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Specific heat and susceptibility of EuSO4
Physica 92B (1977) 369-372 © North-Holland Publishing Company
LETTER TO THE EDITOR SPECIFIC HEAT AND SUSCEPTIBILITY OF EuSO4 E. LAGENDIJK *, F.J.A.M. GRE1DANUS and H.W.J. BLt)TE Kamerlingh Onnes Laboratorium der Ri]ks Universiteit, Leiden, The Netherlands
(Communication No. 432a) Received 30 June 1977
Specific-heat measurements on EuSO4 samples show a phase transition at (0.38 *- 0.02) K. Susceptibility measurements show the phase transition to be antiferromagnetic. The high-temperature tail of the specific heat, the Curie-Weiss constant and the total ordering energy have been calculated assuming that the magnetic interactions between the Eu 2+ ions are purely dipolar. Comparisons of experimental and calculated results indicate the interactions to be mainly dipolar. Some preliminary results on EuCO 3 are included.
1. Introduction M6ssbauer-effect measurements by Ehnholm et al. [ 1 ] on EuSO4 have shown the existence o f a magnetically ordered state below (0.43 -+ 0.05) K. In their paper, these authors suggest that the phase transition is o f the antiferromagnetic type and that dipolar interactions are largely responsible for the onset of magnetic ordering. Transitions to magnetically ordered states should also be observable by measuring the specific heat and the susceptibility. We expect these quantities to be more accurate probes o f the temperature behaviour of the Eu 2+ magnetic moments than the M6ssbauer effect. Besides, we expect them to give more detailed information about the type of ordering and the magnetic interactions involved.
The temperature range of the measurements was 0.1 - 4 K . Powdered samples have been used, prepared according to the methods described in Cooly and Yost [2]. The crystal structure has been described by Mayer et al. [3]. Adiabatic demagnetization devices using CrK alum have been applied to obtain low temperature heat sinks. The specific heat has been measured by the heat-pulse method and the a.c. susceptibility has been measured using a Hartshorn bridge operating at 225 Hz. Both resistance and magnetic thermometry have been applied. Principles of measurement and construction of the apparatus have been described extensively elsewhere[4,5].
3. Results of the measurements
2. Experimental techniques
Specific-heat data on EuSO4, samples I and II, are shown in fig. 1. Before plotting the data, the lattice contribution to the specific heat has been subtracted. This contribution has been estimated by fitting:
Specific-heat measurements have been performed on two samples of EuSO4, labelled I and 11. Further, the a.c. susceptibility of sample I has been measured.
c/R = a - 2 T -2 + a - 3 T -3 + a3 T 3
(1)
to the measured high-temperature data. The first two terms in this polynomial originate from the high-temperature expansion o f the magnetic specific heat; the last tern1 originates from the low-temperature expansion
* Now with the Applied Physics Department, Delft University of Technology, Delft, The Netherlands. 369
L: Lagendi/k et al. / Specific heat and susceptibility of EuSO 4
370 I
I
. . . .
I
of the lattice specific heat in the Debye approximation. The temperature range of the fit was 0.8 - 1.9 K. Values of a_ 2 and a_ 3 obtained from the fit are (0.70 +- 0.07) K 2 and ( - 0 . 3 0 -+ 0.03) K 3 respectively. The corresponding value o f a 3 is 0.005 K -3. Due to uncertainty in the heat capacity of the empty calorimeter, the significance of the a 3 value is in doubt. Using data on the hyperfine interaction (see ref. 1), nuclear contributions to the specific heat can be calculated. It turns out that electric quadrupole interactions can be neglected compared to magnetic hyperfine interactions, so, in the magnetically ordered state, only a term ASzI= remains. This term gives rise to a Schottky-type anomaly in the specific heat. In order to calculate the electronic entropy and energy (section 4), this nuclear contribution has been subtracted. Data on the zero-field a.c. (225 Hz) susceptibility X' are shown in fig. 2. A Curie-Weiss relation has been fitted to the high-temperature data. The Curie-Weiss constant 0 has been used as a parameter in the least-
EuSO~ 20
o sompte I
10
05
02 R ~
O~I 01
I 0,2 ----aB.- T
,
,
I .... I 05 1.0
K
20
Fig. 1. Specific heat c/R of two samples of EuSO 4 as a function o f temperature T. The high-temperature data have been corrected for lattice contributions. The dashed-dotted line shows the specific-heat curve after correction for nuclear contributions.
I
I
I
I
~
1.5
I
~
\
I
I
I
[
f
I
I
I
I
I
I
r
r
\ \
\
\
K-1 \\\\\\
1.0
0.5
_x' C
? 0
0.5
10
15
K
2.0
~ T
Fig. 2. A.c. (225 Hz) susceptibility ×' of EuSO4 divided by the Curie constant C as a function of temperature T. Transition point as inferred f r o m the specific-heat data is indicated by an arrow. The dashed line corresponds to Curie behaviour (x/C = l/T).
E. Lagendi/k et al. / Specific heat and susceptibility of EuSO 4 squares fit. The value of 0 which minimizes the estimated standard error is (-0.1 + 0.1) K. From our measurements we conclude X" to be zero within experimental error in the temperature range of the measurement. Therefore, presumably, the X' data represent the static susceptibility fairly well.
4, Discussion and conclusion The specific-heat data, as shown in fig. 1, indicate a phase transition in EuSO4 at 0.38 K. Some discrepancy is observed between the two EuSO4 samples near the phase transition temperature. We may attribute this discrepancy to relaxation effects. To attain thermal equilibrium after a heat pulse, periods up to about half an hour were needed near and below the transition temperature. Relatively strong relaxation effects in EuSO4 have also been reported in ref. 1. Another source of discrepancies might be a slightly different chemical composition of the two samples. For example, as shown in ref. 1, several samples of divalent europium compounds show some admixture of trivalent europium ions. Because Eu 3+ has a non-magnetic ( J = 0) ground-state, admixture of Eu 3+ should lower the specific heat in proportion. This effect is not observed in fig. 1, so we conclude that the discrepancy cannot be explained by a different Eu 3+ concentration in the samples. Our measurements show a rather rounded specificheat peak. Apart from relaxation effects, possible sources of rounding of the peak are the influence of particle size, lattice defects and chemical inhomogeneities. Because of the observed rounding and the observed differences between the two samples, we fix the uncertainty limits of the transition temperatures at -+0.02 K. This estimated error is much larger than the estimated accuracy of 1% in the absolute measurement of temperature. With these limits, our results on the transition point of EuSO4, Tt = (0.38 -+ 0.02) K, does not differ significantly from that of ref. 1, which is (0.43 + 0.05) K. The specific-heat measurements can be used to study a few more aspects of the phase transition. Assuming the transition to be of magnetic origin, the total entropy change in the ordering should correspond to the number of magnetic degrees of freedom frozen out. As the Eu 2+ ion has a 8S7/2 ground state, the entropy change should amount to R log 8 = 2.079 per mole. Experimentally,
371
the entropy was obtained by integrating c/T. The mean result of the two samples is Soo/R = (2.1 -+ 0.1), which agrees with the expected result. Other parameters of interest are the ground state energy of the ordered system, which can be obtained by integrating the specific heat, and the T -2 coefficient of the high-temperature specific-heat tail. The experimental value of the total ground state energy is Eo/R = (-1.25 -+ 0.03) K. Using the Luttinger and Tisza method, the total ground state energy has been calculated, assuming purely dipolar interactions in the classical, i.e. non-quantum-mechanical, approximation [6]. This method also gives the ground-state ordering type and the energy and ordering type of other allowed states. The lowest calculated energy value is -0.93 K, corresponding to a ferromagnetic ordering along the a axis. The nearest calculated energy value is - 0 . 9 0 K, corresponding to an antiferromagnetic ordering in the a - c plane. So, to explain the energy result, admixture of non-dipolar interactions has to be assumed. Depending on sign, this admixture may change the ordering type Experimental values of the critical entropy and energy are (S~ - Sc)/R = 0.96 (45%) and [Ec/RTN[ = 0.73. The high short-range ordering entropy value and the fact that IEc/RI approaches TN, have been observed in other substances, which are classified dipolar [7]. The calculated dipolar value of the T -2 coefficient is 0.701 K 2, in agreement with the experimental value (0.70 + 0.07) K z (section 3), which indicates that the interactions are mainly dipolar. Concerning the susceptibility data, as shown in fig. 2, they show clear indication of antiferromagnetic behaviour. The calculated values of the Curie-Weiss 0's, assuming a spherical sample shape and purely dipolar interactions, are 0.010 K, -0.012 K and 0.001 K along the a, b and c axes, respectively. These low values of 0 show that deviations from random orientation of the particles will not greatly affect 0. So we can adopt the average value of 0 = 0 K which is the prediction for spherically symmetric dipolar systems. The calculated demagnetizing correction for other sample shape amounts to 0.I 7 ( N - 3~rr),where N is the corresponding demagnetization factor. We consider the geometry of the sample to be best described by randomly oriented, spherically shaped micro-crystals, loosely packed in a cylindrically shaped sample holder. From this configuration we derive a correction due to demagnetization effects of about 0.03 K. So the calculated value assuming di-
372
bz Lagendijk et al. / Specific heat and susceptibility o f EuSO 4
polar interactions only, 0ca~c = 0.03 K, is in agreement with the experimental value 0exp = (0.t -+ 0.1) K (section 3), again indicating the interactions to be mainly dipolar. We conclude that the results on the specific heat and the susceptibility show that the investigated EuSO4 samples order antiferromagnetically at (0.38 +- 0.02) K, the ordering being mainly caused by dipolar interactions.
which is not significantly different from that of ref. 1. Comparison of observed and calculated dipolar values of a - 2 and 0 indicate an appreciable admixture of (super)exchange interactions in the carbonate. We expect to continue our investigations on EuCO3 in the near future.
5. Preliminary data on EuCO3
We thank Dr. J.A. Mydosh for providing us with the EuS04(II ) sample and Prof. Dr. W.J. Huiskamp for his stimulating interest.
We have also performed specific-heat and susceptibility measurements on a EuCO 3 sample. The measurements indicate antiferromagnetic ordering at TN = = (0.80 +- 0,03) K. This TN value differs significantly from the value of ref. 1, T N = (1.05 +- 0.05) K. However, our observed total entropy change is 12% less than the expected value R log 8. A possible explanation is, that the EuCO 3 sample may have contained an appreciable amount of Eu 3+. As the carbonate was prepared from the sulfate [2], this is not implausible. Measurements on diluted samples of 3-dimensional dipolar substances [7] have shown the slope of the T t ( P ) / T t (1) versus p curve at p = 1 (p being the concentration of the magnetic ions) to be about 1.6. When adopting this value and assuming that the entropy shortage is due to magnetic dilution, our tentative estimate of the transition temperature of EuCO 3 would become 0.99 K,
Acknowledgements
References
[1] G.J. Ehnholm, T.E. Katila, O.V. Lounasmaa and P. Reivari, Z. Physik 235 (1970) 289. [2] R.A. Cooly and A.M. Yost, Inorganic synthesis (McGrawHill, New York, 1946) Vol. II, p. 70. [3] I. Mayer, E. Levy and A. Glasner, Acta Cryst. 17 (1964) 1071. [4] R.F. Wielinga, thesis (Leiden, 1968) and K.W. Mess, thesis (Leiden, 1969) (sample I). [5l H.A. Algra, L.J. de Jongh, W.J. Huiskamp and R.L. Carlin, Physica 92B (1977) 187 (sample IlL [6] J.M. Luttinger and L. Tisza, Phys. Rev. 70 (1946) 954. [7] E. Lagendijk, thesis (Leiden, 1972). E. Lagendijk and W.J. Huiskamp, Physica 65 (1973) 118 (Commun. Kamerlingh Onnes Lab., Leiden No. 396c).
LETTER TO THE EDITOR SPECIFIC HEAT AND SUSCEPTIBILITY OF EuSO4 E. LAGENDIJK *, F.J.A.M. GRE1DANUS and H.W.J. BLt)TE Kamerlingh Onnes Laboratorium der Ri]ks Universiteit, Leiden, The Netherlands
(Communication No. 432a) Received 30 June 1977
Specific-heat measurements on EuSO4 samples show a phase transition at (0.38 *- 0.02) K. Susceptibility measurements show the phase transition to be antiferromagnetic. The high-temperature tail of the specific heat, the Curie-Weiss constant and the total ordering energy have been calculated assuming that the magnetic interactions between the Eu 2+ ions are purely dipolar. Comparisons of experimental and calculated results indicate the interactions to be mainly dipolar. Some preliminary results on EuCO 3 are included.
1. Introduction M6ssbauer-effect measurements by Ehnholm et al. [ 1 ] on EuSO4 have shown the existence o f a magnetically ordered state below (0.43 -+ 0.05) K. In their paper, these authors suggest that the phase transition is o f the antiferromagnetic type and that dipolar interactions are largely responsible for the onset of magnetic ordering. Transitions to magnetically ordered states should also be observable by measuring the specific heat and the susceptibility. We expect these quantities to be more accurate probes o f the temperature behaviour of the Eu 2+ magnetic moments than the M6ssbauer effect. Besides, we expect them to give more detailed information about the type of ordering and the magnetic interactions involved.
The temperature range of the measurements was 0.1 - 4 K . Powdered samples have been used, prepared according to the methods described in Cooly and Yost [2]. The crystal structure has been described by Mayer et al. [3]. Adiabatic demagnetization devices using CrK alum have been applied to obtain low temperature heat sinks. The specific heat has been measured by the heat-pulse method and the a.c. susceptibility has been measured using a Hartshorn bridge operating at 225 Hz. Both resistance and magnetic thermometry have been applied. Principles of measurement and construction of the apparatus have been described extensively elsewhere[4,5].
3. Results of the measurements
2. Experimental techniques
Specific-heat data on EuSO4, samples I and II, are shown in fig. 1. Before plotting the data, the lattice contribution to the specific heat has been subtracted. This contribution has been estimated by fitting:
Specific-heat measurements have been performed on two samples of EuSO4, labelled I and 11. Further, the a.c. susceptibility of sample I has been measured.
c/R = a - 2 T -2 + a - 3 T -3 + a3 T 3
(1)
to the measured high-temperature data. The first two terms in this polynomial originate from the high-temperature expansion o f the magnetic specific heat; the last tern1 originates from the low-temperature expansion
* Now with the Applied Physics Department, Delft University of Technology, Delft, The Netherlands. 369
L: Lagendi/k et al. / Specific heat and susceptibility of EuSO 4
370 I
I
. . . .
I
of the lattice specific heat in the Debye approximation. The temperature range of the fit was 0.8 - 1.9 K. Values of a_ 2 and a_ 3 obtained from the fit are (0.70 +- 0.07) K 2 and ( - 0 . 3 0 -+ 0.03) K 3 respectively. The corresponding value o f a 3 is 0.005 K -3. Due to uncertainty in the heat capacity of the empty calorimeter, the significance of the a 3 value is in doubt. Using data on the hyperfine interaction (see ref. 1), nuclear contributions to the specific heat can be calculated. It turns out that electric quadrupole interactions can be neglected compared to magnetic hyperfine interactions, so, in the magnetically ordered state, only a term ASzI= remains. This term gives rise to a Schottky-type anomaly in the specific heat. In order to calculate the electronic entropy and energy (section 4), this nuclear contribution has been subtracted. Data on the zero-field a.c. (225 Hz) susceptibility X' are shown in fig. 2. A Curie-Weiss relation has been fitted to the high-temperature data. The Curie-Weiss constant 0 has been used as a parameter in the least-
EuSO~ 20
o sompte I
10
05
02 R ~
O~I 01
I 0,2 ----aB.- T
,
,
I .... I 05 1.0
K
20
Fig. 1. Specific heat c/R of two samples of EuSO 4 as a function o f temperature T. The high-temperature data have been corrected for lattice contributions. The dashed-dotted line shows the specific-heat curve after correction for nuclear contributions.
I
I
I
I
~
1.5
I
~
\
I
I
I
[
f
I
I
I
I
I
I
r
r
\ \
\
\
K-1 \\\\\\
1.0
0.5
_x' C
? 0
0.5
10
15
K
2.0
~ T
Fig. 2. A.c. (225 Hz) susceptibility ×' of EuSO4 divided by the Curie constant C as a function of temperature T. Transition point as inferred f r o m the specific-heat data is indicated by an arrow. The dashed line corresponds to Curie behaviour (x/C = l/T).
E. Lagendi/k et al. / Specific heat and susceptibility of EuSO 4 squares fit. The value of 0 which minimizes the estimated standard error is (-0.1 + 0.1) K. From our measurements we conclude X" to be zero within experimental error in the temperature range of the measurement. Therefore, presumably, the X' data represent the static susceptibility fairly well.
4, Discussion and conclusion The specific-heat data, as shown in fig. 1, indicate a phase transition in EuSO4 at 0.38 K. Some discrepancy is observed between the two EuSO4 samples near the phase transition temperature. We may attribute this discrepancy to relaxation effects. To attain thermal equilibrium after a heat pulse, periods up to about half an hour were needed near and below the transition temperature. Relatively strong relaxation effects in EuSO4 have also been reported in ref. 1. Another source of discrepancies might be a slightly different chemical composition of the two samples. For example, as shown in ref. 1, several samples of divalent europium compounds show some admixture of trivalent europium ions. Because Eu 3+ has a non-magnetic ( J = 0) ground-state, admixture of Eu 3+ should lower the specific heat in proportion. This effect is not observed in fig. 1, so we conclude that the discrepancy cannot be explained by a different Eu 3+ concentration in the samples. Our measurements show a rather rounded specificheat peak. Apart from relaxation effects, possible sources of rounding of the peak are the influence of particle size, lattice defects and chemical inhomogeneities. Because of the observed rounding and the observed differences between the two samples, we fix the uncertainty limits of the transition temperatures at -+0.02 K. This estimated error is much larger than the estimated accuracy of 1% in the absolute measurement of temperature. With these limits, our results on the transition point of EuSO4, Tt = (0.38 -+ 0.02) K, does not differ significantly from that of ref. 1, which is (0.43 + 0.05) K. The specific-heat measurements can be used to study a few more aspects of the phase transition. Assuming the transition to be of magnetic origin, the total entropy change in the ordering should correspond to the number of magnetic degrees of freedom frozen out. As the Eu 2+ ion has a 8S7/2 ground state, the entropy change should amount to R log 8 = 2.079 per mole. Experimentally,
371
the entropy was obtained by integrating c/T. The mean result of the two samples is Soo/R = (2.1 -+ 0.1), which agrees with the expected result. Other parameters of interest are the ground state energy of the ordered system, which can be obtained by integrating the specific heat, and the T -2 coefficient of the high-temperature specific-heat tail. The experimental value of the total ground state energy is Eo/R = (-1.25 -+ 0.03) K. Using the Luttinger and Tisza method, the total ground state energy has been calculated, assuming purely dipolar interactions in the classical, i.e. non-quantum-mechanical, approximation [6]. This method also gives the ground-state ordering type and the energy and ordering type of other allowed states. The lowest calculated energy value is -0.93 K, corresponding to a ferromagnetic ordering along the a axis. The nearest calculated energy value is - 0 . 9 0 K, corresponding to an antiferromagnetic ordering in the a - c plane. So, to explain the energy result, admixture of non-dipolar interactions has to be assumed. Depending on sign, this admixture may change the ordering type Experimental values of the critical entropy and energy are (S~ - Sc)/R = 0.96 (45%) and [Ec/RTN[ = 0.73. The high short-range ordering entropy value and the fact that IEc/RI approaches TN, have been observed in other substances, which are classified dipolar [7]. The calculated dipolar value of the T -2 coefficient is 0.701 K 2, in agreement with the experimental value (0.70 + 0.07) K z (section 3), which indicates that the interactions are mainly dipolar. Concerning the susceptibility data, as shown in fig. 2, they show clear indication of antiferromagnetic behaviour. The calculated values of the Curie-Weiss 0's, assuming a spherical sample shape and purely dipolar interactions, are 0.010 K, -0.012 K and 0.001 K along the a, b and c axes, respectively. These low values of 0 show that deviations from random orientation of the particles will not greatly affect 0. So we can adopt the average value of 0 = 0 K which is the prediction for spherically symmetric dipolar systems. The calculated demagnetizing correction for other sample shape amounts to 0.I 7 ( N - 3~rr),where N is the corresponding demagnetization factor. We consider the geometry of the sample to be best described by randomly oriented, spherically shaped micro-crystals, loosely packed in a cylindrically shaped sample holder. From this configuration we derive a correction due to demagnetization effects of about 0.03 K. So the calculated value assuming di-
372
bz Lagendijk et al. / Specific heat and susceptibility o f EuSO 4
polar interactions only, 0ca~c = 0.03 K, is in agreement with the experimental value 0exp = (0.t -+ 0.1) K (section 3), again indicating the interactions to be mainly dipolar. We conclude that the results on the specific heat and the susceptibility show that the investigated EuSO4 samples order antiferromagnetically at (0.38 +- 0.02) K, the ordering being mainly caused by dipolar interactions.
which is not significantly different from that of ref. 1. Comparison of observed and calculated dipolar values of a - 2 and 0 indicate an appreciable admixture of (super)exchange interactions in the carbonate. We expect to continue our investigations on EuCO3 in the near future.
5. Preliminary data on EuCO3
We thank Dr. J.A. Mydosh for providing us with the EuS04(II ) sample and Prof. Dr. W.J. Huiskamp for his stimulating interest.
We have also performed specific-heat and susceptibility measurements on a EuCO 3 sample. The measurements indicate antiferromagnetic ordering at TN = = (0.80 +- 0,03) K. This TN value differs significantly from the value of ref. 1, T N = (1.05 +- 0.05) K. However, our observed total entropy change is 12% less than the expected value R log 8. A possible explanation is, that the EuCO 3 sample may have contained an appreciable amount of Eu 3+. As the carbonate was prepared from the sulfate [2], this is not implausible. Measurements on diluted samples of 3-dimensional dipolar substances [7] have shown the slope of the T t ( P ) / T t (1) versus p curve at p = 1 (p being the concentration of the magnetic ions) to be about 1.6. When adopting this value and assuming that the entropy shortage is due to magnetic dilution, our tentative estimate of the transition temperature of EuCO 3 would become 0.99 K,
Acknowledgements
References
[1] G.J. Ehnholm, T.E. Katila, O.V. Lounasmaa and P. Reivari, Z. Physik 235 (1970) 289. [2] R.A. Cooly and A.M. Yost, Inorganic synthesis (McGrawHill, New York, 1946) Vol. II, p. 70. [3] I. Mayer, E. Levy and A. Glasner, Acta Cryst. 17 (1964) 1071. [4] R.F. Wielinga, thesis (Leiden, 1968) and K.W. Mess, thesis (Leiden, 1969) (sample I). [5l H.A. Algra, L.J. de Jongh, W.J. Huiskamp and R.L. Carlin, Physica 92B (1977) 187 (sample IlL [6] J.M. Luttinger and L. Tisza, Phys. Rev. 70 (1946) 954. [7] E. Lagendijk, thesis (Leiden, 1972). E. Lagendijk and W.J. Huiskamp, Physica 65 (1973) 118 (Commun. Kamerlingh Onnes Lab., Leiden No. 396c).