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Magnetic susceptibility of europium trifluoride
J. Plays. Chem. Solids
Pergamon Press 1970, Vol. 3 1, pp. 2639-2642.
MAGNETIC
SUSCEPTIBILITY TRIFLUORIDE
Printed in Great Britain.
OF EUROPIUM
s. KJmN Department of Physics, Colorado State University, Fort Collins, Cola. 80521, U.S.A. P. M. RACCAR* Lincoln Laboratory, M.I.T. Lexington, Mass. 02173, U.S.A.
A. TVETRN Department of Physics, Colorado State University, Fort Collins, Colo. 80521, U.S.A.
(Received 26 Junlrmy 1970) Abstract-Our previous measurement of the magnetic susceptibility of Europium Trifluoride from liquid helium to room temperature has been extended to 750°K. With the aid of the recent spectroscopically determined values of the low-lying energy levels of EuF, a simple crystal field analysis has been used to calculate the expected temperature variation of the susceptibility. When an accurate account is taken of the sample impurities, the calculated and experimental values agree to within approximately 1 per cent over the entire region of measurement. 1. INTRODUCTION
of its unique electronic ground configuration among the rare earth ions, a magnetic singlet with a nearby triplet, the trivalent europium ion has proved to be a popular probe for investigating cooperative [ 11 and covalent effects [2] that occur for the rare earth series. In an attempt to see how well the recent spectroscopic data of Caspers, Rast and Fry[3] on EuF, could be used to predict the magnetic susceptibility of this strongly ionic compound, we have extended our previous helium to room temperature measurements [4] to 750°K. A straightforward application of crystal field theory[5] has enabled us to determine the crystal field e&en-functions of the 3F, excited multiplet; because the susceptibility becomes rapidly insensitive to the details of the energy level structure for this ion we have only roughly estimated the crystal field eigen-functions for the 3F2 multiplet, ignored the splitting for higher J-states and used average values for the multip~et BECAUSE
energies as determined from the data of Caspers et al. This degree of approximation has proven sufficient to explain the variation of the susceptibility of EuF, to within experimental accuracy throughout the entire temperature range. 2. EXPERIMENT
The measurements were performed with the same sample used previously. but whose impurity content was much more accurately determined. A mass spectrographic analysis showed small amounts of inert impurities, but approximately 1000 parts per million of sodium (see Table 1). The presence of the latter leads to the formation of NaEuF, (with europium in a divalent state) matrix and, there-
*The Lincoln Laboratory portion of this work was sponsored by the Department of the Air Force. 2639
Table
Na 0 N C, Li Y Al
1. Impurity content of EuF, sample 10Sppm 200 < 300
Si Cl K Ca
1
SC
200
100 100 5 20
I
2640
S. KERN, P. M. RACCAH
--0 A
0
100
200
and A. TVETEN
CALCULATED FOR EuF,+O~l%Eu PREVIOUS DATA PRESENT DATA
300
400
SO0
SO0
700
TEMPERATURE (*Kf
Fig. 1. Molar magnetic susceptibility of europium trifiuoride vs. temperature.
fore, constitutes the only impurity considered important in its effect upon the susceptibility. The high temperature measurements were performed with a Princeton Applied Research Model FM-l vibrating sample magnetometer, with a Model FM- 15 1 oven attachment. This latter had to be firmly mounted to suppress background signal from interfering with the measurements. With samples of about O-1 g the background amounted to about 2 per cent of the sample signal but was field independent; it, therefore, could be fairly accurately accounted for and did not cause more than a small uncertainty. The results are shown in Fig. 1. 3. CALCULATIONS
In the usual way for a crystal field[5] calculation we assume that the potential for an electron on the cation can be expanded as
where the Unm(B, 4) are tensor operators and the An* are parameters that account for the strength of the crystal field[S]. The ground state for Euf3, 7Fo, is a singlet and can be considered as unaffected by the crystal field. The first excited state is the triplet, 7F1, which is split by the second order terms in the expansion represented by equation (1) into three singlets which may be represented in (JM) notation as, Ila) = ILO) Ilb) = -!t/z [I15 I) + II,-l>l Ilc) =&~ll,l)-IL-01
(2)
where the states on the left hand side are given by the free ion J value from which the crystal field state is derived. Ignoring 4th order terms, the same 2nd order parameters derived from
MAGNETIC
SUSCEPTIBILITY
the ‘F1 splittings were applied to the ‘Fz multiplet to approximately determine its crystal field eige~unctions. The susceptibility from 0 to 800°K was then calculated using [6]
OF EUROPIUM
TRIFLUORIDE
2641
ed line in the figure is the sum of the calculated results plus the contribution of the 0.1% of Eu+* present. The magnitude of this contribution is computed by a simple Curie dependence for the Eu+~ susceptibility, a reasonable
with (L~JMIMkPjL’S’J’M’)
= (-l)J-M(_;
;
;cij (LSJIMkljL’S’J’)
(4)
where (LSJIIMkiIL’S’J’)
x t-11
= (l,l~SW~/L-t2S~~l,l,S’L’J’)
= S,, tl@J+l)(~‘+
WL’+
1)’
l,+lb+s+J’
J
x t-11 ,+L+J+s{f ;, “s}
(5)
for the ‘F, and rFz multiplets, and the Van Vleck formula[7] for the upper states. The results of this calculation are given in Table 2 and plotted as the solid line in Fig. 1; the dash-
assumption for the 4y configuration {a halffilled shell) to all but very low temperatures, The experimental points fall within one per cent of the calculated curve.
Table 2. Calcumagnetic lated susceptibility of EuF,
is clear that the agreement of the measured and calculated magnetic susceptibility is good and would, perhaps, suggest the use of EuF3 as a magnetic standard which is both easy to prepare, and chemically stable in air over a wide temperature region. In view of the current high interest in the magnetic behavior of Europic compounds, further refinements in the calculations, involving crystal-field and spin-orbit mixing effects, are presently in progress.
4. CONCLUSIONS
T (“K) 0 50 ml
150 200 250 300 400 500 600 700 800
X (cgs units) 5*88 (10-3) 5-88
5.80 5.53 5.11 4.69 4.32 3.73 3.34 3.05 2.82 2.65 ( 1O-3)
It
REFERENCES 1. HUANG N. L. and VAN VLECKJ. H..J. appl. Phys. 40,1144 (1969). 2. BURNS G. and AXE J. D., Optical Properties of Ions in Crystals (Edited by H. M. Grosswhite and H. W. Moos). Interscience, New York (1967).
2642
S. KERN,
P. M. RACCAH
3. CASPERS H. H., RAST H. E. and FRY J. L.. J. them. Phys. 47,4505 (1967). 4. KERN S. and RACCAH P. M., J. Phys. Chem. Solids 26,1625 (1965). 5, HUTCHINGS M. T., Solid State Physics (Edited by F. Seitz and D. Turnbull), Vol. 16. Academic Press, New York (1964).
and A. TVETEN
6. SHORE B. W. and MENZEL D. H., Principles of Atomic Spectra, p. 363. Wiley, New York (1968). Their equation on p. 363 is missing a factor of 2 in front ofChe second 6~s’ term. 7. VAN VLECK J. H., The Theory of Electric and Magnetic Susceptibilities, p. 233. Oxford Universities Press (1932).
Pergamon Press 1970, Vol. 3 1, pp. 2639-2642.
MAGNETIC
SUSCEPTIBILITY TRIFLUORIDE
Printed in Great Britain.
OF EUROPIUM
s. KJmN Department of Physics, Colorado State University, Fort Collins, Cola. 80521, U.S.A. P. M. RACCAR* Lincoln Laboratory, M.I.T. Lexington, Mass. 02173, U.S.A.
A. TVETRN Department of Physics, Colorado State University, Fort Collins, Colo. 80521, U.S.A.
(Received 26 Junlrmy 1970) Abstract-Our previous measurement of the magnetic susceptibility of Europium Trifluoride from liquid helium to room temperature has been extended to 750°K. With the aid of the recent spectroscopically determined values of the low-lying energy levels of EuF, a simple crystal field analysis has been used to calculate the expected temperature variation of the susceptibility. When an accurate account is taken of the sample impurities, the calculated and experimental values agree to within approximately 1 per cent over the entire region of measurement. 1. INTRODUCTION
of its unique electronic ground configuration among the rare earth ions, a magnetic singlet with a nearby triplet, the trivalent europium ion has proved to be a popular probe for investigating cooperative [ 11 and covalent effects [2] that occur for the rare earth series. In an attempt to see how well the recent spectroscopic data of Caspers, Rast and Fry[3] on EuF, could be used to predict the magnetic susceptibility of this strongly ionic compound, we have extended our previous helium to room temperature measurements [4] to 750°K. A straightforward application of crystal field theory[5] has enabled us to determine the crystal field e&en-functions of the 3F, excited multiplet; because the susceptibility becomes rapidly insensitive to the details of the energy level structure for this ion we have only roughly estimated the crystal field eigen-functions for the 3F2 multiplet, ignored the splitting for higher J-states and used average values for the multip~et BECAUSE
energies as determined from the data of Caspers et al. This degree of approximation has proven sufficient to explain the variation of the susceptibility of EuF, to within experimental accuracy throughout the entire temperature range. 2. EXPERIMENT
The measurements were performed with the same sample used previously. but whose impurity content was much more accurately determined. A mass spectrographic analysis showed small amounts of inert impurities, but approximately 1000 parts per million of sodium (see Table 1). The presence of the latter leads to the formation of NaEuF, (with europium in a divalent state) matrix and, there-
*The Lincoln Laboratory portion of this work was sponsored by the Department of the Air Force. 2639
Table
Na 0 N C, Li Y Al
1. Impurity content of EuF, sample 10Sppm 200 < 300
Si Cl K Ca
1
SC
200
100 100 5 20
I
2640
S. KERN, P. M. RACCAH
--0 A
0
100
200
and A. TVETEN
CALCULATED FOR EuF,+O~l%Eu PREVIOUS DATA PRESENT DATA
300
400
SO0
SO0
700
TEMPERATURE (*Kf
Fig. 1. Molar magnetic susceptibility of europium trifiuoride vs. temperature.
fore, constitutes the only impurity considered important in its effect upon the susceptibility. The high temperature measurements were performed with a Princeton Applied Research Model FM-l vibrating sample magnetometer, with a Model FM- 15 1 oven attachment. This latter had to be firmly mounted to suppress background signal from interfering with the measurements. With samples of about O-1 g the background amounted to about 2 per cent of the sample signal but was field independent; it, therefore, could be fairly accurately accounted for and did not cause more than a small uncertainty. The results are shown in Fig. 1. 3. CALCULATIONS
In the usual way for a crystal field[5] calculation we assume that the potential for an electron on the cation can be expanded as
where the Unm(B, 4) are tensor operators and the An* are parameters that account for the strength of the crystal field[S]. The ground state for Euf3, 7Fo, is a singlet and can be considered as unaffected by the crystal field. The first excited state is the triplet, 7F1, which is split by the second order terms in the expansion represented by equation (1) into three singlets which may be represented in (JM) notation as, Ila) = ILO) Ilb) = -!t/z [I15 I) + II,-l>l Ilc) =&~ll,l)-IL-01
(2)
where the states on the left hand side are given by the free ion J value from which the crystal field state is derived. Ignoring 4th order terms, the same 2nd order parameters derived from
MAGNETIC
SUSCEPTIBILITY
the ‘F1 splittings were applied to the ‘Fz multiplet to approximately determine its crystal field eige~unctions. The susceptibility from 0 to 800°K was then calculated using [6]
OF EUROPIUM
TRIFLUORIDE
2641
ed line in the figure is the sum of the calculated results plus the contribution of the 0.1% of Eu+* present. The magnitude of this contribution is computed by a simple Curie dependence for the Eu+~ susceptibility, a reasonable
with (L~JMIMkPjL’S’J’M’)
= (-l)J-M(_;
;
;cij (LSJIMkljL’S’J’)
(4)
where (LSJIIMkiIL’S’J’)
x t-11
= (l,l~SW~/L-t2S~~l,l,S’L’J’)
= S,, tl@J+l)(~‘+
WL’+
1)’
l,+lb+s+J’
J
x t-11 ,+L+J+s{f ;, “s}
(5)
for the ‘F, and rFz multiplets, and the Van Vleck formula[7] for the upper states. The results of this calculation are given in Table 2 and plotted as the solid line in Fig. 1; the dash-
assumption for the 4y configuration {a halffilled shell) to all but very low temperatures, The experimental points fall within one per cent of the calculated curve.
Table 2. Calcumagnetic lated susceptibility of EuF,
is clear that the agreement of the measured and calculated magnetic susceptibility is good and would, perhaps, suggest the use of EuF3 as a magnetic standard which is both easy to prepare, and chemically stable in air over a wide temperature region. In view of the current high interest in the magnetic behavior of Europic compounds, further refinements in the calculations, involving crystal-field and spin-orbit mixing effects, are presently in progress.
4. CONCLUSIONS
T (“K) 0 50 ml
150 200 250 300 400 500 600 700 800
X (cgs units) 5*88 (10-3) 5-88
5.80 5.53 5.11 4.69 4.32 3.73 3.34 3.05 2.82 2.65 ( 1O-3)
It
REFERENCES 1. HUANG N. L. and VAN VLECKJ. H..J. appl. Phys. 40,1144 (1969). 2. BURNS G. and AXE J. D., Optical Properties of Ions in Crystals (Edited by H. M. Grosswhite and H. W. Moos). Interscience, New York (1967).
2642
S. KERN,
P. M. RACCAH
3. CASPERS H. H., RAST H. E. and FRY J. L.. J. them. Phys. 47,4505 (1967). 4. KERN S. and RACCAH P. M., J. Phys. Chem. Solids 26,1625 (1965). 5, HUTCHINGS M. T., Solid State Physics (Edited by F. Seitz and D. Turnbull), Vol. 16. Academic Press, New York (1964).
and A. TVETEN
6. SHORE B. W. and MENZEL D. H., Principles of Atomic Spectra, p. 363. Wiley, New York (1968). Their equation on p. 363 is missing a factor of 2 in front ofChe second 6~s’ term. 7. VAN VLECK J. H., The Theory of Electric and Magnetic Susceptibilities, p. 233. Oxford Universities Press (1932).