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Kondo behaviour in an extremely low carrier concentration system: CeP
Physica B 171 (1991) North-Holland
324-328
Kondo behaviour system: CeP
in an extremely
Y.S. Kwon”, Y. Haga”, 0.
Nakamurab,
low carrier concentration
T. Suzuki”
and T. Kasuya”
“Department of Physics, Tohoku University, Sendai, Japan ‘Hachioji Research Center, Casio Ltd., Hachioji, Japan
Electrical resistivity, magnetic susceptibility and specific heat under a magnetic field were measured in single crystalline CeP. The exerpiments show a Kondo behaviour of the system caused by a f, exited state at high temperatures, and a large mass enhancement caused by a F, ground state at low temperatures. An interesting magnetic phase diagram was also obtained
Today it is known that there are several substances that present Kondo or heavy-fermion behaviour with very low carrier concentration. Some of them are the magnetically ordered Ce monopnictides [l], the Yb monopnictides, presenting strongly reduced magnetic moments [2], the nonmagnetic system Yb,As, [3], and others. A system to bear in mind is Sm,Se,, that is an insulator [4], showing a heavy-fermion behaviour without any free carrier. It seems difficult to make an extension of the single impurity Kondo model to understand the physics of these systems. Among the Ce monopnictides, band calculations describing CeP predict it to be a semiconductor or semimetal with a very small overlap of the bands at the Fermi level [5]. In this sense, this is a typical example of a low carrier concentration system, presenting Kondo behaviour, which makes it a very interesting system in order to study this rare phenomenon. Unfortunately, it has been shown that several of the physical properties of CeP are strongly sample dependent [6], and for that reason the studies were not extended. We were interested to study the role of the extremely low carrier concentration in CeP, and the properties coming out from it. So we decided that it was important and necessary to grow very good single crystals to obtain reli0921.4526/91/$03.50
0
1991 - Elsevier
Science
Publishers
able experimental results, because the balance between the number of electrons and holes could be easily lost by a very small amount of impurities or lack of stoichiometry. After several tests, we were able to get a single crystal rather large and pure using the recrystallization method from an initial mixture of Ce and P with a Ce : P ratio of 1: 1.1 (sample 2). This excess of P in the alloy produces a very high partial pressure of the P (higher than ten atmospheres) at the recrystallization temperatures (2400°C). The lattice parameter (5.945 A), and the Neel temperature (TN = 10 K) of sample 2 are larger than those previously reported [6]. Figure 1
Temperature
Fig. 1. Temperature CeP single crystal.
B.V. (North-Holland)
dependence
(K
)
of electrical
resistivity
of
Y.S.
E
Kwon et al.
I Kondo behaviour in CeP
0.06
s-.
3
a
0.04
1
0.02
1
C=O
0
100 Temperature
8 Kemuimol
200
300
(K)
Fig. 2. Temperature dependence of magnetic susceptibility and inverse susceptibility of CeP. Black points: experimental results of inverse susceptibility. White points: experimental results of susceptibility. Solid line: calculation taking into account several parameters; A crystalline field splitting, r,-r, exchange between r, state, DQ-DQ Van Vleck type exchange between r, and r,.
shows the temperature dependence of the electrical resistivity of sample 2, as compared with sample 1. The latter was obtained from a starting mixture with a Ce : P ratio being 1: 1. The experimental data differ very much from the ones
reported in the experiments in ref. [6], but our results are similar to experiments published on CeAs. This compound has a carrier concentration of 0.001 electron/Cc atom, as obtained by the Shubnikov-dHvA effect [8]. We were able to observe the Shubnikov-dHvA oscillations in sample 2, but this effect was not seen in sample 1. We believe that this means that the quality of sample 1 is worse than that of sample 2. The carrier concentration determined by Shubnikov-dHvA effect on sample 2 is nearly the same as the value obtained for CeAs. Optical reflectivity measurements made on both samples (1 and 2) show that they have the same carrier concentration, as they present almost the same plasma edge [9]. Now we describe some physical properties presented by sample 1. Figure 2 shows the temperature dependence of the magnetic susceptibility which cannot be explained by the simple crystal field model; in particular, the reduced magnitude of this property at a higher temperature is to be noted. We were able to fit the data following the
2T
:enFerat
325
ure
!Kl
Fig. 3. Specific heat under magnetic fields, of CeP and LaP.
Y.S. Kwon et al. I Kondo behaviour in CeP
326
, ,[, , , , OO
Temperat Fig. 4. Magnetic
6
I_.
I
phase
diagram
obtained
.
20
10
are
(K!
from
a specific
30
heat peak
for CeP.
I
-4 z E
-
E 7
H=O
___-
IT
-.-.-
5T
In 2 -..-..-
,L
C ‘0
Fig. 5. Temperature
I
I 10
dependence
of magnetic
I
IOT
I
I 1
20 T (K)
entropy
of CeP after
subtraction
of that of LaP
Y.S.Kwon et al. I Kondo behaviour in CeP
same steps as in ref. [7], taking into account the exchange coupling with a r,, with a parameter of about -50 K, and a Van Vleck type of exchange interaction between a r, and a r, with a parameter of about 21 K; the crystal field overall splitting was taken as 170 K. The exchange parameter of 50K may correspond with the Kondo temperature. In fact, the temperature dependence of the electrical resistivity of the sample above 70 K reflects individual Kondo scattering. Figure 3 shows the temperature dependence of the specific heat under several magnetic fields. A sharp peak at zero field appears at 10 K, a temperature that corresponds with the peak in the resistivity. The peak splits in a double peak when the applied field is just below 5 T. This splitting increase with the field, moving to higher and lower temperatures as the field is increased.
327
Above 5 T, the lower temperature peak seems to split once again. Figure 4 presents the magnetic phase diagram of the sample, which looks similar to that of CeSb [ll] under pressure [lo]. In fact, measurements of electrical resistivities under pressure in CeAs and CeP give evidence that those systems have a state similar to that of CeSb [ll] under pressure. In CeP, that change occurs at a rather low pressure (2.5 kbar.) We believe that the external magnetic field may also induce a similar state in CeP as that of CeSb. In order to complete and clarify the magnetic phase diagram, neutron diffraction studies and magnetization experiments are necessary. The curve of magnetic entropy, which was obtained substracting the specific heat of LaP of that of CeP, is shown in fig. 5. The entropy value at T = TN is only 80% of that expected from the r’ doublet,
CeP
z E
N’
2
200-
: l. 0 .
H=lOT
A
5T
x
3T
0
0
IOO-
01 0
I
1
5
I
T2( K2)
Fig. 6. CIT vs. T2 for CeP.
I 10
I
328
Y.S.
Kwon et al. I Kondo behaviour in CeP
and the entropy curves under a magnetic field coincide with each other at about 35 K. Figure 6 presents the C/T curve versus T* for CeP. The relation C/T = y + p T* is well satisfied below TN. The p T* term is caused by antiferromagnetic spin waves, and a small turn up of C/T that appears at low magnetic fields is smeared out at higher fields. The obtained value of y is 17 mJ/ mol K2. A fairly large mass enhancement was observed due to the following reasons: (i) The y value in LaP is nearly zero within the experimental error. (ii) The y va 1u e in CeP is nearly the same as that of CeSb and CeBi, possessing carrier concentrations of about 2-3% per Ce atom as can be determined by the dHvA effect, with mass enhancement factors of about 25, this is mainly due to the fact that the large p-hole is strongly mixed with the f state of Ce. We remember now that the carrier concentration of CeP is one order of magnitude smaller than that of CeSb and CeBi. The question is why such a large mass enhancement could occur for such a small carrier concentration. We believe that the main reason for this is that the 4f level of Ce in CeP is very near to the Fermi level, which situates it in a state very near to enter in a valence fluctuation state, as in CeN. In fact, the shallow peak of the photoemission spectrum of CeP has the largest intensity among the Ce monopnictides, due to the strongest c-f mixing
effect [ll]. It remains a serious theoretical problem to understand how a system with such a tiny carrier concentration could get a large mass enhancement.
References [l] T.
Suzuki,
Y.S. Kwon, S. Ozeki, Y. Haga and T. Proc. of the 25th Yamada Conf., ed., M. Date, Osaka (1990), to be published. A. Oyamada, C. Ayache, T. Suzuki, J. Rossat-Mignod and T. Kasuya, in: Proc. of the 25th Yamada Conf., ed., M. Date, Osaka (1990) to be published. A. Ochiai, T. Suzuki and T. Kasuya, J. Phys. Sot. Jpn., to be published. T. Furuno, K. Ando, S. Kunii, A. Ochiai, H. Suzuki, M. Fujioka, T. Suzuki, W. Sakaki and T. Kasuya, J. Magn. & Magn. Mater. 76 & 77 (1988) 117. A. Hasegawa, J. Phys. C: Solid State Phys. 13 (1980) 6147. F. Hulliger and H.R. Ott, 2. Phys. B 20 (1978) 47. Y. Aoki and T. Kasuya, Solid State Commun. 36 (1980) 317. Y.S. Kwon, Y. Haga, S. Ozeki, T. Suzuki and T. Kasuya, in: Proc. of the 25th Yamada Conf., ed., M. Date, Osaka (1990), to be published. Y.S. Kwon, to be published. T. Komatsubara, T. Suzuki, M. Kawakami, S. Kunii, T. Fujita, Y. Ishikawa, A. Takase, K. Kojima, M. Suzuki, K. Takegahara and T. Kasuya, J. Magn. & Magn. Mater. 15-18 (1980) 963. T. Suzuki, Y. Nakabayashi, A. Ochiai, T. Kasuya, K. Sugiyama and M. Date, J. Magn. & Magn. Mater. 63 & 64 (1987) 58.
Kasuya, in:
[2]
[3] [4]
[5] [6] [7] [8]
[9] [lo]
[ll]
324-328
Kondo behaviour system: CeP
in an extremely
Y.S. Kwon”, Y. Haga”, 0.
Nakamurab,
low carrier concentration
T. Suzuki”
and T. Kasuya”
“Department of Physics, Tohoku University, Sendai, Japan ‘Hachioji Research Center, Casio Ltd., Hachioji, Japan
Electrical resistivity, magnetic susceptibility and specific heat under a magnetic field were measured in single crystalline CeP. The exerpiments show a Kondo behaviour of the system caused by a f, exited state at high temperatures, and a large mass enhancement caused by a F, ground state at low temperatures. An interesting magnetic phase diagram was also obtained
Today it is known that there are several substances that present Kondo or heavy-fermion behaviour with very low carrier concentration. Some of them are the magnetically ordered Ce monopnictides [l], the Yb monopnictides, presenting strongly reduced magnetic moments [2], the nonmagnetic system Yb,As, [3], and others. A system to bear in mind is Sm,Se,, that is an insulator [4], showing a heavy-fermion behaviour without any free carrier. It seems difficult to make an extension of the single impurity Kondo model to understand the physics of these systems. Among the Ce monopnictides, band calculations describing CeP predict it to be a semiconductor or semimetal with a very small overlap of the bands at the Fermi level [5]. In this sense, this is a typical example of a low carrier concentration system, presenting Kondo behaviour, which makes it a very interesting system in order to study this rare phenomenon. Unfortunately, it has been shown that several of the physical properties of CeP are strongly sample dependent [6], and for that reason the studies were not extended. We were interested to study the role of the extremely low carrier concentration in CeP, and the properties coming out from it. So we decided that it was important and necessary to grow very good single crystals to obtain reli0921.4526/91/$03.50
0
1991 - Elsevier
Science
Publishers
able experimental results, because the balance between the number of electrons and holes could be easily lost by a very small amount of impurities or lack of stoichiometry. After several tests, we were able to get a single crystal rather large and pure using the recrystallization method from an initial mixture of Ce and P with a Ce : P ratio of 1: 1.1 (sample 2). This excess of P in the alloy produces a very high partial pressure of the P (higher than ten atmospheres) at the recrystallization temperatures (2400°C). The lattice parameter (5.945 A), and the Neel temperature (TN = 10 K) of sample 2 are larger than those previously reported [6]. Figure 1
Temperature
Fig. 1. Temperature CeP single crystal.
B.V. (North-Holland)
dependence
(K
)
of electrical
resistivity
of
Y.S.
E
Kwon et al.
I Kondo behaviour in CeP
0.06
s-.
3
a
0.04
1
0.02
1
C=O
0
100 Temperature
8 Kemuimol
200
300
(K)
Fig. 2. Temperature dependence of magnetic susceptibility and inverse susceptibility of CeP. Black points: experimental results of inverse susceptibility. White points: experimental results of susceptibility. Solid line: calculation taking into account several parameters; A crystalline field splitting, r,-r, exchange between r, state, DQ-DQ Van Vleck type exchange between r, and r,.
shows the temperature dependence of the electrical resistivity of sample 2, as compared with sample 1. The latter was obtained from a starting mixture with a Ce : P ratio being 1: 1. The experimental data differ very much from the ones
reported in the experiments in ref. [6], but our results are similar to experiments published on CeAs. This compound has a carrier concentration of 0.001 electron/Cc atom, as obtained by the Shubnikov-dHvA effect [8]. We were able to observe the Shubnikov-dHvA oscillations in sample 2, but this effect was not seen in sample 1. We believe that this means that the quality of sample 1 is worse than that of sample 2. The carrier concentration determined by Shubnikov-dHvA effect on sample 2 is nearly the same as the value obtained for CeAs. Optical reflectivity measurements made on both samples (1 and 2) show that they have the same carrier concentration, as they present almost the same plasma edge [9]. Now we describe some physical properties presented by sample 1. Figure 2 shows the temperature dependence of the magnetic susceptibility which cannot be explained by the simple crystal field model; in particular, the reduced magnitude of this property at a higher temperature is to be noted. We were able to fit the data following the
2T
:enFerat
325
ure
!Kl
Fig. 3. Specific heat under magnetic fields, of CeP and LaP.
Y.S. Kwon et al. I Kondo behaviour in CeP
326
, ,[, , , , OO
Temperat Fig. 4. Magnetic
6
I_.
I
phase
diagram
obtained
.
20
10
are
(K!
from
a specific
30
heat peak
for CeP.
I
-4 z E
-
E 7
H=O
___-
IT
-.-.-
5T
In 2 -..-..-
,L
C ‘0
Fig. 5. Temperature
I
I 10
dependence
of magnetic
I
IOT
I
I 1
20 T (K)
entropy
of CeP after
subtraction
of that of LaP
Y.S.Kwon et al. I Kondo behaviour in CeP
same steps as in ref. [7], taking into account the exchange coupling with a r,, with a parameter of about -50 K, and a Van Vleck type of exchange interaction between a r, and a r, with a parameter of about 21 K; the crystal field overall splitting was taken as 170 K. The exchange parameter of 50K may correspond with the Kondo temperature. In fact, the temperature dependence of the electrical resistivity of the sample above 70 K reflects individual Kondo scattering. Figure 3 shows the temperature dependence of the specific heat under several magnetic fields. A sharp peak at zero field appears at 10 K, a temperature that corresponds with the peak in the resistivity. The peak splits in a double peak when the applied field is just below 5 T. This splitting increase with the field, moving to higher and lower temperatures as the field is increased.
327
Above 5 T, the lower temperature peak seems to split once again. Figure 4 presents the magnetic phase diagram of the sample, which looks similar to that of CeSb [ll] under pressure [lo]. In fact, measurements of electrical resistivities under pressure in CeAs and CeP give evidence that those systems have a state similar to that of CeSb [ll] under pressure. In CeP, that change occurs at a rather low pressure (2.5 kbar.) We believe that the external magnetic field may also induce a similar state in CeP as that of CeSb. In order to complete and clarify the magnetic phase diagram, neutron diffraction studies and magnetization experiments are necessary. The curve of magnetic entropy, which was obtained substracting the specific heat of LaP of that of CeP, is shown in fig. 5. The entropy value at T = TN is only 80% of that expected from the r’ doublet,
CeP
z E
N’
2
200-
: l. 0 .
H=lOT
A
5T
x
3T
0
0
IOO-
01 0
I
1
5
I
T2( K2)
Fig. 6. CIT vs. T2 for CeP.
I 10
I
328
Y.S.
Kwon et al. I Kondo behaviour in CeP
and the entropy curves under a magnetic field coincide with each other at about 35 K. Figure 6 presents the C/T curve versus T* for CeP. The relation C/T = y + p T* is well satisfied below TN. The p T* term is caused by antiferromagnetic spin waves, and a small turn up of C/T that appears at low magnetic fields is smeared out at higher fields. The obtained value of y is 17 mJ/ mol K2. A fairly large mass enhancement was observed due to the following reasons: (i) The y value in LaP is nearly zero within the experimental error. (ii) The y va 1u e in CeP is nearly the same as that of CeSb and CeBi, possessing carrier concentrations of about 2-3% per Ce atom as can be determined by the dHvA effect, with mass enhancement factors of about 25, this is mainly due to the fact that the large p-hole is strongly mixed with the f state of Ce. We remember now that the carrier concentration of CeP is one order of magnitude smaller than that of CeSb and CeBi. The question is why such a large mass enhancement could occur for such a small carrier concentration. We believe that the main reason for this is that the 4f level of Ce in CeP is very near to the Fermi level, which situates it in a state very near to enter in a valence fluctuation state, as in CeN. In fact, the shallow peak of the photoemission spectrum of CeP has the largest intensity among the Ce monopnictides, due to the strongest c-f mixing
effect [ll]. It remains a serious theoretical problem to understand how a system with such a tiny carrier concentration could get a large mass enhancement.
References [l] T.
Suzuki,
Y.S. Kwon, S. Ozeki, Y. Haga and T. Proc. of the 25th Yamada Conf., ed., M. Date, Osaka (1990), to be published. A. Oyamada, C. Ayache, T. Suzuki, J. Rossat-Mignod and T. Kasuya, in: Proc. of the 25th Yamada Conf., ed., M. Date, Osaka (1990) to be published. A. Ochiai, T. Suzuki and T. Kasuya, J. Phys. Sot. Jpn., to be published. T. Furuno, K. Ando, S. Kunii, A. Ochiai, H. Suzuki, M. Fujioka, T. Suzuki, W. Sakaki and T. Kasuya, J. Magn. & Magn. Mater. 76 & 77 (1988) 117. A. Hasegawa, J. Phys. C: Solid State Phys. 13 (1980) 6147. F. Hulliger and H.R. Ott, 2. Phys. B 20 (1978) 47. Y. Aoki and T. Kasuya, Solid State Commun. 36 (1980) 317. Y.S. Kwon, Y. Haga, S. Ozeki, T. Suzuki and T. Kasuya, in: Proc. of the 25th Yamada Conf., ed., M. Date, Osaka (1990), to be published. Y.S. Kwon, to be published. T. Komatsubara, T. Suzuki, M. Kawakami, S. Kunii, T. Fujita, Y. Ishikawa, A. Takase, K. Kojima, M. Suzuki, K. Takegahara and T. Kasuya, J. Magn. & Magn. Mater. 15-18 (1980) 963. T. Suzuki, Y. Nakabayashi, A. Ochiai, T. Kasuya, K. Sugiyama and M. Date, J. Magn. & Magn. Mater. 63 & 64 (1987) 58.
Kasuya, in:
[2]
[3] [4]
[5] [6] [7] [8]
[9] [lo]
[ll]