magn. Mater. 63&64 (1987) 441. [17] F.G. Aliev, H. E1 Mfarrej, S. Vieira and R. Villar, Solid State Commun 91 (1994) 775. [18] I. Affieck, A.W.W. Ludwig, H.B. Pang and D.L. Cox, Phys. Rev. B 45 (1992) 7918. E19] N.E. Alekseevskii, F.G. Aliev, N.B. Brandt, V.V. Moshchalkov and A.V. Mitin, JETP Lett. 43 (1986) 482. [20] P. Coleman, P.W. Anderson and T.V. Ramakrishnan, Phys. Rev. Lett. 55 (1985) 414.
Physica B 223&224 (1996) 464 466
Evolution of calorimetric, magnetic and transport properties of UxThl-xBe13 (0.64 < x <_ 1) solid solutions F.G. Aliev 1, H. E1 Mfarrej, S. Vieira, R. Villar* Dpto Fisica de la Materia Condensada, C-Ill, Universidad Autonoma de Madrid, 28049, Madrid, Spain
Abstract We have recently found that Uo.9Tho.lBel3 displays a non-Fermi liquid ground state which is consistent with predictions of the quadrupolar Kondo effect (QKE). We report the evolution of transport, calorimetric and magnetic properties of U~Thl xBe13 (0.64 ___x < 1) solid solutions. The magnetoresistance of Uo.9Tho.lBe13 is compared with those of UBei3 and Uo.64Tho.36Bei3. We present the first experimental study of the Hall effect in the heavy fermion compound with a non-Fermi liquid ground state, with a drastic reduction of the small field Hall resistivity in the QKE state. The field dependence is opposite to those found previously for Kondo lattices.
The search for the theoretical and experimental realization of a non-Fermi liquid (NFL) ground state in strongly correlated electron systems has attracted much attention since the discovery of marginal Fermi liquid behaviour in the new oxide superconductors I-l]. After Nozieres and Blandin predicted [2] the existence of a non-Fermi liquid fixed point in the "overscreened" multichannel Kondo model, the realization of the ground state corresponding to a specific case (two-channel, spiniz Kondo) was proposed [-3] and recently observed [-4] for electron-assisted tunnelling between two-level systems. Another important possibility of experimental observation of two-channel (electric quadrupolar) Kondo effect was predicted by Cox [5] to clarify the origin of heavy fermions in the U-based compounds. Experimental support of this suggestion found recently in U~Y 1 ~Pd3(x _< 0.2) [6] and in some other compounds [-7] is not completely evident because the temperature dependences of the resistivity disagrees with the predicted x f T behaviour
[-8]. * Corresponding author. Also at: Department of Physics, Moscow State University, 119899 Moscow, Russian Federation.
We review here the low-temperature properties of Uo.9Tho.lBel3 where a non-Fermi liquid ground state observed in the specific heat and the magnetic susceptibility, is complemented for the first time by the predicted temperature dependence of the electrical resistivity. In Uo.9Tho.lBe~3 we have previously reported a nonanalytic (logarithmic versus T ) increase of the molar electronic heat capacity Ce/T in the temperature range 0.8 6 K [10]. This behaviour reflects the formation of a N F L ground state. A magnetic field of 8 T produces a small (about 10%) decrease of CU T for T < 0.8 K. The UBe13 sample shows a sharp superconducting transition with an onset of 0.89 K and a width of about 0.05 K. The magnetic susceptibility of the Uo.gTho.xBex3 compound in the temperature interval (1.7 < T < 10K) displays a temperature dependence Z = Z0(1 - A~-T) [11] corresponding to Q K E [12]. The temperature dependence of the electrical resistivity in the range 0.45 < T < 6 K is described by the asymptotic behaviour: p ~po + BxfT with B~40(2) ×10 6QcmK-1/2 and po~17(l) × 10 6 ~ c m [17]. The x / T law of p(T) and z ( T ) is suppressed in Uo.64Tho.36Be13. According to current theories, the logarithmic divergence of the linear term in the specific heat may be
0921-4526/96/$15.00 ~( 1996 Elsevier Science B.V. All rights reserved PII S092 1 - 4 5 2 6 ( 9 6 ) 0 0 1 4 9 - 4
465
F.G. Aliev et al. / Physica B 223&224 (1996) 464 466
understood in one of three ways: (i) a manifestation of the magnetic two-channel Kondo effect (TCKE) [-2, 15], (ii) as a possible realization of the quadrupolar TCKE with U atoms in the nonmagnetic ground state, the so-called quadrupolar Kondo effect (QKE) [-5] or (iii) as being due to the presence of a second-order magnetic phase transition at T = 0 K [13]. Substitution of Th for U in UxThl xBel3 has been shown to depress the superconducting critical temperature Tc which vanishes near x ~ 0.93, with some type of magnetic order below T~ for 0.96 < x < 0.98 [14]. This magnetic region of the T - x phase diagram lies relatively far from x = 0.9 in which we observe NFL behaviour. For the magnetic TCKE (i), theoretical calculations of the heat capacity in a magnetic field show a dramatic evolution toward the normal Fermi liquid behaviour [15]. The QKE, originally developed [-5] to describe the low-temperature properties of UBe13 is, in our opinion, the most suitable to describe our results. The important aspect of this approach is the realization of the nonmagnetic doublet F3 in the ground state of U-atom while local quadrupolar moments create an effective "spin-½". For this reason a weak magnetic field dependence of the low-temperature heat capacity is expected. A large negative magnet•resistance observed in UBet3 at low temperatures [16] was mentioned by Cox [5] as one of the most important inconsistencies with QKE model. We find a very small positive magnet•resistance (about 1% in H < 6T) for Uo.9Tho.lBe]3 at T < 2K, which qualitatively agrees with the calculations [18] for the QKE with strong coupling. Fig. 1 compares Ap(6 T)/p for three U~Th] ~Be~3 solid solutions. Fig. 2(a) shows the magnetic field dependences of the Hall resistivity of Uo.9Tho.~Bex3. Between 4 and 10 K the Hall coefficient gradually decreases when temperature falls down and is field independent in the whole interval of magnetic fields. Below 3 K the situation changes qualitatively. For fields higher above 2T we still observe a linear dependence of the Hall resistivity on the field, but for H < 2 T it apparently shows nonlinearity. To insure this transformation of the small field Hall effect, we carried out studies of its temperature (1.9 < T < 9K) dependence in fixed magnetic fields at 2 T and 6 T. The curves separate below 3 K (Fig. 2(b)). The Hall effect in Uo.gTho.lBet3 strongly deviates from that of UBe13 [19], supporting strongly the nonmagnetic nature of the ground state of U0.gTho. 1Bet 3. According to Affteck et al. [18], the QKE fixed point should exactly lie half way between zero and infinity Kondo coupling 2k. If a small magnetic field, not affecting the channels symmetry, is applied, then the resulting phase shifts will be 6~) = + ¼~ and - ¼~ for a spin-up (i = 1) and spin-down (i = 2) channel indexes correspondingly. As long as both electrons are coupled and free
1.021 U0.9Th0.1Be13 1.02 U0.64Th0.36Be13 b
° o~
a
•
~=jt
I[ i ~0198"-]1
+-
Ii6Ill 3K I I
ItI ,,i
o
I~ ~! ~
_
Ill==
D
I
•
5 lO H(m) 5
9K I 151(] I
I
5
lO
H(T)
I
10
15
I
I
20 I
T(K) g~
0.0t ~"
-0.1
n
H=6T
UBe13 U0.64Th0.36Be13 U0.9Th0.1Be13
Fig. 1. Magnetic field dependences of the normalized resistivity of Uo.9ThojBe13 (a) and Uo.6+Tho.36Be13(b). Temperature dependence of the normalized magnetoresistivity in the field H = 6 T for UBe13 (from Ref. 1-17]), Uo.9ThojBet3 and Uo.6+Tho.36Bel3.
electron channels are absent, the ordinary Hall effect part is absent: R ° = 0. The anomalous Hall effect part R~ part may be obtained by summing the skew scattering contributions [20], corresponding to each of the scattering channels R~ = R~/1 + R ~ 2 = ~sin 62{sin( - 4n - 3 2 ) + s i n ( ¼ n - 62)} = 0. Therefore, in the limit of small magnetic fields for the non-Fermi liquid QKE ground state one may expect to observe no Hall effect contribution. If we consider the formation of the NFL ground state as a "bosonization" of the spectrum due to a gradual disappearance of the fermi•n-type excitation modes in favour of the prevailing boson-type ones, then the QKE ground state may possibly be physically analogous to those found when approaching, from a higher temperature, the superconducting transition in the interval where the fluctuations of the superconducting order parameter become dominating. The principal difference with superconductors may be that in QKE the Bose condensation does not occur down to T = 0. In conclusion, thermodynamic, magnetic and transport characteristic of Uo.9Tho.1 Bex3 were observed to be consistent with the predictions of the QKE.
466
F.G. Aliev et al. /Physica B 223&224 (1996) 464-466
,,--, 2E-7
_ (a)
10 K / o
4K
•
E E ..E O
-,...- 1E-7
°°
A D []
OE+O 0
2
[] 2 . 5 K 4
H(T) @!
0 o3 E
(b) 4E-10
"lrY
@
2T
6T 0E+0
I
2'w
4
T(K) Fig. 2. (a) The magnetic field dependence of the Hall resistivity of Uo.9Tho.lBel 3 at different fixed temperatures. The solid lines are fits to a linear versus field dependence. (b) Temperature dependences of the Hall coefficient of Uo.gTh0.1Be13 measured in two fixed magnetic fields. We would Andreev for discussions. Grant MAT
like to acknowledge J.L. M a r t i n e z and A.V. help in the experiment and F. G u i n e a for The work in M a d r i d was s u p p o r t e d by 92-0170 from Plan Nacional de Materiales.
References [1] C.M. Varma, P.B. Littewood, S. Schmitt-Rink, E. Abrahams and A.E. Ruckenstein, Phys. Rev. Lett. 63 (1989) 1996.
[2] P. Nozieres and A. Blandin, J. Phys. (Paris) 41 (1989) 193. [3] A. Muramatsu and F. Guinea, Phys. Rev. Lett. 86 (1986) 2337. [4] D.C. Ralph, A.W.W. Ludwig, J. von Delft and R.A. Buhrman, Phys. Rev. Lett. 72 (1994) 1064. [5] D.L. Cox, Phys. Rev. Lett. 59 (1987) 1240. [6] C.L. Seamen, M.B. Malple, B.W. Lee, S. Ghamaty, M.S. Torikachvili, J.S. Kang, L.Z. Liu, J.W. Allen and D.L. Cox, Phys. Rev. Lett. 67 (1991) 2882. [7] M.B. Maple, C.L. Seaman, D.A. Gajewski, Y. Dalichaouch, V.B. Barbetta, M.C. de Andrade, H.A. Mook, D.E. MacLaughlin, H.G. Lukefahr and O.O. Bernal, J. Low Temp. Phys. 95 (1994) 225. [8] A.W.W. Ludwig and I. Affleck, Phys. Rev. Lett. 67 (1991) 3160. [9] H.R. Ott, H. Rudiger, Z. Fisk and J.L. Smith, Phys. Rev. B 31 (1985) 1651. [10] F.G. Aliev, S. Vieira, R. Villar, H.P. van der Meulen, K. Bakker and A.V. Andreev, JETP Lett. 58 (1993) 762. [11] F.G. Aliev, S. Vieira, R. Villar, J.L. Martinez, C.L. Seaman and M.B. Maple, Physica B 206&207 (1995) 454. [12] M. McElfresh, M.B. Maple, J.O Willis, D. Schiferl, J.L. Smith, Z. Fisk and D.L. Cox, Phys. Rev. B 48 (1993) 10395. [13] B. Andraka and A.M. Tsvelik, Phys. Rev. Lett. 67 (1991) 2886. [14] R.H. Heffner, D.W. Cooke, Z. Fisk, R.L. Hutson, M.E. Schillaci, J.L. Smith, J.O. Willis, D.E. MacLaughlin, C. Boekema. R.L. Lichti, A.B. Denison and J. Oostens, Phys. Rev. Lett. 57 (1986) 1255. [15] P.D. Sacramento and P. Schlottmann, Phys. Lett. A 142 (1989) 245. [16] B. Batlogg, D.J. Bishop, E. Bucher, B. Golding, A. Ramires, Z. Fisk, J.L. Smith and H.R. Ott, J. Magn. Magn. Mater. 63&64 (1987) 441. [17] F.G. Aliev, H. E1 Mfarrej, S. Vieira and R. Villar, Solid State Commun 91 (1994) 775. [18] I. Affieck, A.W.W. Ludwig, H.B. Pang and D.L. Cox, Phys. Rev. B 45 (1992) 7918. E19] N.E. Alekseevskii, F.G. Aliev, N.B. Brandt, V.V. Moshchalkov and A.V. Mitin, JETP Lett. 43 (1986) 482. [20] P. Coleman, P.W. Anderson and T.V. Ramakrishnan, Phys. Rev. Lett. 55 (1985) 414.