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EPR of Gd3+ - doped CeF3 single crystal: Linewidth variation with temperature
Solid State Communications, ~01.62,~o.ll, Printed in Great Britain.
EPR
Gd3+-
OF
LINEWIDTH
pp.729-733,
DOPED
SINGLE
CeF3
VARIATION
1987.
WITH
0038-1098/87
$3.00
Pergamon Journals
CRYS
+
.OO
Ltd.
TAL
TEMPERATURE
S. K. Misra,
Physics
Department,
Concordia University, 1455 de Maisonneuve, Montr&.l, Q&bee H3GlM8, Canada G. Bacquet
Laboratoire
de Physique
Boulevard
and F. Fabre
des Solides Associg au CNRS, UniversitC 31062 Toulouse C&lex, France
Received
6 February
West,
Paul Sabatier,
1987 by E.F. Bertaut
Abstract : Detailed X-band EPR study of a Gd3+-doped CeF3 single crystal has been made from 4.2 to 473 K, with particular attention to EPR linewidths. In general, it is found that there are four regions over which the log-log plot of the linewidth versus temperature is linear, implying separate power-law dependences of the linewidth. Gd3+ spin Hamiltonian parameters in CeF3 have been estimated at various temperatures from the line positions. From the linewidth variation with temperature the Debye temperature has determined to be about 140 K. R&sum& : On a &udie la variation de la largeur des raies de r&onance du spectre de Gd 3+ dans CeFe3 entre 4,2 et 473 K. 11 y a, en g&&al, quatre regions ob la representation log-log de la variation de la largeur de la raie en fonction de la temperature est linCaire, impliquant des lois de variation diffgrentes. $ a egalement d&terming les param& tres de 1'Hamiltonien tde spin de Gd dans CeF3 aux diverses temp&atures. A partir de la variation de la largeur de raie en fonction de la tea&-ature , on estime h 140 K la valeur de la -temperature de Debye.
1. Introduction
charge-induced-dipole and superposition models have been presented by Lewis and Misra 5 andMisra et al. 6.
EPR of Gd3+-doped cerium trifluoride (CeF3) single crystalwas first reported by Sharma ' at X-band at room temperature. Misra et al. ' published more detailed measurements to estimate rigorously the spin Hamiltonian (S.H.) parameters using a least-squares fitting technique and computer diagonalization of the S.H. matrix 3 ; how ever, because of the lower sensitivity of the homodyne spectrometer, they were not able to obtain well-resolved EPR spectra below room temperature. Korezak and Subotowicz ' made X-band EPR linewidth studies from 120 to 293 K on Gd3+-doped CeF3, investigating in detail only the highest-field transition (5/2 f) T/2). The position of this transition is quite susceptible to the distribution of the S.H. parameter b; within the crystal. For true linewidth studies one should rather choose the central transition (-l/2 l/2) whose position depends on the parameter bs in second-order of approximation only, unlike depends on bz other transitions whose position in zero-order of approximation. Korezak and Subotowicz ' determined the value of the Debyetemperature OD to be about 200 K for CeF3 from the behavior of the linewidth of the highest-field transition. As well, they found that theCe3+host spin-lattice relaxation time ',, as estimated from the linewidths varies as T-" (n Q 2) for T > BD. Theoretical calculations of the S.H. parameters for Gd3+-doped CeF3 using the point-
It is the purpose of the present paper to report yet more detailed single crystal X-band EPR measurements of Gd3+-doped CeF3 with special emphasis on linewidths, extending the previous measurements to the temperature range 4.2 - 47'3 K, concentrating mainly on the (-l/2 t--fl/2) transition ; the behavior of the other experimentally observed transitions have also been included. The line positions will be employed to estimate the S.H. parameters at various temperatures. The linewidth of the central transition will be exploited to deduce the power-law dependence T-n of the spinlattice relaxation time -cl of the host Ce3+ ions. Finally, the Debye temperature will be estimated from the linewidth behavior as a function of temperature.
2. Sample preparation, and experimental
crystal structure arrangement
High quality single ':rys:a: of Gd3+-doped (0.01 mole %) CeF3 were grown in a dynamic helium atmosphere in a modified Stockbarger-type furnace. For further details, see Ref. 2. 'There are three crystal structures as determined from X- ay measurements ; these are D zh (P 63/mcmJ ',i". On tii &eE$d /mslCJ8, and D4jd (P 3~1) perturbed angular correlation measurements 'i and' 729
730
EPR OF Gd3+ - DOPED CeF3 SINGLE CRYSTAL
neutron-diffraction
studies l2 yield the space measurements were carried ",;:cm): Our . a E line century series X-band Varian spectrometer, using a 25 kHz field modudulation, fitted with a ESR 900 Oxford Instruments continuous flow cryostat (4 -300 K) or a V 4540 Varian variable temperature accessory (300 - 473 K). ::+;;;
3. Experimental
Vol.
62, No.
while those of the first/seventh and second / sixth transitions are exhibited in Figs. 2a and 2b respectively. The line positions and the over-
resul?s
Since the main focus of the present investigation was the linewidth studies, no effort was made to study the angular variation of spectra, which has been reported in detail in Ref. 2. Overlap of EPR spectra corresponding to three physically inequivalent, but magnetically equivalent, pairs of Gd3+ ions in the unit cell are observed at any orientation of the magnetic field. The present measurements were made for the external magnetic field orientation B // B for one of the physically inequivalent ions. At this orientation, the overall splitting of the "allowed" lines (AM = + 1, M being the electronic magnetic quantum number) is the largest. Thus i; coincides with the principal axis of the b$ tensor appearing in the S.H. (Sec. 4). The i; axis lies in the cleavage plane, obtained by dropping the crystal in liquid nitrogen and breaking it. As the Gd3+ electronic spin S = 7/2, there were observed seven allowed fine lines. Thecontribution of isotopes with non-zero nuclear spin was not resolved. It was not possible to measure the positions or linewidths of all the transitions in the investigated temperature range, because of overlapping of spectra due to the three physically inequivalent ions. Below 97.5 K, only the central transition could be discerned ; between97.5 and 145 K only the first (-7/2 * -5/2), the central, and the last (5/2 +-+ 7/2) transitions (in order of increasing field) could be discerned. At 160 and 1'75K all but the third and the fifth lines could be resolved. Between 200 and 293 K all the seven allowed transitions, while at 373 K all but the third allowed transitions could be clearly discerned. The first derivative peak-topeak linewidth of the central transition is displayed in Fig. 1 as a function of temperature,
100 TEMPERATURE FIG. 2
500 ( K)
Tempe+rature dependence of the linewidths for B //?. of (a) the first (square) and seventh (circle) lines; and (b) the second (upper triangle) and sixth (lower triangle) lines, as observed for increasing B.
all splitting of the spectra (separation of the outerlines) as functions of temperature are plotted in Fig. 3. It is noted from this figure that the maximum overall splitting of the lines occurs at 175 K. This is also reflected in the value of the parameter bs being the largest at 175 K (see Table I). It was found, from a detailed numerical fit, that the first derivative line shape fits a Lorentzian absorption line shape.
4. Spin Hamiltonian
parameters
The following spin Hamiltonian yas used to fit the spectra for Gd3+-doped CeF3 .
4
FIG.
I
10
11
50 100 TEMPERATURE (K)
500
t +
Temperature dependence of the linewidth of the (-l/Z* l/2) transition for B //5, the direction which corresponds to !jQ" EI'R maximum overall splitting of the Gd spectrum in CeF3.
c
m=O,L2,+4
(7)
;
m=C>_r_ +?+I$+6 where the 02 are the spin operators as defined hy libragam and 3leaney 13 . The S.h. parameters were evaluated by the use of a least squares pro-
Vol. 62, No. II
EPR OF Gd3+ - DOPED CeF3 SINGLE CRYSTAL
I
I
I
731
fj..... .
.. . * *
I
.
100
I
400 TEMPERATURE ( K)
FIti.3
Variation of the line positions (mint) and of the overall splitting (circle) as functions of temperature for 5 // 2.
Table 1. Spin Hamiltonian parameters for Gd3+-doped CeF3 at various temperatures. The parameters bf are expressed in units of GHz. Th.eerrors are as computed using a statistical method 20. n' represents the number of line positions simultaneouslyfitted to evaluate the parameters. For n' = 1, the g value has been estimated from the condition hU = g wB Bc, where u = 9.235 GHz, from the line position BC OS the central transition. A positive sign has been assumed for bs in accordance with the szgn determined for Ga3+-doped LaF3 2.
T(K) L.2
Rzz
“Z
all + 0.001 all -+O.OOl
2 b2 all? 0.05
1 b40 all _+ 0.001
b: all LO.05
b: all+O.O$
n
2.054
52.5
2.052
75
2.044
97.5
2.042
0.661
-
0.09
3
115
2.018
0.675
- 0.09
3
125
l.gll
0.701
- 0.05
160
1.452
0.712
_ 0.40
0.008
- 0.35
175
1.947
0.717
-
0.41
0.007
- 0.37
3.57
0.001
3 5 5
200
1.950
0.707
-
- 0.28
0.01
223
1.950
0.700
- 0.50
0.010
- 0.28
0.07
7
250
1.950
0.700
- 0.50
0.010
- 0.28
0.07
7
293
1.950
0.700
- 0.40
0.010
_ 0.28
0.07
7
373
2.000
0.690
- 0.10
0.010
- 0.28
0.07
6
473
2.000
0.690
- 0.10
0.000
0.00
0.00
6
7
EPR OF Gd3+ - DOPE:D CeF3 SINGLE CRYSTAL
732
cedure, fitting all the observed line positions simultaneously, and numerically diagonalizing the S.H. matrix 3. Depending+on the number of the line positions available for B // 8, only some or all gz.2, b;, b;, b4", bc and b$ could be estimated at various temperatures. These are listed in Table I. 5. Linewidths
and relaxation
times
The temperature variation of the EPR linewidths of Gd3+ in CeF3 lattice can be explained to be due to the fast spin-lattice relaxation of the host Ce3+ ions, which modulates the dipolar and exchange interactions between the host (Ce3+) and the probe (Gd3+) parsmagnetic ions, resulting in what is called the host spin-lattice relaxation narrowing 'lr. The conditions for the applicability of this are provided for in the Fzchange , and narrowing theories of Anderson and Weiss of Kubo and Tomita l6 . These are : (i) km&, xz] gdip
= 0
; (ii)
@Jmod,
SGd-
= 0,
(iii)j(,mod
>>
(for strong narrowipg) ; and (iv) the matrix between different unpertubated elements of gdi states of&,.mus E be negligible. Here'&_.mod is the Hamiltonian responsible for the modulationof the dipolar fields on the Gd3+ ions due to the superposition of the spin-orb't coupling and the 5+ ions (with inorbit-lattice coupling in Ce creasing temperature d% mod becomes large and the dipolar field on Gd3+ ions is weakened ; thus the lines become narrower dipolar interaction of Gdi' ?o~~pwT,'~r~~~F~3'he ions, and :
X,
= gcd wB B C (4. j
Conditions (i) and&i) are clearly fulfilled as xmod contains the spin Operators of the Ce3+ ions, while $_,,contains the spin operators of Gd3+ ions ; thus the two commutators in (i) and (ii) are between different spins. Conditions (iv) is easily seen to be satisfied, since ABdip z 50 mT, while a(a is determined by a field, on the average of Z 300 mT at X-band (9.235 GHz). Condition (iii) is satisfied only at temperatures high enough (2 100 K) where the spin-lattice relaxation time T, of the Ce3+ ions presumably becomes quite small. Since all these conditions are ;Ftisfied in the present case one can express h AB
T, = 34(ga
(2)
)3 N* p2 S'(S+l) B 0
In (2) AB and g are the linewidth and the g factor of the probe ion @d3+, S' is the effective spin of the host ion Ce3+ (S' = l/2), N is the number of host ions per unit volume, which can be calculated from the crystallographic data, and a0 = 1.26 x 10e6 H m-1 is the magnetic permeability constant, required to convert to appropriate units. From (2) it is clear that at T > 100 K,T~ is proportional to AB ; thus r1 follows the same power-law dependence T-" as does AB. Some typical values of T1 as calculated from the linewidth of the (-l/2 +-+ l/2) transition are as follows : 5.7 x 10-13s at 105 K, 4.6 x 10-1&s at 125 K, 2.9 x lO-l3~ at 160 K, 2.5 x 10-13s at 175 K, 1.9 x lo-'3s at 200 K and 1.7 x 10-13s at 473 K.
Vol. 62, No.
II
It is estimated (Fig. 2) that in the powerlaw dependence ABC~ T-" the values of n for the central transition are : n = 0.05 for T < 70 K, n = 1.2 for 70 K < T < 140 K, n = 1.8 for 140 K < T < 200 K and n = 0.02 above 200 K. The Debye model yields n = 2 for two-phonon Raman scattering for T >> BD 13. Thus the present measurements suggest a value of the Debye temperature OD s 140 K for CeF3. This is to be compared with the value of Q, 200 K reported in Ref. 4 which was deduced from the behavior of the linewidth of the transition (5/Z - 7/2), which is quite sensitive to the distribution of b; over the crystal as pointed out in Sec. 1. Concerning the slopes of the linewidth variations of the other transitions, the following should be noted. First transition : n = 2 (100 230 K) and n = 0.41 above ; second and sixth transitions have the same slopes : n = 1.81 (150 230 K) and n = 0.35 above 300 K ; and the seventh transition : n = 0.89 (97 - 145 K), 3.3 (145 200 K) and z C above. Since the linewidth behavior AB 0 T-" is such that n < 2 for all temperatures below 140 K, it can be concluded that at these temperatures none of the Raman, the Orbach, the three-phonon, the local mode, or the collision process is predominant, as these processes dictate a behavior such that n >> 2 ". On the other hand, the dipoledipole interaction between the probe Gd3+ and might provide an explanation of host Ce3+ ions . the observed power-law dependences of the linewidth upon temperature. This is based upon the fact that a detailed computation, taking into account the dipole-dipole interaction between the probe and host parama netic ions Monte-Carlo method for Gd ?+ linewidtis"qptbthe Y1-x Cl3 . 6~20 (X = 0.5, 0.25) host yieldedX a satisfactory explanation of the observed Gd3+ linewidth behavior as a function of temperature I.8 As for the relative linewidths of the various transitions, it is seen that at RT the linewidths in increasing order of B, are 7.9 2 0.6 ; 10.1 ) 0.6 ; 14.4 + 0.6 ; 8.05 + 0.3 ; IO L 0.6 ; 10.2 20.6 ; 7.6-+ 0.6 mT, whose relative ratios are : 1.0 : 1.3 : 7.8 : 1.0 : 1.3 : 1.3 : 1. These should be compared with the relative ratios due to the "lifetime broadening" lg which are 1.0 : 1.77 : 2.23 : 2.38 : 2.23 : 1.77 : 1.0, if the "lifetime broadening" is caused by dipolar or exchange interaction. On the other hand, when Jahn-Teller "lifetime broadening" is effective the relative ratios are 1 : 1.99 : 2.82 : 3.18 : 2.82 : 1.99 : 1.0 lg. Since the observed relative ratios of our linewidths are not as large as those predicted by these two mechanisms, it can be concluded that the distribution of the parameter b: over the crystal is rather significant in CeF3. For, the farther out is a transition from the central one, the more sensitive is its position to the value of bz. 6. Concluding
remarks
The results reported in this paper represent an extension of the previous measurements down to 4.2 K. The determination of spin-lattice relaxation times at various temperatures above 100 K, and that of the Debye temperature, are based on the linewidth of the(. /2++1/2)transition, rather
Vol. 62, No. II
EPR OF Gd3+ - DOPED CeF3 SINGLE CRYSTAL
insensitive to the distribution of the S.H. parameter b0 over the crystal ; thus, the oresent results s8 ould be considered more reliable than those reported in Ref. 4, which were based on the linewidth of the highest-field transition, quite sensitive to the distribution of bz. Finally, the present values of the S.H. parameters determined below and above R.T. for Gd3+-doped CeF3
were previously
733
unavailable.
One of the authors (S.K.M) is Acknowledgments.grateful to the Natural Sciences and Engineering Research ~ounc~il. of Canada for partial financial support (grant no A 4485), and to the Concordia University Computer Centre for facilities to calculate the S.H. parameters .
References 1. 2.
V.K. Sharma, J. Chem. Phys. 54, 496 (1971). S.K. Misra, P. Mikolajczak a% S. Korczak, J. Chem. Phys. 74, 922 (1981). S.K. Misra, J. Msg. Reson. 3, 403 (1976). 43: W. Korczak and M. Subotowicz, Phys. Stat. Sol. (b) 111, 455 (1982). S.K. Misra, Phys. Rev. B 3, 5. N.R. Lewisand 3425 (1983). 6. S.K. Misra, P. Mikolajczak and N.R. Lewis, Phys. Rev. B 24, 3729 (1981). Chem. (Leipzig) 5_, 272 7. I. Oftdel, Z.?hys. (1929 ; l3, 190 (1931) ; R.W.G. Wyckoff, Crystal Structures (Interscience, New York, 1948), Vol. II, Chap. 8. 8. K.Schlyter, Ark. Kemiz, 73 (1952). 98 9. M. Mansmann, 2. Anorg. Allgem. Chem. m, (1964) ; Z. Kristallogr. 122, 375 (1965). 10. A. Zalkin, D.H. Templeton and T.E. Hopkins, Inorg. Chem. $, 1466 (1966). L.O. Andersson and W.G. Proctor, Z. Kristal11. logr. x, 366 (1968).
12. 13.
14. 15.
16. 17. 18.
19. 20.
C. de Rango, G. Tsoucaris and Ch. Zelwer, C. R. Acad. Sci. Ser. B 263, 64 (1965). A. Abragam and B. Bleaney, in: Electron Paramagnetic Resonance of Transition Ions (Clarendon, Oxford, 1970). T. Mitsuma, J. Phys. Sot. Japan '7, 129 (1962) . P.W. Anderson and P.R. Weiss, Rev. Mod. Phys. 25, 269 (1953). R. Kubo and K. Tomita, J. Phys. Sot. Japan 9, 888 (1954). K.N. Shrivastava, Phys. Stat. Sol. (b) 117, 437 (1983). S.K. Misra and U. Orhun, to be published ; U. Orhun, M. SC. Thesis, Concordia University, Mont&al, 1986). K.W.H. Stevens and T.S. Plaskett, Phys. Rev. B 0, 1817 (1979). S.K. Misra and S. Subramanian, J. Phys. C -15 7199 (1982).
EPR
Gd3+-
OF
LINEWIDTH
pp.729-733,
DOPED
SINGLE
CeF3
VARIATION
1987.
WITH
0038-1098/87
$3.00
Pergamon Journals
CRYS
+
.OO
Ltd.
TAL
TEMPERATURE
S. K. Misra,
Physics
Department,
Concordia University, 1455 de Maisonneuve, Montr&.l, Q&bee H3GlM8, Canada G. Bacquet
Laboratoire
de Physique
Boulevard
and F. Fabre
des Solides Associg au CNRS, UniversitC 31062 Toulouse C&lex, France
Received
6 February
West,
Paul Sabatier,
1987 by E.F. Bertaut
Abstract : Detailed X-band EPR study of a Gd3+-doped CeF3 single crystal has been made from 4.2 to 473 K, with particular attention to EPR linewidths. In general, it is found that there are four regions over which the log-log plot of the linewidth versus temperature is linear, implying separate power-law dependences of the linewidth. Gd3+ spin Hamiltonian parameters in CeF3 have been estimated at various temperatures from the line positions. From the linewidth variation with temperature the Debye temperature has determined to be about 140 K. R&sum& : On a &udie la variation de la largeur des raies de r&onance du spectre de Gd 3+ dans CeFe3 entre 4,2 et 473 K. 11 y a, en g&&al, quatre regions ob la representation log-log de la variation de la largeur de la raie en fonction de la temperature est linCaire, impliquant des lois de variation diffgrentes. $ a egalement d&terming les param& tres de 1'Hamiltonien tde spin de Gd dans CeF3 aux diverses temp&atures. A partir de la variation de la largeur de raie en fonction de la tea&-ature , on estime h 140 K la valeur de la -temperature de Debye.
1. Introduction
charge-induced-dipole and superposition models have been presented by Lewis and Misra 5 andMisra et al. 6.
EPR of Gd3+-doped cerium trifluoride (CeF3) single crystalwas first reported by Sharma ' at X-band at room temperature. Misra et al. ' published more detailed measurements to estimate rigorously the spin Hamiltonian (S.H.) parameters using a least-squares fitting technique and computer diagonalization of the S.H. matrix 3 ; how ever, because of the lower sensitivity of the homodyne spectrometer, they were not able to obtain well-resolved EPR spectra below room temperature. Korezak and Subotowicz ' made X-band EPR linewidth studies from 120 to 293 K on Gd3+-doped CeF3, investigating in detail only the highest-field transition (5/2 f) T/2). The position of this transition is quite susceptible to the distribution of the S.H. parameter b; within the crystal. For true linewidth studies one should rather choose the central transition (-l/2 l/2) whose position depends on the parameter bs in second-order of approximation only, unlike depends on bz other transitions whose position in zero-order of approximation. Korezak and Subotowicz ' determined the value of the Debyetemperature OD to be about 200 K for CeF3 from the behavior of the linewidth of the highest-field transition. As well, they found that theCe3+host spin-lattice relaxation time ',, as estimated from the linewidths varies as T-" (n Q 2) for T > BD. Theoretical calculations of the S.H. parameters for Gd3+-doped CeF3 using the point-
It is the purpose of the present paper to report yet more detailed single crystal X-band EPR measurements of Gd3+-doped CeF3 with special emphasis on linewidths, extending the previous measurements to the temperature range 4.2 - 47'3 K, concentrating mainly on the (-l/2 t--fl/2) transition ; the behavior of the other experimentally observed transitions have also been included. The line positions will be employed to estimate the S.H. parameters at various temperatures. The linewidth of the central transition will be exploited to deduce the power-law dependence T-n of the spinlattice relaxation time -cl of the host Ce3+ ions. Finally, the Debye temperature will be estimated from the linewidth behavior as a function of temperature.
2. Sample preparation, and experimental
crystal structure arrangement
High quality single ':rys:a: of Gd3+-doped (0.01 mole %) CeF3 were grown in a dynamic helium atmosphere in a modified Stockbarger-type furnace. For further details, see Ref. 2. 'There are three crystal structures as determined from X- ay measurements ; these are D zh (P 63/mcmJ ',i". On tii &eE$d /mslCJ8, and D4jd (P 3~1) perturbed angular correlation measurements 'i and' 729
730
EPR OF Gd3+ - DOPED CeF3 SINGLE CRYSTAL
neutron-diffraction
studies l2 yield the space measurements were carried ",;:cm): Our . a E line century series X-band Varian spectrometer, using a 25 kHz field modudulation, fitted with a ESR 900 Oxford Instruments continuous flow cryostat (4 -300 K) or a V 4540 Varian variable temperature accessory (300 - 473 K). ::+;;;
3. Experimental
Vol.
62, No.
while those of the first/seventh and second / sixth transitions are exhibited in Figs. 2a and 2b respectively. The line positions and the over-
resul?s
Since the main focus of the present investigation was the linewidth studies, no effort was made to study the angular variation of spectra, which has been reported in detail in Ref. 2. Overlap of EPR spectra corresponding to three physically inequivalent, but magnetically equivalent, pairs of Gd3+ ions in the unit cell are observed at any orientation of the magnetic field. The present measurements were made for the external magnetic field orientation B // B for one of the physically inequivalent ions. At this orientation, the overall splitting of the "allowed" lines (AM = + 1, M being the electronic magnetic quantum number) is the largest. Thus i; coincides with the principal axis of the b$ tensor appearing in the S.H. (Sec. 4). The i; axis lies in the cleavage plane, obtained by dropping the crystal in liquid nitrogen and breaking it. As the Gd3+ electronic spin S = 7/2, there were observed seven allowed fine lines. Thecontribution of isotopes with non-zero nuclear spin was not resolved. It was not possible to measure the positions or linewidths of all the transitions in the investigated temperature range, because of overlapping of spectra due to the three physically inequivalent ions. Below 97.5 K, only the central transition could be discerned ; between97.5 and 145 K only the first (-7/2 * -5/2), the central, and the last (5/2 +-+ 7/2) transitions (in order of increasing field) could be discerned. At 160 and 1'75K all but the third and the fifth lines could be resolved. Between 200 and 293 K all the seven allowed transitions, while at 373 K all but the third allowed transitions could be clearly discerned. The first derivative peak-topeak linewidth of the central transition is displayed in Fig. 1 as a function of temperature,
100 TEMPERATURE FIG. 2
500 ( K)
Tempe+rature dependence of the linewidths for B //?. of (a) the first (square) and seventh (circle) lines; and (b) the second (upper triangle) and sixth (lower triangle) lines, as observed for increasing B.
all splitting of the spectra (separation of the outerlines) as functions of temperature are plotted in Fig. 3. It is noted from this figure that the maximum overall splitting of the lines occurs at 175 K. This is also reflected in the value of the parameter bs being the largest at 175 K (see Table I). It was found, from a detailed numerical fit, that the first derivative line shape fits a Lorentzian absorption line shape.
4. Spin Hamiltonian
parameters
The following spin Hamiltonian yas used to fit the spectra for Gd3+-doped CeF3 .
4
FIG.
I
10
11
50 100 TEMPERATURE (K)
500
t +
Temperature dependence of the linewidth of the (-l/Z* l/2) transition for B //5, the direction which corresponds to !jQ" EI'R maximum overall splitting of the Gd spectrum in CeF3.
c
m=O,L2,+4
(7)
;
m=C>_r_ +?+I$+6 where the 02 are the spin operators as defined hy libragam and 3leaney 13 . The S.h. parameters were evaluated by the use of a least squares pro-
Vol. 62, No. II
EPR OF Gd3+ - DOPED CeF3 SINGLE CRYSTAL
I
I
I
731
fj..... .
.. . * *
I
.
100
I
400 TEMPERATURE ( K)
FIti.3
Variation of the line positions (mint) and of the overall splitting (circle) as functions of temperature for 5 // 2.
Table 1. Spin Hamiltonian parameters for Gd3+-doped CeF3 at various temperatures. The parameters bf are expressed in units of GHz. Th.eerrors are as computed using a statistical method 20. n' represents the number of line positions simultaneouslyfitted to evaluate the parameters. For n' = 1, the g value has been estimated from the condition hU = g wB Bc, where u = 9.235 GHz, from the line position BC OS the central transition. A positive sign has been assumed for bs in accordance with the szgn determined for Ga3+-doped LaF3 2.
T(K) L.2
Rzz
“Z
all + 0.001 all -+O.OOl
2 b2 all? 0.05
1 b40 all _+ 0.001
b: all LO.05
b: all+O.O$
n
2.054
52.5
2.052
75
2.044
97.5
2.042
0.661
-
0.09
3
115
2.018
0.675
- 0.09
3
125
l.gll
0.701
- 0.05
160
1.452
0.712
_ 0.40
0.008
- 0.35
175
1.947
0.717
-
0.41
0.007
- 0.37
3.57
0.001
3 5 5
200
1.950
0.707
-
- 0.28
0.01
223
1.950
0.700
- 0.50
0.010
- 0.28
0.07
7
250
1.950
0.700
- 0.50
0.010
- 0.28
0.07
7
293
1.950
0.700
- 0.40
0.010
_ 0.28
0.07
7
373
2.000
0.690
- 0.10
0.010
- 0.28
0.07
6
473
2.000
0.690
- 0.10
0.000
0.00
0.00
6
7
EPR OF Gd3+ - DOPE:D CeF3 SINGLE CRYSTAL
732
cedure, fitting all the observed line positions simultaneously, and numerically diagonalizing the S.H. matrix 3. Depending+on the number of the line positions available for B // 8, only some or all gz.2, b;, b;, b4", bc and b$ could be estimated at various temperatures. These are listed in Table I. 5. Linewidths
and relaxation
times
The temperature variation of the EPR linewidths of Gd3+ in CeF3 lattice can be explained to be due to the fast spin-lattice relaxation of the host Ce3+ ions, which modulates the dipolar and exchange interactions between the host (Ce3+) and the probe (Gd3+) parsmagnetic ions, resulting in what is called the host spin-lattice relaxation narrowing 'lr. The conditions for the applicability of this are provided for in the Fzchange , and narrowing theories of Anderson and Weiss of Kubo and Tomita l6 . These are : (i) km&, xz] gdip
= 0
; (ii)
@Jmod,
SGd-
= 0,
(iii)j(,mod
>>
(for strong narrowipg) ; and (iv) the matrix between different unpertubated elements of gdi states of&,.mus E be negligible. Here'&_.mod is the Hamiltonian responsible for the modulationof the dipolar fields on the Gd3+ ions due to the superposition of the spin-orb't coupling and the 5+ ions (with inorbit-lattice coupling in Ce creasing temperature d% mod becomes large and the dipolar field on Gd3+ ions is weakened ; thus the lines become narrower dipolar interaction of Gdi' ?o~~pwT,'~r~~~F~3'he ions, and :
X,
= gcd wB B C (4. j
Conditions (i) and&i) are clearly fulfilled as xmod contains the spin Operators of the Ce3+ ions, while $_,,contains the spin operators of Gd3+ ions ; thus the two commutators in (i) and (ii) are between different spins. Conditions (iv) is easily seen to be satisfied, since ABdip z 50 mT, while a(a is determined by a field, on the average of Z 300 mT at X-band (9.235 GHz). Condition (iii) is satisfied only at temperatures high enough (2 100 K) where the spin-lattice relaxation time T, of the Ce3+ ions presumably becomes quite small. Since all these conditions are ;Ftisfied in the present case one can express h AB
T, = 34(ga
(2)
)3 N* p2 S'(S+l) B 0
In (2) AB and g are the linewidth and the g factor of the probe ion @d3+, S' is the effective spin of the host ion Ce3+ (S' = l/2), N is the number of host ions per unit volume, which can be calculated from the crystallographic data, and a0 = 1.26 x 10e6 H m-1 is the magnetic permeability constant, required to convert to appropriate units. From (2) it is clear that at T > 100 K,T~ is proportional to AB ; thus r1 follows the same power-law dependence T-" as does AB. Some typical values of T1 as calculated from the linewidth of the (-l/2 +-+ l/2) transition are as follows : 5.7 x 10-13s at 105 K, 4.6 x 10-1&s at 125 K, 2.9 x lO-l3~ at 160 K, 2.5 x 10-13s at 175 K, 1.9 x lo-'3s at 200 K and 1.7 x 10-13s at 473 K.
Vol. 62, No.
II
It is estimated (Fig. 2) that in the powerlaw dependence ABC~ T-" the values of n for the central transition are : n = 0.05 for T < 70 K, n = 1.2 for 70 K < T < 140 K, n = 1.8 for 140 K < T < 200 K and n = 0.02 above 200 K. The Debye model yields n = 2 for two-phonon Raman scattering for T >> BD 13. Thus the present measurements suggest a value of the Debye temperature OD s 140 K for CeF3. This is to be compared with the value of Q, 200 K reported in Ref. 4 which was deduced from the behavior of the linewidth of the transition (5/Z - 7/2), which is quite sensitive to the distribution of b; over the crystal as pointed out in Sec. 1. Concerning the slopes of the linewidth variations of the other transitions, the following should be noted. First transition : n = 2 (100 230 K) and n = 0.41 above ; second and sixth transitions have the same slopes : n = 1.81 (150 230 K) and n = 0.35 above 300 K ; and the seventh transition : n = 0.89 (97 - 145 K), 3.3 (145 200 K) and z C above. Since the linewidth behavior AB 0 T-" is such that n < 2 for all temperatures below 140 K, it can be concluded that at these temperatures none of the Raman, the Orbach, the three-phonon, the local mode, or the collision process is predominant, as these processes dictate a behavior such that n >> 2 ". On the other hand, the dipoledipole interaction between the probe Gd3+ and might provide an explanation of host Ce3+ ions . the observed power-law dependences of the linewidth upon temperature. This is based upon the fact that a detailed computation, taking into account the dipole-dipole interaction between the probe and host parama netic ions Monte-Carlo method for Gd ?+ linewidtis"qptbthe Y1-x Cl3 . 6~20 (X = 0.5, 0.25) host yieldedX a satisfactory explanation of the observed Gd3+ linewidth behavior as a function of temperature I.8 As for the relative linewidths of the various transitions, it is seen that at RT the linewidths in increasing order of B, are 7.9 2 0.6 ; 10.1 ) 0.6 ; 14.4 + 0.6 ; 8.05 + 0.3 ; IO L 0.6 ; 10.2 20.6 ; 7.6-+ 0.6 mT, whose relative ratios are : 1.0 : 1.3 : 7.8 : 1.0 : 1.3 : 1.3 : 1. These should be compared with the relative ratios due to the "lifetime broadening" lg which are 1.0 : 1.77 : 2.23 : 2.38 : 2.23 : 1.77 : 1.0, if the "lifetime broadening" is caused by dipolar or exchange interaction. On the other hand, when Jahn-Teller "lifetime broadening" is effective the relative ratios are 1 : 1.99 : 2.82 : 3.18 : 2.82 : 1.99 : 1.0 lg. Since the observed relative ratios of our linewidths are not as large as those predicted by these two mechanisms, it can be concluded that the distribution of the parameter b: over the crystal is rather significant in CeF3. For, the farther out is a transition from the central one, the more sensitive is its position to the value of bz. 6. Concluding
remarks
The results reported in this paper represent an extension of the previous measurements down to 4.2 K. The determination of spin-lattice relaxation times at various temperatures above 100 K, and that of the Debye temperature, are based on the linewidth of the(. /2++1/2)transition, rather
Vol. 62, No. II
EPR OF Gd3+ - DOPED CeF3 SINGLE CRYSTAL
insensitive to the distribution of the S.H. parameter b0 over the crystal ; thus, the oresent results s8 ould be considered more reliable than those reported in Ref. 4, which were based on the linewidth of the highest-field transition, quite sensitive to the distribution of bz. Finally, the present values of the S.H. parameters determined below and above R.T. for Gd3+-doped CeF3
were previously
733
unavailable.
One of the authors (S.K.M) is Acknowledgments.grateful to the Natural Sciences and Engineering Research ~ounc~il. of Canada for partial financial support (grant no A 4485), and to the Concordia University Computer Centre for facilities to calculate the S.H. parameters .
References 1. 2.
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C. de Rango, G. Tsoucaris and Ch. Zelwer, C. R. Acad. Sci. Ser. B 263, 64 (1965). A. Abragam and B. Bleaney, in: Electron Paramagnetic Resonance of Transition Ions (Clarendon, Oxford, 1970). T. Mitsuma, J. Phys. Sot. Japan '7, 129 (1962) . P.W. Anderson and P.R. Weiss, Rev. Mod. Phys. 25, 269 (1953). R. Kubo and K. Tomita, J. Phys. Sot. Japan 9, 888 (1954). K.N. Shrivastava, Phys. Stat. Sol. (b) 117, 437 (1983). S.K. Misra and U. Orhun, to be published ; U. Orhun, M. SC. Thesis, Concordia University, Mont&al, 1986). K.W.H. Stevens and T.S. Plaskett, Phys. Rev. B 0, 1817 (1979). S.K. Misra and S. Subramanian, J. Phys. C -15 7199 (1982).