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The influence of crystalline electric field on the low temperature properties of CeCd11
Journal of Magnetism and Magnetic North-Holland, Amsterdam
Materials
75 (1988) 355-360
355
THE INFLUENCE OF CRYSTALLINE ELECTRIC FIELD ON THE LOW TEMPERATURE PROPERTIES OF CeCd,,
J. TANG
and K.A. GSCHNEIDNER,
Jr.
Ames L.aboratov *, Departments of Physics and Materials Iowa State University, Ames, IA 50011, USA
Received
Science and Engineering,
28 July 1988
Low temperature heat capacity, magnetic susceptibility and ac resistivity were measured on CeCd,,. Evidence is reported property measurements. The for the existence. of a crystalline electric field (CEF) effect in CeCd,, in these low temperature symmetry into three doublets, with an energy equal to ground state of the Ce3+ ion, 2Fs,z. is split by CEF of tetragonal E, = 0, E, = 17.5 K and E, = 80.2 K, respectively. The magnetic entropy up to 70 K was calculated from heat capacity data. The magnetic susceptibility follows a CEF modified Curie-Weiss behavior with an effective moment of pert = 2.57~~ indicating that 4f-electrons of Ce 3+ ions are localized. Comparison of the ac resistivity of our sample with spin-disorder resistivity in presence of CEF is also discussed.
b,
1. Introduction CeCd,, crystallizes in cubic BaHg,,-type structure, with a Ce-Ce distance d = 6.59 A [l]. Detailed examination of the structure reveals that a Ce atom is surrounded by 12 nearest neighboring Cd atoms and 8 second nearest neighboring Cd atoms. Fig. 1 shows the atomic arrangement in CeCd,,. The neighboring Cd forms a polyhedron of tetragonal symmetry about the Ce atom. Under the crystalline electric field (CEF), the 6-fold degenerate ground state of Ce3+ ion, 2F5,2, will be split into three doublets. According to the CEF Hamiltonian for Ce3+ ion (J = 5/2) with tetragonal symmetry [2], HCEF = B;O;
+ B4”0,” -I-B,40,4,
(1)
where coefficients B,” and operators Onm were defined in Hutchings [3]. The final eigenstates consist of three doublets 1k l/2), a I+ 5/2) + * Supported by USDOE, Office of Basic Energy Sciences, Division of Materials Sciences, under Contract No. W-7405ENG-82.
0304-8853/88/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
Fig. 1. A projection along the c-axis of the atomic arrangement of CeCd,,. The solid circles show the arrangement of the Cd atoms about a Ce atom. The big circles represent the Ce atoms and the small ones the Cd atoms. The value(s) next to an atom indicate the distance(s) along the c-axis from the a-b plane.
B.V.
356
J. Tang, K.A. Gschneidner, Jr. / Low
temperature properties of CeCd,,
and CEF
1T 3/2) and b 1i- 5/2) - a ] T 3/2). The actual energy levels of these doublets and the values of a and b depend upon the coefficients B,!!. This CEF splitting will influence the behavior of heat capacity, magnetic susceptibility and electrical resistivity of CeCd,, over the temperature range comparable to the energies of splitting. Low temperature property measurements, especially the heat capacity, allowed us to determine the energies of this 3-level CEF in CeCd,,.
b
2. Experimental
0
IO
20
30
40
TEMPERATURE
CeCd,, and LaCd,, were prepared by melting stoichiometric amounts of the constituents in a sealed tantalum crucible under helium atmosphere using a resistance furnace. The samples were then heat treated at 580°C for 4 days. Metallography showed that the samples were single phase and X-ray diffraction confirmed the previously reported crystal structure. OThe lattice parameter of CeCd,, (a = 9.313 & 3 A) is close to the value reported earlier 9.319 A [1,4]. The low temperature calorimeter used in this research is an isolation heat-pulse type with a mechanical switch [5]. The magnetic susceptibility measurement was carried out using a Faraday magnetometer in a field H = 0.96 T [6]. A conventional four point probe technique was used for the ac resistivity measurement.
60
70
Fig. 2. Heat capacities of CeCd,, and LaCd,, from 1.5 to 70 K. The inset shows an expanded version of the data below 20 K. Not all of the data points are shown.
the similar lattice constants (a = 9.339 A for LaCd,, [l] and 9.313 A for CeCd,,) and the same outer electronic configurations of the two compounds (Ce is trivalent, see section 5, Magnetic susceptibility). Therefore, the difference between the two heat capacities (&cd,, - CLaCd,,) should represent the contributions essentially due to the 4f-electrons in the Ce3+ ion. The shape of curve versus temperature (see fig. 4) (CCeCd,, - G&l,,) shows a fairly sharp bump at = 7 K and a broader bump at = 25 K, suggesting the existence of 3-level CEF effect. The main peak near T = 7 K is due to
3. Heat capacity
A
1.0 -
The heat capacity of CeCd,, was measured over the temperature range 1.5 K < T < 70 K, and it is shown in fig. 2. Also shown in fig. 2 is the heat capacity of LaCd,,, which is isostructural with CeCd,,. The more typical C/T vs. T2 is shown in fig. 3. The temperature dependence is quite unusual and the magnitude above 6 K (36 K2) is quite large (= 800 mJ/mol K’). Below 2 K, it appears that CeCd,, may be tending towards ordering magnetically. In order to understand this behavior we have assumed that the electronic and lattice heat capacities of CeCd,, are the same as that of LaCd,,. This is quite reasonable because of
50 (K)
CeC4,
.
-
0.9 Y al 0.7 a $ 0.6 _( ;I 2 0.5
r’ ,+
0.3 0.2 0.4 1J, -t 0
, , , , , , , , , , , , , , , ,: IO
20
30
40
50
60
70
80
90
100
T*(K*)
Fig. 3. A C/T vs. T* plot for CeCd,,. The crosses are for a sample weighing 1.58 g and the dots are for a sample weighing 14.21 g.
J. Tang, K.A. Gschneidner, Jr. / Low temperature properties
0 Fig. 4. The difference
10
of the two heat capacities
20
30 40 TEMPERATURE (K)
(CCeCd,, - CLaCd,,) (+),
the excitation of 4f-electron from ground state level to the 1st excited level and the 25 K shoulder could be due to the excitation from the 1st excited level to the 2nd excited level. To make sure this interpretation is correct we calculated the magnetic heat capacity of a 3-level CEF system, which takes the form
of CeCd,,
50
and C,-,,
60
R Ef exp( - El/T) ( [ +(Ez-Ed2
exp(-(E,
70
experiment is obvious. Energy levels and the constant y’ obtained in this manner are: E, = 0,
(3)
E, = 17.5 K,
(4)
E, = 80.2 K,
(5) K*.
(6)
+ E; exp( - E/T)
+E2)/T)])
IO
I
9.13
__________
X(T’[l
357
+ y’T (line). Inset: energy levels of the CEF
y’ = 9.0 mJ/mol CCEF =
and CEF
-------
I
I
_~____~_~~~~~_~_~~__~__
+exp(-E,/T)
0
i2
(2) where R is the universal gas constant, E, and E, are the energies (in K) of the 1st and 2nd excited levels, respectively. After several trials of fitting, c cEF to &cd,, - &cd,,, good agreement between the two was obtained when we added a small linear term y’T to the calculated Cc,,. Shown in fig. 4 (solid line) is the function Cc,, + y’T. The agreement between this function and the
8.
0
CeW,
0
2 s
0 0
: ‘; 8
6-
:
4
ooo
0 0 0 0
zi
0
o EXPERIMENTAL ENTROPY --CALCULATED CEF ENTROPY_
20
01O 0
I
IO
I
20
Fig. 5. Entropy
I
I
30 40 TEMPERATURE (K)
associated
I
50
with the CEF.
I
60
I 70
J. Tang, K.A. Gschneidner, Jr. / Low
358
E, = 17.5 K is one of the lowest CEF splittings found in Ce compounds. The only Ce compound having a lower CEF splitting, that we know of, is cerium ethylsulphate with E, = 6.6 K [7]. Usually, CEF splittings occur at temperatures 5 times to an order of magnitude higher. y’T is the electronic contribution to heat capacThe ity of CeCd,, in excess of that of LaCd,,. electronic specific heat constant, y, and the Debye temperature 0, of LaCd,, are 17 mJ/mol K2 and 280 K, respectively, and were obtained from a least squares fit of the data to a C/T versus T2 plot between 1.3 and 2.5 K. Adding y’ to the y of LaCd,,, the electric specific heat constant is estimated to be 26 mJ/mol K2 for CeCd,,. The Debye temperature of CeCd,, is assumed to be 280 K. The magnetic entropy, S,,,, associated with our heat capacity data was also calculated. Near T = 70 K, S, reaches a value close to 9.13 J/mol K (fig. 5) which is the expected value for a 3-level CEF system
S cEF = R In(m)
= R In 3 = 9.13 J/mol
K.
(7)
In the above expression, m is the number of doublets in a CEF system [8], where m = 3 in our case. The agreement between the experimental
temperature properties of CeCd,,
and CEF
entropy and the theoretical value confirms the splitting of a 3-level CEF. Since J = 5/2 for Ce3+, we expect the total magnetic entropy Sz = R ln(2J + 1) = R In 6. Knowing the entropy associated with CEF is R In 3, we believe that the difference (R In 6 - R In 3 = R In 2) is associated with magnetic ordering below T = 1.3 K. Because of the low temperature limit of our apparatus we were unable to make measurements below 1.3 K, but the tendency toward magnetic ordering at a lower temperature can be clearly seen from the upturn in heat capacity at T = 2 K (and is also evident in the magnetic susceptibility, see section 5). Also it is not difficult to understand that the offset between the experiment and Cc,, + y’T (fig. 4) below = 10 K is due to the non-zero tail of the magnetic ordering peak. 4. AC resistivity The ac resistivity of our CeCd,, sample is shown in fig. 6. The resistivity data over a wider temperature range is also shown in the fig. 6 inset. We can see that there is a resistivity drop near T = 7 K as temperature decreases. We believe that this is associated with the spin-disorder resistivity of a CEF system. Since the 2nd excited level lies high
0
o EXPERIMENTAL 2.50
a/---
---SPIN-DISORDER
B’
CeCd,,
2 2.25 0
/’
$2.00 6
1.75
b E
1.50
/‘O /‘Cl0 0
/‘O NO
‘0
/O
N-0
.bB
i+ 1.25
I
I
I
2
4
6
1
8
I
I
I
I
lo
12
14
16
I
18
TEMPERATURE (K1 Fig. 6. Experimental
resistivity
of CeCd,, (circles); and p,,,, = p,, + pS (line), with A = 0.394, B = 4.04, C = 2.20 and p,, = 0.655 ~0 cm. Inset: experimental data over a wider temperature range.
J. Tang K.A. Gschneidner, Jr. / LAW temperature properties
above both the ground and the 1st excited levels, we assumed that the 2nd excited level remains unoccupied over the temperature of concern and treat resistivity as a 2-level system. According to Rao and Wallace [9], the spin-disorder resistivity of a 2-level CEF system can be derived from the first Born approximation. It follows below: A+Bexp(-E,/T) “=
1 + exp(-E,/T)
of CeCd,,
359
and CEF
data can be expressed for T> 4 K
by the following
equation
where C = 0.830 emu K/mol,
(11)
O=
(12)
-5.5
K,
(Y= - 5.7 X lop4 emu/mol,
(13)
C + (1 +
exp(-&/T))(l + exp(&/T))
’ (8)
where A, B and C can be determined from fitting the experimental data to this equation. The total resistivity is composed of three parts. One is the spin-disorder resistivity p, as discussed above, another comes from the phonon scattering of conducting electrons or,,, and the third part is the temperature independent residual resistivity due to impurities pa. Since the phonon scattering resistivity near liquid helium temperature is about two orders of magnitude smaller than experimental resistivity (estimated from the Debye temperature) [lo], we neglected phonon scattering resistivity Q. Therefore, the total resistivity is the sum of two parts Pm = PO + Ps.
and f is the modification factor due to CEF (see below). The experimental susceptibility (in the form as XT) and the fit of the data to eq. (10) are shown in fig. 7. The term C/(T - 0) in eq. (10) is the Curie-Weiss paramagnetic contribution from 4f-electrons of Ce3+ ions. The value of C = 0.830 corresponds to an effective moment perr = 2.57~,, which is close to the expected theoretical value of a free Ce3+ ion pert = 2.54~~ [ll]. This indicates that the 4f-electrons in CeCd,, are well localized in agreement with a large Ce-Ce distance d = 6.59 A. The negative paramagnetic Curie temperature 0 = -5.5 K infers that the system will order antiferromagnetically at low temperature. Actually, the tendency toward magnetic ordering was seen from heat capacity data at T-c 2 K, as mentioned earlier (section 3) and is seen in the inset of fig. 7.
(9)
This equation was taken to fit- the experimental data for temperature 1.5 K i'T < 20 K, and the constants A, B, C and p0 were determined. Such a determined equation is shown in fig. 6 together with the experimental data. The values of A, B, C and p,, are given in the caption of fig. 6. We see that, in spite of a slight difference between experiment and eq. (9), the drop of resistivity near T = 7 K can be explained with spin-disorder resistivity as expressed by eq. (9).
5. Magnetic susceptibility The magnetic susceptibility measurement was carried out at a field H = 0.96 T over the temperature range 1.5 K < T < 250 K. The experimental
0.31 ’ 0
’
50
’
’
loo
’
’
’
’
200 150 TEMPERATURE(K)
’
’
250
’
’
300
Fig. 7. Magnetic susceptibility times the temperature vs. temperature for CeCd,, - a comparison of experiment with theory. The inset shows the low temperature region on an expanded scale.
J. Tang, K.A. Gschneidner, Jr. / Low temperature properties
360
The 2nd term in eq. (lo), (Y, comes from the orbital motion of core electrons. Since the diamagnetic susceptibility of Cd metal is about - 20 X 1O-6 emu-per-g-atom [12], we expect that the Larmor diamagnetic susceptibility of CeCd,, would have a value of the same magnitude. The experimental value (Y= - 5.7 X 10e4 emu-per-mol, which is - 52 X 10e6 emu-per-g-atom of Cd, is in fair agreement with the value for pure Cd metal. Under the influence of CEF, the magnetic susceptibility of a 3-level system will be modified by multiplying a factor f=
P: +~f exd--h/T) +~f exd-b/T) 1 + exp( - E,/T)
of CeCd, I and CEF
can be explained by spin-disorder resistivity in presence of CEF. Both the heat capacity and magnetic susceptibility indicate that CeCd,, orders slightly below 2 K.
Acknowledgements The authors wish to thank B.J. Beaudry and K. Funke for their assistance in preparing the sample, and D.K. Finnemore (Ames Laboratory) and S.K. Malik (Tata Institute of Fundamental Research) for their valuable comments and suggestions.
+ exp( - E/T)
04 to the Curie-Weiss term (see eq. 10) [13], where constants pi, pz and p3 depend on the values of coefficients B,"in eq. (1). These constants have been determined from our experiment, p, = 0.97, p2 = 0.99 and p3 = 1.05. Since all of them are in the vicinity of unity, the factor f has a weak temperature dependence, which explains why the influence of CEF is hardly observed in magnetic susceptibility. Note that the large temperature dependence shown in fig. 7 is due to the Curie-Weiss portion of eq. (10) [C/(T - 0)] and not f.
5. Conclusion The existence of CEF effect in CeCd,, was established. The heat capacity data and associated magnetic entropy confirmed the splitting of a 6fold degenerate ground state into three doublets. AC resistivity showed a drop near T = 7 K which
References 111I. Johnson and R.M. Yonco, Metall. Trans. 1 (1970) 905. M. Loewenhaupt, F. Steglich, 121S. Horn, E. Holland-Moritz, H. Scheuer, A. Benoit and J. Flouquet, Phys. Rev. B 23 (1981) 3171. Solid State Phys. 16 (1964) 227. [31 N. Hutchings, [41 A. Iandelli and R. Ferro, Gazz. Chim. Ital. 84 (1954) 463. Jr., B.J. Beaudry and U. [51 K. Ikeda, K.A. Gschneidner, Atzmony, Phys. Rev. B 25 (1982) 4604. Jr., T-W.E. Tsang, F.A. 161 R.J. Stierman, K.A. Gschneidner, Schmidt, P. Klavins, R.N. Shelton, J. Queen and S. Legvold, J. Magn. Magn. Mat. 36 (1983) 249. 171 H. Meyer and P.L. Smith, J. Phys. Chem. Solid 9 (1959) 285. 181 E. Gopal, Specific Heats at Low Temp. (Plenum, New York, 1966) p. 105. [91 V. Rao and W. Wallace, Phys. Rev. B 2 (1970) 4613. [lOI N. Mott and H. Jones, The Theory of Properties of Metals and Alloys (Dover, New York, 1958) p. 274. to Solid State Phys., 6th ed. (John illI C. Kittel, Introduction Wiley, New York, 1986) p. 405. of Chemistry and Physics, WI R. Weast, CRC Handbook 68th ed. (CRC Press, Cleveland, 1987) p. E-119. [13] H. Fischer, E. Swartz, R. Pohl, B. Jones, J. Wilkins and Z. Fisk, Phys. Rev. B 36 (1987) 5330.
Materials
75 (1988) 355-360
355
THE INFLUENCE OF CRYSTALLINE ELECTRIC FIELD ON THE LOW TEMPERATURE PROPERTIES OF CeCd,,
J. TANG
and K.A. GSCHNEIDNER,
Jr.
Ames L.aboratov *, Departments of Physics and Materials Iowa State University, Ames, IA 50011, USA
Received
Science and Engineering,
28 July 1988
Low temperature heat capacity, magnetic susceptibility and ac resistivity were measured on CeCd,,. Evidence is reported property measurements. The for the existence. of a crystalline electric field (CEF) effect in CeCd,, in these low temperature symmetry into three doublets, with an energy equal to ground state of the Ce3+ ion, 2Fs,z. is split by CEF of tetragonal E, = 0, E, = 17.5 K and E, = 80.2 K, respectively. The magnetic entropy up to 70 K was calculated from heat capacity data. The magnetic susceptibility follows a CEF modified Curie-Weiss behavior with an effective moment of pert = 2.57~~ indicating that 4f-electrons of Ce 3+ ions are localized. Comparison of the ac resistivity of our sample with spin-disorder resistivity in presence of CEF is also discussed.
b,
1. Introduction CeCd,, crystallizes in cubic BaHg,,-type structure, with a Ce-Ce distance d = 6.59 A [l]. Detailed examination of the structure reveals that a Ce atom is surrounded by 12 nearest neighboring Cd atoms and 8 second nearest neighboring Cd atoms. Fig. 1 shows the atomic arrangement in CeCd,,. The neighboring Cd forms a polyhedron of tetragonal symmetry about the Ce atom. Under the crystalline electric field (CEF), the 6-fold degenerate ground state of Ce3+ ion, 2F5,2, will be split into three doublets. According to the CEF Hamiltonian for Ce3+ ion (J = 5/2) with tetragonal symmetry [2], HCEF = B;O;
+ B4”0,” -I-B,40,4,
(1)
where coefficients B,” and operators Onm were defined in Hutchings [3]. The final eigenstates consist of three doublets 1k l/2), a I+ 5/2) + * Supported by USDOE, Office of Basic Energy Sciences, Division of Materials Sciences, under Contract No. W-7405ENG-82.
0304-8853/88/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
Fig. 1. A projection along the c-axis of the atomic arrangement of CeCd,,. The solid circles show the arrangement of the Cd atoms about a Ce atom. The big circles represent the Ce atoms and the small ones the Cd atoms. The value(s) next to an atom indicate the distance(s) along the c-axis from the a-b plane.
B.V.
356
J. Tang, K.A. Gschneidner, Jr. / Low
temperature properties of CeCd,,
and CEF
1T 3/2) and b 1i- 5/2) - a ] T 3/2). The actual energy levels of these doublets and the values of a and b depend upon the coefficients B,!!. This CEF splitting will influence the behavior of heat capacity, magnetic susceptibility and electrical resistivity of CeCd,, over the temperature range comparable to the energies of splitting. Low temperature property measurements, especially the heat capacity, allowed us to determine the energies of this 3-level CEF in CeCd,,.
b
2. Experimental
0
IO
20
30
40
TEMPERATURE
CeCd,, and LaCd,, were prepared by melting stoichiometric amounts of the constituents in a sealed tantalum crucible under helium atmosphere using a resistance furnace. The samples were then heat treated at 580°C for 4 days. Metallography showed that the samples were single phase and X-ray diffraction confirmed the previously reported crystal structure. OThe lattice parameter of CeCd,, (a = 9.313 & 3 A) is close to the value reported earlier 9.319 A [1,4]. The low temperature calorimeter used in this research is an isolation heat-pulse type with a mechanical switch [5]. The magnetic susceptibility measurement was carried out using a Faraday magnetometer in a field H = 0.96 T [6]. A conventional four point probe technique was used for the ac resistivity measurement.
60
70
Fig. 2. Heat capacities of CeCd,, and LaCd,, from 1.5 to 70 K. The inset shows an expanded version of the data below 20 K. Not all of the data points are shown.
the similar lattice constants (a = 9.339 A for LaCd,, [l] and 9.313 A for CeCd,,) and the same outer electronic configurations of the two compounds (Ce is trivalent, see section 5, Magnetic susceptibility). Therefore, the difference between the two heat capacities (&cd,, - CLaCd,,) should represent the contributions essentially due to the 4f-electrons in the Ce3+ ion. The shape of curve versus temperature (see fig. 4) (CCeCd,, - G&l,,) shows a fairly sharp bump at = 7 K and a broader bump at = 25 K, suggesting the existence of 3-level CEF effect. The main peak near T = 7 K is due to
3. Heat capacity
A
1.0 -
The heat capacity of CeCd,, was measured over the temperature range 1.5 K < T < 70 K, and it is shown in fig. 2. Also shown in fig. 2 is the heat capacity of LaCd,,, which is isostructural with CeCd,,. The more typical C/T vs. T2 is shown in fig. 3. The temperature dependence is quite unusual and the magnitude above 6 K (36 K2) is quite large (= 800 mJ/mol K’). Below 2 K, it appears that CeCd,, may be tending towards ordering magnetically. In order to understand this behavior we have assumed that the electronic and lattice heat capacities of CeCd,, are the same as that of LaCd,,. This is quite reasonable because of
50 (K)
CeC4,
.
-
0.9 Y al 0.7 a $ 0.6 _( ;I 2 0.5
r’ ,+
0.3 0.2 0.4 1J, -t 0
, , , , , , , , , , , , , , , ,: IO
20
30
40
50
60
70
80
90
100
T*(K*)
Fig. 3. A C/T vs. T* plot for CeCd,,. The crosses are for a sample weighing 1.58 g and the dots are for a sample weighing 14.21 g.
J. Tang, K.A. Gschneidner, Jr. / Low temperature properties
0 Fig. 4. The difference
10
of the two heat capacities
20
30 40 TEMPERATURE (K)
(CCeCd,, - CLaCd,,) (+),
the excitation of 4f-electron from ground state level to the 1st excited level and the 25 K shoulder could be due to the excitation from the 1st excited level to the 2nd excited level. To make sure this interpretation is correct we calculated the magnetic heat capacity of a 3-level CEF system, which takes the form
of CeCd,,
50
and C,-,,
60
R Ef exp( - El/T) ( [ +(Ez-Ed2
exp(-(E,
70
experiment is obvious. Energy levels and the constant y’ obtained in this manner are: E, = 0,
(3)
E, = 17.5 K,
(4)
E, = 80.2 K,
(5) K*.
(6)
+ E; exp( - E/T)
+E2)/T)])
IO
I
9.13
__________
X(T’[l
357
+ y’T (line). Inset: energy levels of the CEF
y’ = 9.0 mJ/mol CCEF =
and CEF
-------
I
I
_~____~_~~~~~_~_~~__~__
+exp(-E,/T)
0
i2
(2) where R is the universal gas constant, E, and E, are the energies (in K) of the 1st and 2nd excited levels, respectively. After several trials of fitting, c cEF to &cd,, - &cd,,, good agreement between the two was obtained when we added a small linear term y’T to the calculated Cc,,. Shown in fig. 4 (solid line) is the function Cc,, + y’T. The agreement between this function and the
8.
0
CeW,
0
2 s
0 0
: ‘; 8
6-
:
4
ooo
0 0 0 0
zi
0
o EXPERIMENTAL ENTROPY --CALCULATED CEF ENTROPY_
20
01O 0
I
IO
I
20
Fig. 5. Entropy
I
I
30 40 TEMPERATURE (K)
associated
I
50
with the CEF.
I
60
I 70
J. Tang, K.A. Gschneidner, Jr. / Low
358
E, = 17.5 K is one of the lowest CEF splittings found in Ce compounds. The only Ce compound having a lower CEF splitting, that we know of, is cerium ethylsulphate with E, = 6.6 K [7]. Usually, CEF splittings occur at temperatures 5 times to an order of magnitude higher. y’T is the electronic contribution to heat capacThe ity of CeCd,, in excess of that of LaCd,,. electronic specific heat constant, y, and the Debye temperature 0, of LaCd,, are 17 mJ/mol K2 and 280 K, respectively, and were obtained from a least squares fit of the data to a C/T versus T2 plot between 1.3 and 2.5 K. Adding y’ to the y of LaCd,,, the electric specific heat constant is estimated to be 26 mJ/mol K2 for CeCd,,. The Debye temperature of CeCd,, is assumed to be 280 K. The magnetic entropy, S,,,, associated with our heat capacity data was also calculated. Near T = 70 K, S, reaches a value close to 9.13 J/mol K (fig. 5) which is the expected value for a 3-level CEF system
S cEF = R In(m)
= R In 3 = 9.13 J/mol
K.
(7)
In the above expression, m is the number of doublets in a CEF system [8], where m = 3 in our case. The agreement between the experimental
temperature properties of CeCd,,
and CEF
entropy and the theoretical value confirms the splitting of a 3-level CEF. Since J = 5/2 for Ce3+, we expect the total magnetic entropy Sz = R ln(2J + 1) = R In 6. Knowing the entropy associated with CEF is R In 3, we believe that the difference (R In 6 - R In 3 = R In 2) is associated with magnetic ordering below T = 1.3 K. Because of the low temperature limit of our apparatus we were unable to make measurements below 1.3 K, but the tendency toward magnetic ordering at a lower temperature can be clearly seen from the upturn in heat capacity at T = 2 K (and is also evident in the magnetic susceptibility, see section 5). Also it is not difficult to understand that the offset between the experiment and Cc,, + y’T (fig. 4) below = 10 K is due to the non-zero tail of the magnetic ordering peak. 4. AC resistivity The ac resistivity of our CeCd,, sample is shown in fig. 6. The resistivity data over a wider temperature range is also shown in the fig. 6 inset. We can see that there is a resistivity drop near T = 7 K as temperature decreases. We believe that this is associated with the spin-disorder resistivity of a CEF system. Since the 2nd excited level lies high
0
o EXPERIMENTAL 2.50
a/---
---SPIN-DISORDER
B’
CeCd,,
2 2.25 0
/’
$2.00 6
1.75
b E
1.50
/‘O /‘Cl0 0
/‘O NO
‘0
/O
N-0
.bB
i+ 1.25
I
I
I
2
4
6
1
8
I
I
I
I
lo
12
14
16
I
18
TEMPERATURE (K1 Fig. 6. Experimental
resistivity
of CeCd,, (circles); and p,,,, = p,, + pS (line), with A = 0.394, B = 4.04, C = 2.20 and p,, = 0.655 ~0 cm. Inset: experimental data over a wider temperature range.
J. Tang K.A. Gschneidner, Jr. / LAW temperature properties
above both the ground and the 1st excited levels, we assumed that the 2nd excited level remains unoccupied over the temperature of concern and treat resistivity as a 2-level system. According to Rao and Wallace [9], the spin-disorder resistivity of a 2-level CEF system can be derived from the first Born approximation. It follows below: A+Bexp(-E,/T) “=
1 + exp(-E,/T)
of CeCd,,
359
and CEF
data can be expressed for T> 4 K
by the following
equation
where C = 0.830 emu K/mol,
(11)
O=
(12)
-5.5
K,
(Y= - 5.7 X lop4 emu/mol,
(13)
C + (1 +
exp(-&/T))(l + exp(&/T))
’ (8)
where A, B and C can be determined from fitting the experimental data to this equation. The total resistivity is composed of three parts. One is the spin-disorder resistivity p, as discussed above, another comes from the phonon scattering of conducting electrons or,,, and the third part is the temperature independent residual resistivity due to impurities pa. Since the phonon scattering resistivity near liquid helium temperature is about two orders of magnitude smaller than experimental resistivity (estimated from the Debye temperature) [lo], we neglected phonon scattering resistivity Q. Therefore, the total resistivity is the sum of two parts Pm = PO + Ps.
and f is the modification factor due to CEF (see below). The experimental susceptibility (in the form as XT) and the fit of the data to eq. (10) are shown in fig. 7. The term C/(T - 0) in eq. (10) is the Curie-Weiss paramagnetic contribution from 4f-electrons of Ce3+ ions. The value of C = 0.830 corresponds to an effective moment perr = 2.57~,, which is close to the expected theoretical value of a free Ce3+ ion pert = 2.54~~ [ll]. This indicates that the 4f-electrons in CeCd,, are well localized in agreement with a large Ce-Ce distance d = 6.59 A. The negative paramagnetic Curie temperature 0 = -5.5 K infers that the system will order antiferromagnetically at low temperature. Actually, the tendency toward magnetic ordering was seen from heat capacity data at T-c 2 K, as mentioned earlier (section 3) and is seen in the inset of fig. 7.
(9)
This equation was taken to fit- the experimental data for temperature 1.5 K i'T < 20 K, and the constants A, B, C and p0 were determined. Such a determined equation is shown in fig. 6 together with the experimental data. The values of A, B, C and p,, are given in the caption of fig. 6. We see that, in spite of a slight difference between experiment and eq. (9), the drop of resistivity near T = 7 K can be explained with spin-disorder resistivity as expressed by eq. (9).
5. Magnetic susceptibility The magnetic susceptibility measurement was carried out at a field H = 0.96 T over the temperature range 1.5 K < T < 250 K. The experimental
0.31 ’ 0
’
50
’
’
loo
’
’
’
’
200 150 TEMPERATURE(K)
’
’
250
’
’
300
Fig. 7. Magnetic susceptibility times the temperature vs. temperature for CeCd,, - a comparison of experiment with theory. The inset shows the low temperature region on an expanded scale.
J. Tang, K.A. Gschneidner, Jr. / Low temperature properties
360
The 2nd term in eq. (lo), (Y, comes from the orbital motion of core electrons. Since the diamagnetic susceptibility of Cd metal is about - 20 X 1O-6 emu-per-g-atom [12], we expect that the Larmor diamagnetic susceptibility of CeCd,, would have a value of the same magnitude. The experimental value (Y= - 5.7 X 10e4 emu-per-mol, which is - 52 X 10e6 emu-per-g-atom of Cd, is in fair agreement with the value for pure Cd metal. Under the influence of CEF, the magnetic susceptibility of a 3-level system will be modified by multiplying a factor f=
P: +~f exd--h/T) +~f exd-b/T) 1 + exp( - E,/T)
of CeCd, I and CEF
can be explained by spin-disorder resistivity in presence of CEF. Both the heat capacity and magnetic susceptibility indicate that CeCd,, orders slightly below 2 K.
Acknowledgements The authors wish to thank B.J. Beaudry and K. Funke for their assistance in preparing the sample, and D.K. Finnemore (Ames Laboratory) and S.K. Malik (Tata Institute of Fundamental Research) for their valuable comments and suggestions.
+ exp( - E/T)
04 to the Curie-Weiss term (see eq. 10) [13], where constants pi, pz and p3 depend on the values of coefficients B,"in eq. (1). These constants have been determined from our experiment, p, = 0.97, p2 = 0.99 and p3 = 1.05. Since all of them are in the vicinity of unity, the factor f has a weak temperature dependence, which explains why the influence of CEF is hardly observed in magnetic susceptibility. Note that the large temperature dependence shown in fig. 7 is due to the Curie-Weiss portion of eq. (10) [C/(T - 0)] and not f.
5. Conclusion The existence of CEF effect in CeCd,, was established. The heat capacity data and associated magnetic entropy confirmed the splitting of a 6fold degenerate ground state into three doublets. AC resistivity showed a drop near T = 7 K which
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