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The effect of the exchange interaction on the specific heat of Pr(Ni1−cCoc)5compounds
Journal of
ELSEVIER
Journal of Magnetism and Magnetic Materials 162 (1996) 314-318
magneUc materials
The effect of the exchange interaction on the specific heat of Pr(Nil_cCoc) 5 compounds R. K u e n t z l e r a,l D. S c h m i t t b,, A. T a r i c a lnstitut de Physique et Chimie des Mat~riaux de Strasbourg, 67084 Strasbourg C~dex, France b Laboratoire de Magn~tisme Louis N~el, CNRS, BP 166, 38042 Grenoble C~dex 9, France c Department of Physics, King Fahd Universi~ of Petroleum and Minerals, KFUPM Box 359, Dhahran 31261, Saudi Arabia Received 22 March 1995; revised 9 November 1995
Abstract
The specific heat of Pr(Ni I - cCo,)5 compounds with c < 0.20 has been measured at temperatures between 1.5 and 50 K. The substitution of Co for Ni is found to reduce the height of the large peak observed in the specific heat of PrNi 5 and to increase the peak temperature. The reduction of the peak height is explained by the effect of the exchange field of Co on Pr 3÷ ions. The substitution appears to modify the crystal field parameters. Keywords: Specific heat; Exchange; Crystal field
1. Introduction The study of RNi 5 compounds (R = rare earth) is essential for a fundamental understanding of their magnetism and that of the technologically important isomorphous RCo 5 compounds in which Co is magnetic and the magnetization and anisotropy of the R and Co sublattices are comparable in magnitude and in competition. It is therefore difficult to separate their contributions to the magnetic properties of these compounds. In the RNi 5 series, on the other hand, Ni is essentially non-magnetic and hence one is studying the R ions practically in isolation. Of the RNi 5 compounds, PrNi 5 is perhaps the
* Corresponding author. Fax: schmiu@ grmag.polycnrs-gre-fr. J Deceased.
+33-7688-1191;
email:
most interesting. It does not order down to the lowest temperature due to the crystal field (CF) split singlet ground state of Pr ( J = 4) [l]. This state, however, is not well separated from the higher energy levels. Therefore, one observes a large Van Vleck susceptibility in the basal plane, enhanced by a strong nuclear hyperfine interaction. In this compound the specific heat [1-3] and the susceptibility [1,4,5] show a large peak at about 14 K, resulting in the first case from the Schottky term in the specific heat and in the latter from the competition between the Van Vleck and the Curie susceptibilities. Recently, we investigated single crystals of the compounds Pr(Ni t cCoc) 5 for 0.00 < c < 0.20 by means of magnetization and susceptibility measurements [6]. Ferromagnetism appears for c > 0.05, induced by the exchange field originating from cobalt. All the compounds show a broad peak at about 15 K on the temperature dependence of the magnetization,
0304-8853/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S 0 3 0 4 - 8 8 5 3 ( 9 6 ) 0 0 2 9 3 - 4
R. Kuentzler et aL / Journal of Magnetism and Magnetic Materials 162 (1996) 314-318
which can be attributed to the CF effect of Pr. The substitution of Co for Ni does not cause the maximum of the peak to move to a higher temperature to any noticeable degree. We have now investigated the specific heat of polycrystalline compounds of the same concentration in order to study the effect of the exchange interaction on the thermal properties of PrNi 5. The specific heat of the isomorphous compound YNi 5 has also been measured in order to separate the electronic and lattice specific heat of the praseodymium compounds.
2. Experimental details Seven samples with c = 0.00, 0.01, 0.05, 0.10, 0.20 and 0.30 and the compound YNi 5 were prepared by melting together stoichiometric amounts of 99.9% pure rare earths and specpure Ni and Co in a cold crucible induction furnace at the Laboratoire Louis Ndel. They were melted then turned over and remelted for a minimum of three times for good homogeneity under a high purity argon atmosphere. There was virtually no weight loss during the melt. The resulting buttons, which weighed about 10 g each, were then heat treated at 1040°C for four days under a vacuum of p < 10 - 7 Torr. X-ray powder studies of the compounds confirmed the hexagonal Haucke phase structure and the absence of any significant impurity phase. Some of the specific heat measurements were initially made in Strasbourg by a quasi-adiabatic method in the temperature interval 1.5 K < T < 20 K. Further measurements were made in Grenoble in the temperature interval 1.5 K < T < 50 K using an ac technique. For the details of this latter technique the reader is referred to Bouvier et al. [7].
3, Results and discussion
together with those obtained previously by Takeshita et al. [8]. The C / T versus T 2 graph for this compound is a straight line for temperatures up to 16 K, and gives a low-temperature Debye temperature of O D = 423 K and a y value of 37.6 m J / K 2 mol. For the same compound Takeshita et al. [8] found O D = 450 K and y = 36.4 m J / K 2 mol. Thus the y values agree very well, while O D differ only by about 6%. For the other non-magnetic compound LaNi 5 of the lanthanide series, Nasu et al. [2] and Radwanski et al. [9] found O D=341 K and y = 3 4 . 3 m J / K 2mol, and O D = 322 K and , / = 36 m J / K 2 moi, respectively. These 3/ values are very close to those of YNi 5, and are rather large compared with other non-magnetic compounds, probably due to an enhancement arising from the 3d electrons of Ni. On the contrary, the O D values differ noticeably between La and Y based compounds, even when considering the two-Debye temperature model described below. Indeed, the ratio O(YNis)/O(LaNi 5) is calculated to be ~ 1.08 from the model while it reaches ~ 1.30 experimentally. Such a discrepancy has already been observed previously [7] and has been attributed to the anomalous behaviour of La based compounds. 3.2. The Pr(Ni /_ , Co ,) 5 compounds
The variation of the total specific heat C versus temperature for the compounds with c = 0.00, 0.05, 0.10 and 0.20 and YNi 5 is shown in Fig. 1. As the 20
• 15
[]
c=O.O Pr(Ni. Co ). / ' c=0.05 ,-c ¢ ~ .
•
c=O.lO
f=
~
.
"
•
el
;F/
U
s ooOO °°
3.1. YNi 5 o
The specific heat of the compound YNi 5 was measured in Strasbourg between 1.5 and 20 K and in Grenoble between 1.5 and 45 K. The two sets of data obtained are in excellent agreement with each other
315
s
~o
~s
zo
zs
30
T (K)
Fig. 1. Temperature variation of the specific heat of YNi~ and of the compounds Pr(Ni I ,.Co,)s with c = 0.00, 0.05, 0.10 and 0.20. The data above 20 K for PrNi 5 are taken from Ref. [1].
316
R. Kuentzler et al./Journal of Magnetism and Magnetic Materials 162 (1996) 314-318
figure shows, all the Pr compounds display a broad peak which becomes broader and less pronounced with increasing Co content. To analyze the data we use the following expression: C = Cel q- Cph "~ A C ,
12
i
10 "6
?
•
~=o.2o ." ~ ¢ ~ - . . ~ t ~ ' ' -
/
j 7' 0
~ --
0
and x4e x
9NkB(T/fgD)3)oOJT(e x [ _
1944N(T/OD)3,
(1)
where N is the number of atoms per formula unit (six in the present case) and fl is in J / K 4 mol. We assume that the host specific heat for this series is well represented by YNi 5 with the proviso that the Debye temperature of the compounds be normalized to that of YNi 5. To do this we proceed as follows. It has been shown by Debye that the mean square displacement for a vibrating atom is proportional to T/(M6) 2) (see, e.g., Ref. [10]). Assuming that all the atoms in a compound have the same mean square displacement we may write for a pseudobinary compound Pr(Ni I _ cCOc)5: O 3 ( Y N i s ) / O 3(pr(Ni]_ cCo,.)5) M /2 +
5(I - c)M i/2 + ~ r,A3/2 M3/2 + .... Ni
,
o
Pr(Nil ~Co) s i
5
i
10
i
i
1S 20 T (K)
"
i
25
30
Fig. 2. Thermal variation of the excess specific heat AC for compounds containing 0, 5, 10 and 20% Co.
1) ~
represent, respectively, the electronic and lattice contributions to the specific heat, and AC the excess specific heat which includes the Schottky/magnetic and nuclear contributions. The latter, however, is expected to be insignificant in the temperature range in which the measurements were made. For T << 6) D the phonon term may be written as: Cph = fiT 3 =
~'.~
• ~6
-
~4
Cel = TT
=
C=0
o c=O.OS , , , ~
8
where
Cph
i
•
~p~lAt3/2
. . . . . co
=
1.27, (2)
and hence O(YNis)/~9(Pr(Ni 1_,Coo) 5) ~ 1.083 for all the compounds investigated. This ratio does not change much because the atomic masses of Ni and Co are very similar. Applying the above equation with LaNi 5 gives a ratio of 1.003 and @D = 340 K
for PrNi 5. This correction, however, gives a poor value for the host specific heat Chost. Therefore, we use YNi 5 for the above correction. It should be noted that Y compounds often give better corrections compared with those obtained with La compounds, as has been shown by Bouvier et al. [7]. We have, therefore, normalized the Debye temperature of the alloys by dividing the temperature of measurements for YNi 5 by 1.083. We shall call this Chosr Subtracting this latter contribution from the total specific heat then provides us with the total magnetic (in the case of PrNi 5, the Schottky) contribution AC, which is shown in Fig. 2 for four of the compounds studied. It is clear from this figure that with increasing Co content, i.e. with increasing exchange interaction: • the peak height decreases slightly, and • the position of the peak moves to higher temperatures. As the cobalt-induced ferromagnetic order, which occurs in compounds with c > 0.05 [6] and which is likely inhomogeneous, does not lead to an anomaly in the AC curves, we will first assume that cobalt does not contribute to the magnetic specific heat AC. Indeed, the magnetization data show that the compounds with c = 0.05, 0.10 and 0.20 have a Tc of 2.5, l0 and 38 K, respectively, temperatures at which no anomaly can be seen on the specific heat variations. Comparing AC with the thermal variation of magnetization (Fig. 4 of Ref. [6]), where the broad peak is attributed to the crystal field effects of the Pr ions, it is worth noting that the two behaviors differ
R. Kuentzler et al. / Journal of Magnetism and Magnetic Materials 162 (1996) 314-318
since the maximum of magnetization does not move to higher temperatures with increasing exchange interaction, i.e. with increasing Co concentration. This will be discussed further below.
10~ 12
]
i
i
317 i
i
P~(Ni 1 cC°c)s
~
o
E
~k
I I l~:~aoocloD D
8
~
6
~
4
3.3. Analysis From the above considerations the excess specific heat AC due to praseodymium alone may be computed from the Schottky contribution of its crystal field levels. This may be cast into the following convenient form: AC =
R / T Z { 2 Ai exp( - A i / T ) / Z - [ ~ A i exp( - A i / T ) / Z ] 2 ) ,
(3)
Z is the partition function, i.e. Z = ~ i A e x p ( - A i / T ) and A / = E i - E0, i = 0,1,2 . . . . . 8; E~ is the ith energy eigenvalue of the relevant Hamiltonian. This is given by:
0
5
10
15
20
25
30
T (K) Fig. 3. Variation with temperature of the computed and experimentally determined excess specific heat for PrNi 5 and Pr(Ni0.gC°0.1)5- The data points for PrNi 5 above 20 K are taken from Ref. [1]. Lines are calculated with an effective field H~n = 0 and 65 kOe for PrNi 5 and Pr(NillgCoo i )5, respectively.
where
0
0
6
6
H = B°Ol~ + B~)O° + B 6 0 6 + B 6 0 6
-
-
gj/.L BHeff "J,
(4) where B,,' are the crystal field parameters and O,,~ are the Stevens equivalent operators and the quantization direction of the CF Hamiltonian is taken along the c-axis. When diagonalizing the above Hamiltonian, however, the direction of the effective exchange field was taken along the b-axis, the easy direction of magnetization of the compounds. The last term represents the exchange interaction, where:
Hen. = nM m + n~x(CO )
(5)
is the total effective field acting on the Pr 3+ ions. In the above equation, Mpr is the induced magnetization on Pr 3+, n the total isotropic bilinear exchange parameter and He×(Co) the exchange field arising from the cobalt sublattice. Considering the effective field Hen. as an adjustable parameter we fitted the variation of the excess specific heat AC with temperature to Eq. (3) using the crystal field parameters of PrNi 5 given by Reiffers et al. [12] for all the compounds studied. Fig. 3 shows the temperature variation of both the experimental and computed AC for both PrNi 5 and Pr(Ni0.9oCo0.1o)5, the corresponding values of H e ft being 0 and 65 kOe, respectively.
For PrNi 5 the peak heights of both curves are almost the same and the peak temperatures differ by only about 1.5 K. The agreement between the two, therefore, is quite satisfactory. Recently, Kim-Ngan et al. [11] measured the specific heat of a single crystal of PrNi 5. The values of their refined CF parameters were found to be very close to those obtained by Reiffers et al. [12] which we used in our computation. While the peak temperatures of their experimental and computed curves agree very well, the heights differ by about 20% and hence the overall agreement is not much better than ours. For the 10% Co compound the peak height is in good agreement with the experimental curve, but the temperature of the experimental and computed curves differs by 6 K. Therefore, the reduction of the peak height is satisfactorily explained by the effect of Hen., while the latter is not sufficient to account for the shift of T,.... . Moreover, this shift is larger than that observed for the susceptibility of the same compositions reported in Ref. [6]. One possible explanation for this is the anticipated change in the CF parameters due to alloying which would act only on the Scbottky term and not on the susceptibility. This is possible because the same matrix elements are not involved in both expressions. The only plausible explanation, therefore, seems to be a modification of the CF parameters due to cobalt substitution. Such an hypothesis, however, remains to be confirmed by additional experiments.
318
R. Kuentzler et a l . / Journal of Magnetism and Magnetic Materials 162 (1996) 314-318
It may be suggested that the effect of the change of volume on specific heat with Co concentration should be taken into account. This, however, is both difficult and will not improve the fit because one may then be forced to change the theoretical value of ~9(non-magnetic)/~9(R compound) in order to describe the lattice contribution better. This means that this ratio will sometimes need to be adjusted which in turn implies that the theory does not need to be perfect. It would also be very useful to measure the specific heat of the compounds under an applied magnetic field in order to follow the evolution of the magnetic component of the specific heat and compare it with the effect of the exchange field induced by the cobalt atoms. In conclusion, we find that, in this series, the effect of cobalt substitution is to reduce the height of the large peak found in the specific heat of PrNi s and to move the maximum of the peak to higher temperatures. The reduction in the peak amplitude is well explained by the effect of the exchange field induced by the cobalt on Pr 3+ ions. However, this exchange field alone does not seem to be sufficient to explain the observed shift in AC(T). A slight re-adjustment of the CF parameters would be necessary to obtain better agreement, subject to the condi-
tion that this does not change the susceptibility curves.
References [1] R.S. Craig, S.G. Sankar, N. Marzouk, V.U.S. Rao, W.E. Wallace and E. Segal, J. Phys. Chem. Solids 33 (1972) 2267. [2] S. Nasu, H.H. Neumann, N. Marzouk, R.S. Craig and W.E. Wallace, J. Phys. Chem. Solids 32 (1971) 2779. [3] D. Andres, S. Darack and H.R. Ott, Phys. Rev. B 19 (1979) 5475. [4] H.R. Ott, K. Andres, E. Bucher and J.P. Maita, Solid State Commun. 18 (1976) 1303. [5] V.M,T.S. Barthem, D. Gignoux, A. Nait-Saada and D. Schmitt, Phys. Rev. B 37 (1988) 1733. [6] A. Ball, D. Gignoux, B. Gorges, D. Schmitt and A. Tari, J. Magn. Magn. Mater. 109 (1992) 185. [7] M. Bouvier, P. Lethuillier and D. Schmitt, Phys. Rev. B 43 (1991) 13 137. [8] T. Takeshita, K.A. Gschneidner Jr., D.K. Thoma and O.D. McMaster, Phys. Rev. B 21 (1980) 5636. [9] R.J. Radwanski, N.H. Kim-Ngan, F.E. Kayzel and J.J.M. Franse, IEEE Trans. Magn. 30 (1994) 843. [10] J.H. Hoffmann, A. Paskin, K.J. Tauer and R.J. Weiss, J. Phys. Chem. Solids 1 (1956) 45. [11] N.H. Kim-Ngan, R.J. Radwanski, F.E. Kayzel and J.J.M. Franse, J. Magn. Magn. Mater. 140-144 (1995) 863. [12] M. Reiffers, Yu.G. Naidyuk, A.G.M. Jensen, P. Wyder, I.K. Yanson, D. Gignoux and D. Schmitt, Phys. Rev. Lett. 62 (1989) 1560.
ELSEVIER
Journal of Magnetism and Magnetic Materials 162 (1996) 314-318
magneUc materials
The effect of the exchange interaction on the specific heat of Pr(Nil_cCoc) 5 compounds R. K u e n t z l e r a,l D. S c h m i t t b,, A. T a r i c a lnstitut de Physique et Chimie des Mat~riaux de Strasbourg, 67084 Strasbourg C~dex, France b Laboratoire de Magn~tisme Louis N~el, CNRS, BP 166, 38042 Grenoble C~dex 9, France c Department of Physics, King Fahd Universi~ of Petroleum and Minerals, KFUPM Box 359, Dhahran 31261, Saudi Arabia Received 22 March 1995; revised 9 November 1995
Abstract
The specific heat of Pr(Ni I - cCo,)5 compounds with c < 0.20 has been measured at temperatures between 1.5 and 50 K. The substitution of Co for Ni is found to reduce the height of the large peak observed in the specific heat of PrNi 5 and to increase the peak temperature. The reduction of the peak height is explained by the effect of the exchange field of Co on Pr 3÷ ions. The substitution appears to modify the crystal field parameters. Keywords: Specific heat; Exchange; Crystal field
1. Introduction The study of RNi 5 compounds (R = rare earth) is essential for a fundamental understanding of their magnetism and that of the technologically important isomorphous RCo 5 compounds in which Co is magnetic and the magnetization and anisotropy of the R and Co sublattices are comparable in magnitude and in competition. It is therefore difficult to separate their contributions to the magnetic properties of these compounds. In the RNi 5 series, on the other hand, Ni is essentially non-magnetic and hence one is studying the R ions practically in isolation. Of the RNi 5 compounds, PrNi 5 is perhaps the
* Corresponding author. Fax: schmiu@ grmag.polycnrs-gre-fr. J Deceased.
+33-7688-1191;
email:
most interesting. It does not order down to the lowest temperature due to the crystal field (CF) split singlet ground state of Pr ( J = 4) [l]. This state, however, is not well separated from the higher energy levels. Therefore, one observes a large Van Vleck susceptibility in the basal plane, enhanced by a strong nuclear hyperfine interaction. In this compound the specific heat [1-3] and the susceptibility [1,4,5] show a large peak at about 14 K, resulting in the first case from the Schottky term in the specific heat and in the latter from the competition between the Van Vleck and the Curie susceptibilities. Recently, we investigated single crystals of the compounds Pr(Ni t cCoc) 5 for 0.00 < c < 0.20 by means of magnetization and susceptibility measurements [6]. Ferromagnetism appears for c > 0.05, induced by the exchange field originating from cobalt. All the compounds show a broad peak at about 15 K on the temperature dependence of the magnetization,
0304-8853/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S 0 3 0 4 - 8 8 5 3 ( 9 6 ) 0 0 2 9 3 - 4
R. Kuentzler et aL / Journal of Magnetism and Magnetic Materials 162 (1996) 314-318
which can be attributed to the CF effect of Pr. The substitution of Co for Ni does not cause the maximum of the peak to move to a higher temperature to any noticeable degree. We have now investigated the specific heat of polycrystalline compounds of the same concentration in order to study the effect of the exchange interaction on the thermal properties of PrNi 5. The specific heat of the isomorphous compound YNi 5 has also been measured in order to separate the electronic and lattice specific heat of the praseodymium compounds.
2. Experimental details Seven samples with c = 0.00, 0.01, 0.05, 0.10, 0.20 and 0.30 and the compound YNi 5 were prepared by melting together stoichiometric amounts of 99.9% pure rare earths and specpure Ni and Co in a cold crucible induction furnace at the Laboratoire Louis Ndel. They were melted then turned over and remelted for a minimum of three times for good homogeneity under a high purity argon atmosphere. There was virtually no weight loss during the melt. The resulting buttons, which weighed about 10 g each, were then heat treated at 1040°C for four days under a vacuum of p < 10 - 7 Torr. X-ray powder studies of the compounds confirmed the hexagonal Haucke phase structure and the absence of any significant impurity phase. Some of the specific heat measurements were initially made in Strasbourg by a quasi-adiabatic method in the temperature interval 1.5 K < T < 20 K. Further measurements were made in Grenoble in the temperature interval 1.5 K < T < 50 K using an ac technique. For the details of this latter technique the reader is referred to Bouvier et al. [7].
3, Results and discussion
together with those obtained previously by Takeshita et al. [8]. The C / T versus T 2 graph for this compound is a straight line for temperatures up to 16 K, and gives a low-temperature Debye temperature of O D = 423 K and a y value of 37.6 m J / K 2 mol. For the same compound Takeshita et al. [8] found O D = 450 K and y = 36.4 m J / K 2 mol. Thus the y values agree very well, while O D differ only by about 6%. For the other non-magnetic compound LaNi 5 of the lanthanide series, Nasu et al. [2] and Radwanski et al. [9] found O D=341 K and y = 3 4 . 3 m J / K 2mol, and O D = 322 K and , / = 36 m J / K 2 moi, respectively. These 3/ values are very close to those of YNi 5, and are rather large compared with other non-magnetic compounds, probably due to an enhancement arising from the 3d electrons of Ni. On the contrary, the O D values differ noticeably between La and Y based compounds, even when considering the two-Debye temperature model described below. Indeed, the ratio O(YNis)/O(LaNi 5) is calculated to be ~ 1.08 from the model while it reaches ~ 1.30 experimentally. Such a discrepancy has already been observed previously [7] and has been attributed to the anomalous behaviour of La based compounds. 3.2. The Pr(Ni /_ , Co ,) 5 compounds
The variation of the total specific heat C versus temperature for the compounds with c = 0.00, 0.05, 0.10 and 0.20 and YNi 5 is shown in Fig. 1. As the 20
• 15
[]
c=O.O Pr(Ni. Co ). / ' c=0.05 ,-c ¢ ~ .
•
c=O.lO
f=
~
.
"
•
el
;F/
U
s ooOO °°
3.1. YNi 5 o
The specific heat of the compound YNi 5 was measured in Strasbourg between 1.5 and 20 K and in Grenoble between 1.5 and 45 K. The two sets of data obtained are in excellent agreement with each other
315
s
~o
~s
zo
zs
30
T (K)
Fig. 1. Temperature variation of the specific heat of YNi~ and of the compounds Pr(Ni I ,.Co,)s with c = 0.00, 0.05, 0.10 and 0.20. The data above 20 K for PrNi 5 are taken from Ref. [1].
316
R. Kuentzler et al./Journal of Magnetism and Magnetic Materials 162 (1996) 314-318
figure shows, all the Pr compounds display a broad peak which becomes broader and less pronounced with increasing Co content. To analyze the data we use the following expression: C = Cel q- Cph "~ A C ,
12
i
10 "6
?
•
~=o.2o ." ~ ¢ ~ - . . ~ t ~ ' ' -
/
j 7' 0
~ --
0
and x4e x
9NkB(T/fgD)3)oOJT(e x [ _
1944N(T/OD)3,
(1)
where N is the number of atoms per formula unit (six in the present case) and fl is in J / K 4 mol. We assume that the host specific heat for this series is well represented by YNi 5 with the proviso that the Debye temperature of the compounds be normalized to that of YNi 5. To do this we proceed as follows. It has been shown by Debye that the mean square displacement for a vibrating atom is proportional to T/(M6) 2) (see, e.g., Ref. [10]). Assuming that all the atoms in a compound have the same mean square displacement we may write for a pseudobinary compound Pr(Ni I _ cCOc)5: O 3 ( Y N i s ) / O 3(pr(Ni]_ cCo,.)5) M /2 +
5(I - c)M i/2 + ~ r,A3/2 M3/2 + .... Ni
,
o
Pr(Nil ~Co) s i
5
i
10
i
i
1S 20 T (K)
"
i
25
30
Fig. 2. Thermal variation of the excess specific heat AC for compounds containing 0, 5, 10 and 20% Co.
1) ~
represent, respectively, the electronic and lattice contributions to the specific heat, and AC the excess specific heat which includes the Schottky/magnetic and nuclear contributions. The latter, however, is expected to be insignificant in the temperature range in which the measurements were made. For T << 6) D the phonon term may be written as: Cph = fiT 3 =
~'.~
• ~6
-
~4
Cel = TT
=
C=0
o c=O.OS , , , ~
8
where
Cph
i
•
~p~lAt3/2
. . . . . co
=
1.27, (2)
and hence O(YNis)/~9(Pr(Ni 1_,Coo) 5) ~ 1.083 for all the compounds investigated. This ratio does not change much because the atomic masses of Ni and Co are very similar. Applying the above equation with LaNi 5 gives a ratio of 1.003 and @D = 340 K
for PrNi 5. This correction, however, gives a poor value for the host specific heat Chost. Therefore, we use YNi 5 for the above correction. It should be noted that Y compounds often give better corrections compared with those obtained with La compounds, as has been shown by Bouvier et al. [7]. We have, therefore, normalized the Debye temperature of the alloys by dividing the temperature of measurements for YNi 5 by 1.083. We shall call this Chosr Subtracting this latter contribution from the total specific heat then provides us with the total magnetic (in the case of PrNi 5, the Schottky) contribution AC, which is shown in Fig. 2 for four of the compounds studied. It is clear from this figure that with increasing Co content, i.e. with increasing exchange interaction: • the peak height decreases slightly, and • the position of the peak moves to higher temperatures. As the cobalt-induced ferromagnetic order, which occurs in compounds with c > 0.05 [6] and which is likely inhomogeneous, does not lead to an anomaly in the AC curves, we will first assume that cobalt does not contribute to the magnetic specific heat AC. Indeed, the magnetization data show that the compounds with c = 0.05, 0.10 and 0.20 have a Tc of 2.5, l0 and 38 K, respectively, temperatures at which no anomaly can be seen on the specific heat variations. Comparing AC with the thermal variation of magnetization (Fig. 4 of Ref. [6]), where the broad peak is attributed to the crystal field effects of the Pr ions, it is worth noting that the two behaviors differ
R. Kuentzler et al. / Journal of Magnetism and Magnetic Materials 162 (1996) 314-318
since the maximum of magnetization does not move to higher temperatures with increasing exchange interaction, i.e. with increasing Co concentration. This will be discussed further below.
10~ 12
]
i
i
317 i
i
P~(Ni 1 cC°c)s
~
o
E
~k
I I l~:~aoocloD D
8
~
6
~
4
3.3. Analysis From the above considerations the excess specific heat AC due to praseodymium alone may be computed from the Schottky contribution of its crystal field levels. This may be cast into the following convenient form: AC =
R / T Z { 2 Ai exp( - A i / T ) / Z - [ ~ A i exp( - A i / T ) / Z ] 2 ) ,
(3)
Z is the partition function, i.e. Z = ~ i A e x p ( - A i / T ) and A / = E i - E0, i = 0,1,2 . . . . . 8; E~ is the ith energy eigenvalue of the relevant Hamiltonian. This is given by:
0
5
10
15
20
25
30
T (K) Fig. 3. Variation with temperature of the computed and experimentally determined excess specific heat for PrNi 5 and Pr(Ni0.gC°0.1)5- The data points for PrNi 5 above 20 K are taken from Ref. [1]. Lines are calculated with an effective field H~n = 0 and 65 kOe for PrNi 5 and Pr(NillgCoo i )5, respectively.
where
0
0
6
6
H = B°Ol~ + B~)O° + B 6 0 6 + B 6 0 6
-
-
gj/.L BHeff "J,
(4) where B,,' are the crystal field parameters and O,,~ are the Stevens equivalent operators and the quantization direction of the CF Hamiltonian is taken along the c-axis. When diagonalizing the above Hamiltonian, however, the direction of the effective exchange field was taken along the b-axis, the easy direction of magnetization of the compounds. The last term represents the exchange interaction, where:
Hen. = nM m + n~x(CO )
(5)
is the total effective field acting on the Pr 3+ ions. In the above equation, Mpr is the induced magnetization on Pr 3+, n the total isotropic bilinear exchange parameter and He×(Co) the exchange field arising from the cobalt sublattice. Considering the effective field Hen. as an adjustable parameter we fitted the variation of the excess specific heat AC with temperature to Eq. (3) using the crystal field parameters of PrNi 5 given by Reiffers et al. [12] for all the compounds studied. Fig. 3 shows the temperature variation of both the experimental and computed AC for both PrNi 5 and Pr(Ni0.9oCo0.1o)5, the corresponding values of H e ft being 0 and 65 kOe, respectively.
For PrNi 5 the peak heights of both curves are almost the same and the peak temperatures differ by only about 1.5 K. The agreement between the two, therefore, is quite satisfactory. Recently, Kim-Ngan et al. [11] measured the specific heat of a single crystal of PrNi 5. The values of their refined CF parameters were found to be very close to those obtained by Reiffers et al. [12] which we used in our computation. While the peak temperatures of their experimental and computed curves agree very well, the heights differ by about 20% and hence the overall agreement is not much better than ours. For the 10% Co compound the peak height is in good agreement with the experimental curve, but the temperature of the experimental and computed curves differs by 6 K. Therefore, the reduction of the peak height is satisfactorily explained by the effect of Hen., while the latter is not sufficient to account for the shift of T,.... . Moreover, this shift is larger than that observed for the susceptibility of the same compositions reported in Ref. [6]. One possible explanation for this is the anticipated change in the CF parameters due to alloying which would act only on the Scbottky term and not on the susceptibility. This is possible because the same matrix elements are not involved in both expressions. The only plausible explanation, therefore, seems to be a modification of the CF parameters due to cobalt substitution. Such an hypothesis, however, remains to be confirmed by additional experiments.
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It may be suggested that the effect of the change of volume on specific heat with Co concentration should be taken into account. This, however, is both difficult and will not improve the fit because one may then be forced to change the theoretical value of ~9(non-magnetic)/~9(R compound) in order to describe the lattice contribution better. This means that this ratio will sometimes need to be adjusted which in turn implies that the theory does not need to be perfect. It would also be very useful to measure the specific heat of the compounds under an applied magnetic field in order to follow the evolution of the magnetic component of the specific heat and compare it with the effect of the exchange field induced by the cobalt atoms. In conclusion, we find that, in this series, the effect of cobalt substitution is to reduce the height of the large peak found in the specific heat of PrNi s and to move the maximum of the peak to higher temperatures. The reduction in the peak amplitude is well explained by the effect of the exchange field induced by the cobalt on Pr 3+ ions. However, this exchange field alone does not seem to be sufficient to explain the observed shift in AC(T). A slight re-adjustment of the CF parameters would be necessary to obtain better agreement, subject to the condi-
tion that this does not change the susceptibility curves.
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