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The heat capacity of LaPd3 and PrPd3 at low temperature
Solid State Communications, Vol. 28, pp. 857-859. Pergamon Press Ltd. 1978. Printed in Great Britain.
THE HEAT CAPACITY OF LaPd3 AND PrPda AT LOW TEMPERATURE J.M. Machado da Silva* Clarendon Laboratory, Oxford, England (Received 3 October 1978 by C. I¢. McCombie) Values of 3' = o.33 -+0.01 mJ/K~-gatom and 0D = 176 -+ 1 Kwere found for LaPda. PrPd3 shows magnetic ordering below 0.6 K and a Schottky anomaly whose maximum lies around 1.8 K. The crystalline field at the Pr3÷ site creates a F3 (doublet) excited state lying 4 K above the I's (triplet) ground state. 1. INTRODUCTION IN THE LAST FEW YEARS there has been considerable interest in the magnetic properties of rare-earth-M3 phase of the AuCu3 structure. Results have been published by Gardner et al. [1] (REPda), by Buschow et al. [2] (REIn2), by Deb Ray et al. [3] (RESn3) and by Hutchens and Wallace [4] (REPb3). In these substances it is believed that the rare-earth ion is in a state of well defined angular momentum J but perturbed by the presence of crystalline electric fields. Among the REM3 phases the strength of the exchange interactions, as shown by the Curie points, varies widely; it seems that in the REPd3 it is one order of magnitude smaller [ 1] than in the other series. The weakness of the exchange interaction in the REPd3 series must be connected with the band structure of these compounds, and the low values for the diamagnetic susceptibility of YPd3, LaPd3 suggest a low density of states at the Fermi surface. This would imply a small value for the electronic specific heat coefficient 3'. Specific heat measurements at low temperatures would clarify this point as well as to locate phase transitions and to shed some light on the degeneracy of the ground state in the magnetic compounds. We have carried out heat capacity measurements on a series of REPda and report here the results on LaPd3 and PrPd3. 2. EXPERIMENTAL PROCEDURE The experiments were performed in a calorimeter employing adiabatic demagnetization of a paramagnetic salt as the cooling process. The method of measurement has been described elsewhere [7]. The samples used in the heat capacity measurements were prepared by Harris [1 ] by arc melting stoichiometric quantities of the pure metals in an argon atmosphere. Metallographic examination of the arc melted * Present address: Centro de Fisica, Universidade do Porto, Portugal.
buttons showed that they were in the single phase condition. Standard chemical techniques which determine the rare-earth content within + 0.4% were used to claeck the composition of some of the REPd3 series. The composition of the analysed alloys agreed with the nominal values within the experimental error. Details of the preparation of the samples can be found in [1 ]. 3. RESULTS The results for LaPda in the temperature range 1.66.9K are shown in Fig. 1 where Cv[RTis plotted vs T 2. It is easily seen that the data are fitted by an equation of the type Cv = 7776 (T/Oo) 3 + 43"T, where Cv is the specific heat per g molecule, 0o is the Debye temperature and 7 is the coefficient of the electronic specific heat of 1 g atom. The values found for 0D and 3' are 176 -+ 1 K and 0.33 -+0.01 mJ K -~ respectively. The specific heat values reported here are substantially smaller than those of Hutchens et al. [8], and do not exhibit the complicated temperature dependence attributed by them to spin fluctuations. However, we agree that the value of 3' is exceptionally small, being one order of magnitude less than is commonly found in La compounds and in La metal. The small value of 7 for LaPd3 is consistent with the low value of the susceptibility measured by Gardner et al. [1 ] and with a weak exchange interaction as discussed above. The heat capacity of PrPd3 was measured from 0.35 to 10.7 K and the results are shown in Fig. 2 as Cv/R vs T. The heat capacity for LaPd3 is also plotted, and below 4 K it is much smaller than that of PrPd3, although they cross at about 8.5 K. We would expect that 0D would be approximately the same for both compounds due to the similarity of the lattices. However, values of 0D for Lain3 and Prln3 [9, 10] differ by 8% with 0o for Prln3 bigger than that for Lain3. Similar differences would account for the low value of the heat capacity of PrPd3 above 8.5 K. The heat capacity
857
858
THE HEAT CAPACITY OF LaPda AND PrPd3 l
I
i
1
I
Vol. 28, No. 10 I
7 CV 6 RT 5 (K'IO~4 3 2 1 I
0
10
I
20 T~IK ~1 30
40
50
Fig. 1. C / R T v s T 2 for LaPd3.
[1.7
I
I
I
[
I
I
l
I
I
I
0.6 0.5
CV o.4 o.3 / !
.0.2 t-
"
""
/"
0.1 I-"/',
~ ~L~''<- . . . . . . . . I
0
1
2
~
~
3
t'-""
-'-t
4
I
5 6 T(K)
Fig. 2. The specific heat of PrPd3. o experimental values. - . . . . Specific heat o f LaPd3. additional to the electronic and lattice terms is associated with magnetic ordering taking place at 0.6 K and characterized by the typical X shape and by a Schottky anomaly due to the interaction of the crystal field on the two 4 f e l e c t r o n s on Pr 3÷. The crystalline electric field on the Pr site due to the charges on the neighbouring ions has cubic symmetry; its effects can therefore be obtained from the results of Lea et al. [ 11 ]. The appropriate Hamiltonian which reflects the cubic symmetry can be expressed as ,J£ = W[x[(04O + 5044)/F(4)]
-- (1 -- Ixl)(O ° -- 21046)F(6)]
I
I
I
7
8
9
I
10 11
Schottky anomaly due to the crystal field. - - - -
where 04°, 0 4, O ° and O~ are angular m o m e n t u m operators and F ( 4 ) and F ( 6 ) are known coefficients; definitions and further details may be found in Lea et al. [11 ]. The parameter x reflects the importance of the fourth and sixth order terms, while W is a scale factor which determines the magnitude o f the crystal field splittings. Tentative values of x and W can be calculated from a point charge model. The result of such calculation [ 1 ] predicts a Us (triplet) ground state and a P3 (doublet) first excited state; however these states will cross over if the sixth order term [11] in the crystal field is sufficiently large to produce values o f x ~ 0.74. This possibility cannot be excluded on the basis of the
Vol. 28, No. 10
THE HEAT CAPACITY OF LaPd3 AND PrPd3
point-charge calculation alone, but the point can be settled by considering the magnitude of the specific heat. For a system with (effectively) two energy levels, the heat capacity represented by the Schottky anomaly is a function of the ratio gt/go of the excited state and ground state degeneracies. If the ground state is 1"3, gl/go = 3/2 and Cmax]R = 0.61, which is much larger than the observed value in Fig. 2. For the 1's ground state, however, gx/go = 2/3 and Crna~/R = 0.31 which is perfectly consistent with the measured values. We conclude that the ground state is indeed Ins, in which case the energy difference E1 between the Ps and 1'3 levels is
859
4.2 K. The full specific heat curve may then be calculated from
C/R = (El/Kr)Z(g,/go) exp (E,/KT) × [1 + (gl/go) exp (E1/KT)]-2 and is plotted for comparison in Fig. 2.
Acknowledgements - We are grateful for the interest and help of Drs. R.W. Hill, W.E. Gardner and I.R. Harris. This research was supported by a grant from The Science Research Council.
REFERENCES 1. GARDNER W.E., PENFOLD J., SMITH T.F. & HARRIS I.R., J. Phys. F2, 133 (1972). 2. BUSCHOWK.H.J., DE WlJN H.W. & VAN DIEPEN A.H., J. Chem. Phys. 50, 137 (1969). 3.
DEB RAY D.K., SOUGI M. & MERIEL P., Paper presented at the Conf. Rare Earths Actinides, Dusham, England, July (1971).
4.
HUTCHENS R.D. & WALLACE W.E., J. Solid State Chem. 3, 564 (1971 ).
5.
HARRIS I.R. & RAYNOR G.V., J. Less Common Metals 9, 263 (1965).
6.
GARDNER W.E.,PENFO LD J.& HARRIS I.R.,J. Phys. Paris, CI139 (1971).
7.
MACHADODASILVAJ.M.,McDERMOTTJ.M.&HILLR.W.,J. Phys. C5, 1573(1972).
8.
HUTCHENS R.D., RAO V.U.S., GREEDEN J.E. & CRAIG R.S.J. Phys. Soc. J.'tpan 32, 451 (1972).
9.
VAN DIEPEN A.M., CRAIG R.S. & WALLACE W.E., J. Phys. Chem. Solids 32, 1867 (197 I).
10.
NASUS.,VANDIEPENA.M.,NEUMANNH.H.&CRAIGR.S.,J. Phys. Chem. Solids32,2773(1971).
11.
LEAK.R., LEASKM.J.M.&WOLFW.P.,J. Phys. Chem. Solids 23, 1381 (1962).
THE HEAT CAPACITY OF LaPd3 AND PrPda AT LOW TEMPERATURE J.M. Machado da Silva* Clarendon Laboratory, Oxford, England (Received 3 October 1978 by C. I¢. McCombie) Values of 3' = o.33 -+0.01 mJ/K~-gatom and 0D = 176 -+ 1 Kwere found for LaPda. PrPd3 shows magnetic ordering below 0.6 K and a Schottky anomaly whose maximum lies around 1.8 K. The crystalline field at the Pr3÷ site creates a F3 (doublet) excited state lying 4 K above the I's (triplet) ground state. 1. INTRODUCTION IN THE LAST FEW YEARS there has been considerable interest in the magnetic properties of rare-earth-M3 phase of the AuCu3 structure. Results have been published by Gardner et al. [1] (REPda), by Buschow et al. [2] (REIn2), by Deb Ray et al. [3] (RESn3) and by Hutchens and Wallace [4] (REPb3). In these substances it is believed that the rare-earth ion is in a state of well defined angular momentum J but perturbed by the presence of crystalline electric fields. Among the REM3 phases the strength of the exchange interactions, as shown by the Curie points, varies widely; it seems that in the REPd3 it is one order of magnitude smaller [ 1] than in the other series. The weakness of the exchange interaction in the REPd3 series must be connected with the band structure of these compounds, and the low values for the diamagnetic susceptibility of YPd3, LaPd3 suggest a low density of states at the Fermi surface. This would imply a small value for the electronic specific heat coefficient 3'. Specific heat measurements at low temperatures would clarify this point as well as to locate phase transitions and to shed some light on the degeneracy of the ground state in the magnetic compounds. We have carried out heat capacity measurements on a series of REPda and report here the results on LaPd3 and PrPd3. 2. EXPERIMENTAL PROCEDURE The experiments were performed in a calorimeter employing adiabatic demagnetization of a paramagnetic salt as the cooling process. The method of measurement has been described elsewhere [7]. The samples used in the heat capacity measurements were prepared by Harris [1 ] by arc melting stoichiometric quantities of the pure metals in an argon atmosphere. Metallographic examination of the arc melted * Present address: Centro de Fisica, Universidade do Porto, Portugal.
buttons showed that they were in the single phase condition. Standard chemical techniques which determine the rare-earth content within + 0.4% were used to claeck the composition of some of the REPd3 series. The composition of the analysed alloys agreed with the nominal values within the experimental error. Details of the preparation of the samples can be found in [1 ]. 3. RESULTS The results for LaPda in the temperature range 1.66.9K are shown in Fig. 1 where Cv[RTis plotted vs T 2. It is easily seen that the data are fitted by an equation of the type Cv = 7776 (T/Oo) 3 + 43"T, where Cv is the specific heat per g molecule, 0o is the Debye temperature and 7 is the coefficient of the electronic specific heat of 1 g atom. The values found for 0D and 3' are 176 -+ 1 K and 0.33 -+0.01 mJ K -~ respectively. The specific heat values reported here are substantially smaller than those of Hutchens et al. [8], and do not exhibit the complicated temperature dependence attributed by them to spin fluctuations. However, we agree that the value of 3' is exceptionally small, being one order of magnitude less than is commonly found in La compounds and in La metal. The small value of 7 for LaPd3 is consistent with the low value of the susceptibility measured by Gardner et al. [1 ] and with a weak exchange interaction as discussed above. The heat capacity of PrPd3 was measured from 0.35 to 10.7 K and the results are shown in Fig. 2 as Cv/R vs T. The heat capacity for LaPd3 is also plotted, and below 4 K it is much smaller than that of PrPd3, although they cross at about 8.5 K. We would expect that 0D would be approximately the same for both compounds due to the similarity of the lattices. However, values of 0D for Lain3 and Prln3 [9, 10] differ by 8% with 0o for Prln3 bigger than that for Lain3. Similar differences would account for the low value of the heat capacity of PrPd3 above 8.5 K. The heat capacity
857
858
THE HEAT CAPACITY OF LaPda AND PrPd3 l
I
i
1
I
Vol. 28, No. 10 I
7 CV 6 RT 5 (K'IO~4 3 2 1 I
0
10
I
20 T~IK ~1 30
40
50
Fig. 1. C / R T v s T 2 for LaPd3.
[1.7
I
I
I
[
I
I
l
I
I
I
0.6 0.5
CV o.4 o.3 / !
.0.2 t-
"
""
/"
0.1 I-"/',
~ ~L~''<- . . . . . . . . I
0
1
2
~
~
3
t'-""
-'-t
4
I
5 6 T(K)
Fig. 2. The specific heat of PrPd3. o experimental values. - . . . . Specific heat o f LaPd3. additional to the electronic and lattice terms is associated with magnetic ordering taking place at 0.6 K and characterized by the typical X shape and by a Schottky anomaly due to the interaction of the crystal field on the two 4 f e l e c t r o n s on Pr 3÷. The crystalline electric field on the Pr site due to the charges on the neighbouring ions has cubic symmetry; its effects can therefore be obtained from the results of Lea et al. [ 11 ]. The appropriate Hamiltonian which reflects the cubic symmetry can be expressed as ,J£ = W[x[(04O + 5044)/F(4)]
-- (1 -- Ixl)(O ° -- 21046)F(6)]
I
I
I
7
8
9
I
10 11
Schottky anomaly due to the crystal field. - - - -
where 04°, 0 4, O ° and O~ are angular m o m e n t u m operators and F ( 4 ) and F ( 6 ) are known coefficients; definitions and further details may be found in Lea et al. [11 ]. The parameter x reflects the importance of the fourth and sixth order terms, while W is a scale factor which determines the magnitude o f the crystal field splittings. Tentative values of x and W can be calculated from a point charge model. The result of such calculation [ 1 ] predicts a Us (triplet) ground state and a P3 (doublet) first excited state; however these states will cross over if the sixth order term [11] in the crystal field is sufficiently large to produce values o f x ~ 0.74. This possibility cannot be excluded on the basis of the
Vol. 28, No. 10
THE HEAT CAPACITY OF LaPd3 AND PrPd3
point-charge calculation alone, but the point can be settled by considering the magnitude of the specific heat. For a system with (effectively) two energy levels, the heat capacity represented by the Schottky anomaly is a function of the ratio gt/go of the excited state and ground state degeneracies. If the ground state is 1"3, gl/go = 3/2 and Cmax]R = 0.61, which is much larger than the observed value in Fig. 2. For the 1's ground state, however, gx/go = 2/3 and Crna~/R = 0.31 which is perfectly consistent with the measured values. We conclude that the ground state is indeed Ins, in which case the energy difference E1 between the Ps and 1'3 levels is
859
4.2 K. The full specific heat curve may then be calculated from
C/R = (El/Kr)Z(g,/go) exp (E,/KT) × [1 + (gl/go) exp (E1/KT)]-2 and is plotted for comparison in Fig. 2.
Acknowledgements - We are grateful for the interest and help of Drs. R.W. Hill, W.E. Gardner and I.R. Harris. This research was supported by a grant from The Science Research Council.
REFERENCES 1. GARDNER W.E., PENFOLD J., SMITH T.F. & HARRIS I.R., J. Phys. F2, 133 (1972). 2. BUSCHOWK.H.J., DE WlJN H.W. & VAN DIEPEN A.H., J. Chem. Phys. 50, 137 (1969). 3.
DEB RAY D.K., SOUGI M. & MERIEL P., Paper presented at the Conf. Rare Earths Actinides, Dusham, England, July (1971).
4.
HUTCHENS R.D. & WALLACE W.E., J. Solid State Chem. 3, 564 (1971 ).
5.
HARRIS I.R. & RAYNOR G.V., J. Less Common Metals 9, 263 (1965).
6.
GARDNER W.E.,PENFO LD J.& HARRIS I.R.,J. Phys. Paris, CI139 (1971).
7.
MACHADODASILVAJ.M.,McDERMOTTJ.M.&HILLR.W.,J. Phys. C5, 1573(1972).
8.
HUTCHENS R.D., RAO V.U.S., GREEDEN J.E. & CRAIG R.S.J. Phys. Soc. J.'tpan 32, 451 (1972).
9.
VAN DIEPEN A.M., CRAIG R.S. & WALLACE W.E., J. Phys. Chem. Solids 32, 1867 (197 I).
10.
NASUS.,VANDIEPENA.M.,NEUMANNH.H.&CRAIGR.S.,J. Phys. Chem. Solids32,2773(1971).
11.
LEAK.R., LEASKM.J.M.&WOLFW.P.,J. Phys. Chem. Solids 23, 1381 (1962).