- Email: [email protected]
Specific heat anomalies at the magnetic ordering temperatures of rare earth-iron laves compounds
Jowr~hl of the L.ess-Common Mrtals, 34 ( 1974) 3 IS--3 19 (“ Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands
315
SPECIFIC HEAT ANOMALIES AT THE MAGNETIC ORDERING TEMPERATURES OF RARE EARTH-IRON LAVES COMPOUNDS
M. P. DARIEL, Nwlear
Resewch
U. ATZMONY
and R. GUISER
Cetztre, Negec, P.O.B. 9001, Beer-Skeoa
( fsrael)
(Received September 4, 1973)
SUMMARY
The magnetic ordering temperatures of rare earth and yttriunl-iron Laves compounds have been determined by measuring the specific heat anomalies in a differential scanning calorimeter. The results are in general agreement with those deduced from magnetization measurements. The specific heat discontinuities at the magnetic ordering temperatures are not consistent with the theoretical expressions derived for ferrites.
INTRODUCTION
The cubic rare earth(Rkiron Laves compounds, RFe,, have been subject to several structural and magnetic investigations ’ - 3. All heavy rare earth-iron Laves compounds are magneti~lly ordered at room temperature with an antiparallel coupling between the moments of the rare-earth and iron sublattices. These compounds are currently of great interest as a result of their very high magnetic anisotropy* and magnetostriction’. The magnetic ordering temperatures of the various RFe, compounds have been derived from magnetization measurements in the ferrimagnetic and paramagnetic regions. The results obtained in the course of the various studies are in general agreement even though some discrepancies are present in several instances. The purpose of the present work was to make use of a differential scanning calorimeter in order to determine the specific heat anomalies of the RFe, compounds in the vicinity of their magnetic ordering temperatures. A relatively simple theoretical expression can be derived for the specific heat anomaly at the Curie temperature of ferromagnets6. This expression was only partly successful when applied.to the ferromagnetic elements”.‘. Theoretical expressions for the specific heat discontinuity at the magnetic ordering temperature of ferrimagnets have been developed by Grosjean and Robrecht’ and by Nielsen’. Experimental verifications of these expressions are scarce and limited to ferrite systems. One of the objects of this study was to provide a test of the validity of the theoretical expressions. This, however, was not borne out by the present results. EXPERIMENTAL
DETAILS
The cubic Laves compounds
were prepared
by arc melting 99.95% pure
M. P. DARIEL,
316
U. ATZMONY,
R. GUISER
rare-earth metals and 99.99% iron under an argon atmosphere and casting into split 5 mm diam. copper molds. The samples were wrapped in tantalum foils, sealed in evacuated quartz capsules and given a week-long anneal at 900°C. Powder diffraction photographs, using CoKcc radiation, showed that additional phases, if present, never amounted to more than 5%. This was also corroborated by metallographic and some electron microprobe examinations. Lattice parameters were in good agreement with previously published results 3. For the specific heat measurements, small discs, about 2 mm thick, with plane, parallel faces were prepared by grinding and polishing. The runs in the differential scanning calorimeter (DuPont, Thermal Analyzer) were carried out under a purified helium atmosphere at a 5 or 10”C/min heating rate. The temperature scale of the instrument had been calibrated by measuring the melting points of pure indium, lead and zinc. A sapphire sample supplied with the instrument was used for the specific heat calibration. In addition, the specific heat of a 200 mg nickel sample was measured from the ambient to above its Curie temperature. The results were within 10% of those published in the literature’j. RESULTS
AND DISCUSSION
The heat capacity anomalies associated with the magnetic ordering were determined in the “time base” mode with a silver sample of similar dimensions serving as dummy reference. This method yielded the most salient anomalies at the ordering temperature, as shown in Fig. 1. Noteworthy is the fact that in spite of the small size of the samples, (average weight 0.3 g), the relatively slight thermal effects associated with a second-order phase transition show up as prominent anomalies in the heat capacity curves. The magnetic ordering temperatures, assumed to correspond to the peaks of the curves, are given in Table I, along with those deduced from magnetization and resistivity measurements’-3~‘0. There appears to be good agreement between the present results and those of Burzo3 but those of Wallace higher than et al.’ and Buschow et u~.~.‘O are in several instances significantly the present ones. The magnetic ordering temperature of TmFe, has been measured by Wallace et al.’ who found Tc=610 K. This value exhibits very poor agreement with the linear relationship of F us. the de Gennes factor, G=(g-1)2J(J+ 1). The lower value found in this study, T,=559 K, is in better agreement with the Tc = a + bG (u and b, constants) plot, Fig. 2, strengthening the view that the exchange interaction in the RFe, compounds is predominantly of the RKKY type. The specific heat at constant pressure of magnetically ordered materials can be written as C,=
C,+C,+C,+AC
where C, is the lattice, C, the electronic, C,,, the magnetic contribution to the specific heat and AC= C,- C,. In the present work all specific heat measurements were only carried out above room temperature, and as no electronic heat capacity measurements are available, there was no possibility of analysing the measured heat capacity in terms of its various components. The discontinuity of the heat capacity at the magnetic ordering temperature may be considered. This discontinuity, GC(per gram), for ferromagnets can be
RARE EARTH-IRON
00
400
500
600
TEMPERATURE
Fig. 1. Specific heat anomalies magnetic ordering temperature.
TABLE
317
LAVES COMPOUNDS
I 700
800
(K)
of the yttrium
and
heavy
rare
earth-iron
Laves
compounds
at the
I
MAGNETIC POUNDS
ORDERING
TEMPERATURES
(K)
YFr, 550 535 535
7x5 793 788
545
803
705 711 697 695
635 635 635
OF
RARE
EARTH-IRON
LAVES
ErFe,
TtnFe,
Rf?f.
614 612 597 598
596 590 574 573
610
608
591
I 2 3 present work IO
566 559
COM-
318
M. P. DARIEL, I
I
I
1
I
I
1
I
U. ATZMONY,
R. CUBER
900-
500 -
I
I
10
5 c:
(g-lYJ(J4)
Fig. 2. Linear dependence of the magnetic ordering temperature, 7& of the yttrium earth-iron Laves compounds on the de Gennes factor G’=(g- l)‘J(/+ 1).
expressed6
within
the molecular
1
15
field approximation
and
heavy
rare
by
sc=SRN/g{5(J+1)/[(J+1)2+J2]} where S is the average number of Bohr magnetons of the moment carrying atoms, N is the number of magnetic atoms per unit volume and the other symbols have their usual meaning. Among the compounds investigated, only YFe, is ferromagnetic. The measured heat capacity of this compound is shown in Fig. 3. The discontinuity at T, was determined by taking the difference C,,,. - Cmi”. . While there was no ambiguity of Cmin, was not straightforward. The procein determining C,,,,,,, the determination dure followed was to extrapolate from the paramagnetic region and this gave a value of 6C=O.O156 Cal/g. Substituting this value into the expression for SC and solving for J, one obtains J= 2 for iron in YFe,. The magnetization curve of YFe, has been determined by Burzo3 and it can be fitted to a Brillouin function with+< J<$. Expressions for the specific heat anomalies of ferromagnets have been developed by Grosjean and Robrecht’ and by Nielsen’ and applied with limited success to ferrite systems. Nielsen’s expansion leads to an expression of the form 6C = a+b(
JR + 1)/J,
where a and b are constants practically independent of JR but which depend on J,,. Comparison of the experimental results (obtained in a form similar to that of YFe, (Fig. 3)) with Nielsen’s expression was not successful. The reasons for the lack of consistency may be due either to the failure of the molecular field
RARE EARTH-IRON
25
319
LAVES COMPOUNDS
t
I 300
I
I 400
I 500
Fig. 3. Specific heat of YFe, ordering temperature.
I 600
as function
1
of temperature.
liC denotes
the discontinuity
approximation in the neighborhood of the Curie temperature in the determination of the heat capacity discontinuities.
at the magnetic
or to the ambiguity
CONCLUSIONS
The differential scanning calorimeter can be successfully used in order to determine accurate magnetic ordering temperatures of small size (< 0.3 mg) compounds. The magnetic ordering temperatures of the heavy rare earth-iron Laves compounds are linearly related to the de Gennes factor. The theoretical .expressions derived in order to account for the discontinuity of the heat capacity of ferrites do not seem applicable to the ferrimagnetic RFe, compounds.
REFERENCES 1 W. E. Wallace and A. E. Skrabek, in K. Vorres (ed.), Rare Earth Research, Breach, New York, 1964, p. 431. 2 K. H. J. Buschow and R. P. van Stapele, d. Appl. Ph~s., 41 (1970) 4066. 3 E. Burzo, Z. Anger. Phys., 32 (1971) 127. 4 M. P. Dariel and U. Atzmony, Intern. J. Muynefism, (1973) in the press. 5 A. E. Clark and H. S. Belson, Phys. Rev. B, 5 (1972) 3642. 6 R. M. Bozorth, Ferromagnetism, Van Nostrand, Princeton. N.J., 1951, p. 734. 7 M. Griffel, R. E. Skochdopole and F. H. Spedding, Ph_rs. Rev., 93 (1954) 657. 8 C. C. Grosjean and G. G. Robrecht, Physica, 36 (1967) 525. 9 0. V. Nielsen, Appl. Sci. Rrs., 20 (1969) 381. IO M. Brouha and K. H. J. Buschow, J. Appl. Phys., 44 (1973) 1813.
Vol. 2, Gordon
and
315
SPECIFIC HEAT ANOMALIES AT THE MAGNETIC ORDERING TEMPERATURES OF RARE EARTH-IRON LAVES COMPOUNDS
M. P. DARIEL, Nwlear
Resewch
U. ATZMONY
and R. GUISER
Cetztre, Negec, P.O.B. 9001, Beer-Skeoa
( fsrael)
(Received September 4, 1973)
SUMMARY
The magnetic ordering temperatures of rare earth and yttriunl-iron Laves compounds have been determined by measuring the specific heat anomalies in a differential scanning calorimeter. The results are in general agreement with those deduced from magnetization measurements. The specific heat discontinuities at the magnetic ordering temperatures are not consistent with the theoretical expressions derived for ferrites.
INTRODUCTION
The cubic rare earth(Rkiron Laves compounds, RFe,, have been subject to several structural and magnetic investigations ’ - 3. All heavy rare earth-iron Laves compounds are magneti~lly ordered at room temperature with an antiparallel coupling between the moments of the rare-earth and iron sublattices. These compounds are currently of great interest as a result of their very high magnetic anisotropy* and magnetostriction’. The magnetic ordering temperatures of the various RFe, compounds have been derived from magnetization measurements in the ferrimagnetic and paramagnetic regions. The results obtained in the course of the various studies are in general agreement even though some discrepancies are present in several instances. The purpose of the present work was to make use of a differential scanning calorimeter in order to determine the specific heat anomalies of the RFe, compounds in the vicinity of their magnetic ordering temperatures. A relatively simple theoretical expression can be derived for the specific heat anomaly at the Curie temperature of ferromagnets6. This expression was only partly successful when applied.to the ferromagnetic elements”.‘. Theoretical expressions for the specific heat discontinuity at the magnetic ordering temperature of ferrimagnets have been developed by Grosjean and Robrecht’ and by Nielsen’. Experimental verifications of these expressions are scarce and limited to ferrite systems. One of the objects of this study was to provide a test of the validity of the theoretical expressions. This, however, was not borne out by the present results. EXPERIMENTAL
DETAILS
The cubic Laves compounds
were prepared
by arc melting 99.95% pure
M. P. DARIEL,
316
U. ATZMONY,
R. GUISER
rare-earth metals and 99.99% iron under an argon atmosphere and casting into split 5 mm diam. copper molds. The samples were wrapped in tantalum foils, sealed in evacuated quartz capsules and given a week-long anneal at 900°C. Powder diffraction photographs, using CoKcc radiation, showed that additional phases, if present, never amounted to more than 5%. This was also corroborated by metallographic and some electron microprobe examinations. Lattice parameters were in good agreement with previously published results 3. For the specific heat measurements, small discs, about 2 mm thick, with plane, parallel faces were prepared by grinding and polishing. The runs in the differential scanning calorimeter (DuPont, Thermal Analyzer) were carried out under a purified helium atmosphere at a 5 or 10”C/min heating rate. The temperature scale of the instrument had been calibrated by measuring the melting points of pure indium, lead and zinc. A sapphire sample supplied with the instrument was used for the specific heat calibration. In addition, the specific heat of a 200 mg nickel sample was measured from the ambient to above its Curie temperature. The results were within 10% of those published in the literature’j. RESULTS
AND DISCUSSION
The heat capacity anomalies associated with the magnetic ordering were determined in the “time base” mode with a silver sample of similar dimensions serving as dummy reference. This method yielded the most salient anomalies at the ordering temperature, as shown in Fig. 1. Noteworthy is the fact that in spite of the small size of the samples, (average weight 0.3 g), the relatively slight thermal effects associated with a second-order phase transition show up as prominent anomalies in the heat capacity curves. The magnetic ordering temperatures, assumed to correspond to the peaks of the curves, are given in Table I, along with those deduced from magnetization and resistivity measurements’-3~‘0. There appears to be good agreement between the present results and those of Burzo3 but those of Wallace higher than et al.’ and Buschow et u~.~.‘O are in several instances significantly the present ones. The magnetic ordering temperature of TmFe, has been measured by Wallace et al.’ who found Tc=610 K. This value exhibits very poor agreement with the linear relationship of F us. the de Gennes factor, G=(g-1)2J(J+ 1). The lower value found in this study, T,=559 K, is in better agreement with the Tc = a + bG (u and b, constants) plot, Fig. 2, strengthening the view that the exchange interaction in the RFe, compounds is predominantly of the RKKY type. The specific heat at constant pressure of magnetically ordered materials can be written as C,=
C,+C,+C,+AC
where C, is the lattice, C, the electronic, C,,, the magnetic contribution to the specific heat and AC= C,- C,. In the present work all specific heat measurements were only carried out above room temperature, and as no electronic heat capacity measurements are available, there was no possibility of analysing the measured heat capacity in terms of its various components. The discontinuity of the heat capacity at the magnetic ordering temperature may be considered. This discontinuity, GC(per gram), for ferromagnets can be
RARE EARTH-IRON
00
400
500
600
TEMPERATURE
Fig. 1. Specific heat anomalies magnetic ordering temperature.
TABLE
317
LAVES COMPOUNDS
I 700
800
(K)
of the yttrium
and
heavy
rare
earth-iron
Laves
compounds
at the
I
MAGNETIC POUNDS
ORDERING
TEMPERATURES
(K)
YFr, 550 535 535
7x5 793 788
545
803
705 711 697 695
635 635 635
OF
RARE
EARTH-IRON
LAVES
ErFe,
TtnFe,
Rf?f.
614 612 597 598
596 590 574 573
610
608
591
I 2 3 present work IO
566 559
COM-
318
M. P. DARIEL, I
I
I
1
I
I
1
I
U. ATZMONY,
R. CUBER
900-
500 -
I
I
10
5 c:
(g-lYJ(J4)
Fig. 2. Linear dependence of the magnetic ordering temperature, 7& of the yttrium earth-iron Laves compounds on the de Gennes factor G’=(g- l)‘J(/+ 1).
expressed6
within
the molecular
1
15
field approximation
and
heavy
rare
by
sc=SRN/g{5(J+1)/[(J+1)2+J2]} where S is the average number of Bohr magnetons of the moment carrying atoms, N is the number of magnetic atoms per unit volume and the other symbols have their usual meaning. Among the compounds investigated, only YFe, is ferromagnetic. The measured heat capacity of this compound is shown in Fig. 3. The discontinuity at T, was determined by taking the difference C,,,. - Cmi”. . While there was no ambiguity of Cmin, was not straightforward. The procein determining C,,,,,,, the determination dure followed was to extrapolate from the paramagnetic region and this gave a value of 6C=O.O156 Cal/g. Substituting this value into the expression for SC and solving for J, one obtains J= 2 for iron in YFe,. The magnetization curve of YFe, has been determined by Burzo3 and it can be fitted to a Brillouin function with+< J<$. Expressions for the specific heat anomalies of ferromagnets have been developed by Grosjean and Robrecht’ and by Nielsen’ and applied with limited success to ferrite systems. Nielsen’s expansion leads to an expression of the form 6C = a+b(
JR + 1)/J,
where a and b are constants practically independent of JR but which depend on J,,. Comparison of the experimental results (obtained in a form similar to that of YFe, (Fig. 3)) with Nielsen’s expression was not successful. The reasons for the lack of consistency may be due either to the failure of the molecular field
RARE EARTH-IRON
25
319
LAVES COMPOUNDS
t
I 300
I
I 400
I 500
Fig. 3. Specific heat of YFe, ordering temperature.
I 600
as function
1
of temperature.
liC denotes
the discontinuity
approximation in the neighborhood of the Curie temperature in the determination of the heat capacity discontinuities.
at the magnetic
or to the ambiguity
CONCLUSIONS
The differential scanning calorimeter can be successfully used in order to determine accurate magnetic ordering temperatures of small size (< 0.3 mg) compounds. The magnetic ordering temperatures of the heavy rare earth-iron Laves compounds are linearly related to the de Gennes factor. The theoretical .expressions derived in order to account for the discontinuity of the heat capacity of ferrites do not seem applicable to the ferrimagnetic RFe, compounds.
REFERENCES 1 W. E. Wallace and A. E. Skrabek, in K. Vorres (ed.), Rare Earth Research, Breach, New York, 1964, p. 431. 2 K. H. J. Buschow and R. P. van Stapele, d. Appl. Ph~s., 41 (1970) 4066. 3 E. Burzo, Z. Anger. Phys., 32 (1971) 127. 4 M. P. Dariel and U. Atzmony, Intern. J. Muynefism, (1973) in the press. 5 A. E. Clark and H. S. Belson, Phys. Rev. B, 5 (1972) 3642. 6 R. M. Bozorth, Ferromagnetism, Van Nostrand, Princeton. N.J., 1951, p. 734. 7 M. Griffel, R. E. Skochdopole and F. H. Spedding, Ph_rs. Rev., 93 (1954) 657. 8 C. C. Grosjean and G. G. Robrecht, Physica, 36 (1967) 525. 9 0. V. Nielsen, Appl. Sci. Rrs., 20 (1969) 381. IO M. Brouha and K. H. J. Buschow, J. Appl. Phys., 44 (1973) 1813.
Vol. 2, Gordon
and