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E.P.R. of a Γ8 quartet under uniaxial stress
Volume 28A, number 11
E.P.R.
PHYSICS
OF A l-6 QUARTET
LETTERS
UNDER
10 March 1969
UNIAXIAL
STRESS
J. M. BAKER and G. CURRELL Oxford, U.K.
Clarendon Laboratory,
Received 17 February 1969
Measurementsof the shifts of EPR lines for Dy3+ in CaF produced by uniaxial stress show unambieuouslv for the first time that there are terms withI > f in the stress induced crystal field
%l
B&l9m
The effect of a crystalline electric field upon the configuration 4fn may be described by a term in the Hamiltonian: V, = cl, qm &., where the a,,,, are angular momentum operators which transform like spherical harmonics Ylm [l]. 1 may take values, 2,4 and 6, and the values of m depend upon the symmetry of the site. In particular for a cubic site 1 = 4 and 6, and m = 0 and 4 only. If uniaxial stress is applied to a crystal the Blm change; and for a cubic site the symmetry is lowered so as to introduce new Blm, particularly those for 1 = 2, which are absent for the unstrained crystal. The discussion of the changes ABlm for non-cubic crystals is very complicated because of the large number of elastic constants. For a cubic crystal the situation is simpler because there are only three elastic constants: ~11, ~12 and ~44. On a point charge model the A Blm are calculable in terms of these three parameters. A point charge model is known to be bad for calculating the Blm, particularly for I= 4 and 6; for example for Tm2+ in CaF2 it leads to an underestimate of B4m by a factor of four and of B6, by a factor of ten [2]. The importance of contributions to Blm from overlap and covalency with ligand ions has been demonstrated by several authors [3]. In general it can be shown that two independent parameters are needed to specify the ABfm for each value of 1 for the strain components (E and T2) which do not preserve cubic. symmetry; and two more are needed to describe the effect upon 1 = 4,6 terms of those components (p 1) which do preserve cubic symmetry. Several experiments have been reported [4] on the effect of uniaxial stress upon the g-values of the lowest doublet for rare earth ions. Such information is difficult to interpret unambiguously because only two independent bits of information
can be measured for a doublet, corresponding to theg-shift for two different directions of the applied stress P. As this is insufficient to solve for the eight parameters, considerable assumptions have to be made in order to make progress with an interpretation. For example Sroubek et al., [4] were able to devise a very plausible model for explaining their measurements on the doublet states of Yb3+ in ThO2 and Ho2+ in CaF2 by assuming that I= 2 terms are correctly predicted by the point charge model, and that the predictions of this model have to be scaled up for I= 4 and1 = 6 terms by factors of 4 and 10 respectively, as for the unstrained crystal field. There is not enough experimental evidence to check these assumptions. In fact, as only two bits of independent information could be measured it would be possible to interpret them on the assumption that only E= 2 terms are important, but the values of the parameters would be very different from those given by the point charge model. This difficulty always occurs when one can observe EPR only in a ground doublet. Much more information is available if one measures the effect of stress upon a system with r6 quartet ground state. The stress induces a first order splitting between the two component doublets, and also produces different g-shifts for the two doublets. For some directions of P and H second order shifts (aP2) are produced, but these are simply related to the zero field splitting between the doublets. By studying the g-shifts for a fixed direction of P but different directions for Hone may differentiate between the effects of (E and T2) and A1 strains. Measurements for stress in two directions, ideally (OOl} and (ill), gives independent information. From this information one may deduce all of the parameters 735
Volume
28A, number
11
PHYSICS
Table 1 Line shifts produced State Direction of P, H P dependence of A H Units of AH Experimental AH Calculated A H 1. Point charge 2. Modified point charge 3. 1 = 2 only
r7
(111) (ii2) Linear mG/kg cm-2 + 2.15
by stress
r7 Linear mG/kg cm-2 + 2.86
(~,l)o~O) 1 mG/kg cms2 - 20.0
+ 20.4 + 2.5 + 2.5
- 12.4 - 15.6 - 20.0
+ 20.4 + 2.5 + 2.5
*****
1969
P r7
(110) (111)
describing the effects of E and T2 strain corn: ponents, and one relationship between the two parameters describing the A1 strains. The final bit of information need to solve the problem completely can only be obtained by measuring the stress induced change in separation of two of the crystal field levels. However from measurements within the F6 quartet one should be able to show whether the I = 4,6 terms are important. We have made measurements on Dy3+ in CaF2 at X band (-SkHz), where EPR is observable in both the l? ground state and the r, doublet at 7.35 cm -1\5]. Although experimental difficulties have so far frustrated a complete determination of the parameters the measurements we have made so far, which are summarised in table 1, do lead to some definite conclusions. Table 1 represents the average of several measurements for each direction and the last two columns have been checked in different crystals. These are compared in row 6 with the point charge model, where I = 2 terms dominate in each case. In row 7 we have used the model of Sroubek et al. This gives a better prediction of the g shifts but does not improve the discrepancy between the F7 g shift and the second order shift of the F6 line for ~(001). Row 6 uses a third model in which 1 = 4,6 terms are ignored and the 1 = 2 parameters
736
10 March
LETTERS
r8 (001) (100) Quadratic mG/ (kg cm-2)2 - 1.19 - 12.2 - 16.4 - 33.6
are chosen to fit the g shifts; its predictions are equally poor. In fact the two measurements for P(OO1) can only be reconciled by using much larger sixth order terms. In this connection it is interesting that calculations of the change of covalent contributions indicate that sixth order terms may vary much more rapidly than fourth order terms [6]. Thus these measurements indicate both that the point charge model is poor and that there are sizeable contributions from 1 = 4 and 1 = 6 components.
References Canad. J. Phys. 40 (1962) 1670. 1. H.A.Buckmaster, 2. B. Bleaney, Proc Roy. Sot. A 277 (1964) 289. 3. J. D. Axe and G. Burns, Phys. Rev. 152 (1966) 331. R. E. Watson and R. A. Freeman, Phys. Rev. 156 (1967) 251; M. M. Ellis and D. J. Newman, J. Chem. Phys. 47 (1967) 1968. 4. Z. Sroubek, M. Tachiki, P. H. Zimmermann and R. Orbach, Phys. Rev. 165 (1968) 435; M. M. Zaitov and L. Ya. Shekun, Zh. Eksp i Teor. Fiz. 26 (1968) 8’76; T. D. Black and P. L. Donoho, Phys. Rev. 170 (1968) 462. Phys. Rev. 132 (1963) 5. R. W. Bierig and M. J.Weber, 164; W. Low, Phys. Rev. 134 (1964) A1479. 6. J.M. Baker, J. Phys. C. 1 (1968) 1670.
E.P.R.
PHYSICS
OF A l-6 QUARTET
LETTERS
UNDER
10 March 1969
UNIAXIAL
STRESS
J. M. BAKER and G. CURRELL Oxford, U.K.
Clarendon Laboratory,
Received 17 February 1969
Measurementsof the shifts of EPR lines for Dy3+ in CaF produced by uniaxial stress show unambieuouslv for the first time that there are terms withI > f in the stress induced crystal field
%l
B&l9m
The effect of a crystalline electric field upon the configuration 4fn may be described by a term in the Hamiltonian: V, = cl, qm &., where the a,,,, are angular momentum operators which transform like spherical harmonics Ylm [l]. 1 may take values, 2,4 and 6, and the values of m depend upon the symmetry of the site. In particular for a cubic site 1 = 4 and 6, and m = 0 and 4 only. If uniaxial stress is applied to a crystal the Blm change; and for a cubic site the symmetry is lowered so as to introduce new Blm, particularly those for 1 = 2, which are absent for the unstrained crystal. The discussion of the changes ABlm for non-cubic crystals is very complicated because of the large number of elastic constants. For a cubic crystal the situation is simpler because there are only three elastic constants: ~11, ~12 and ~44. On a point charge model the A Blm are calculable in terms of these three parameters. A point charge model is known to be bad for calculating the Blm, particularly for I= 4 and 6; for example for Tm2+ in CaF2 it leads to an underestimate of B4m by a factor of four and of B6, by a factor of ten [2]. The importance of contributions to Blm from overlap and covalency with ligand ions has been demonstrated by several authors [3]. In general it can be shown that two independent parameters are needed to specify the ABfm for each value of 1 for the strain components (E and T2) which do not preserve cubic. symmetry; and two more are needed to describe the effect upon 1 = 4,6 terms of those components (p 1) which do preserve cubic symmetry. Several experiments have been reported [4] on the effect of uniaxial stress upon the g-values of the lowest doublet for rare earth ions. Such information is difficult to interpret unambiguously because only two independent bits of information
can be measured for a doublet, corresponding to theg-shift for two different directions of the applied stress P. As this is insufficient to solve for the eight parameters, considerable assumptions have to be made in order to make progress with an interpretation. For example Sroubek et al., [4] were able to devise a very plausible model for explaining their measurements on the doublet states of Yb3+ in ThO2 and Ho2+ in CaF2 by assuming that I= 2 terms are correctly predicted by the point charge model, and that the predictions of this model have to be scaled up for I= 4 and1 = 6 terms by factors of 4 and 10 respectively, as for the unstrained crystal field. There is not enough experimental evidence to check these assumptions. In fact, as only two bits of independent information could be measured it would be possible to interpret them on the assumption that only E= 2 terms are important, but the values of the parameters would be very different from those given by the point charge model. This difficulty always occurs when one can observe EPR only in a ground doublet. Much more information is available if one measures the effect of stress upon a system with r6 quartet ground state. The stress induces a first order splitting between the two component doublets, and also produces different g-shifts for the two doublets. For some directions of P and H second order shifts (aP2) are produced, but these are simply related to the zero field splitting between the doublets. By studying the g-shifts for a fixed direction of P but different directions for Hone may differentiate between the effects of (E and T2) and A1 strains. Measurements for stress in two directions, ideally (OOl} and (ill), gives independent information. From this information one may deduce all of the parameters 735
Volume
28A, number
11
PHYSICS
Table 1 Line shifts produced State Direction of P, H P dependence of A H Units of AH Experimental AH Calculated A H 1. Point charge 2. Modified point charge 3. 1 = 2 only
r7
(111) (ii2) Linear mG/kg cm-2 + 2.15
by stress
r7 Linear mG/kg cm-2 + 2.86
(~,l)o~O) 1 mG/kg cms2 - 20.0
+ 20.4 + 2.5 + 2.5
- 12.4 - 15.6 - 20.0
+ 20.4 + 2.5 + 2.5
*****
1969
P r7
(110) (111)
describing the effects of E and T2 strain corn: ponents, and one relationship between the two parameters describing the A1 strains. The final bit of information need to solve the problem completely can only be obtained by measuring the stress induced change in separation of two of the crystal field levels. However from measurements within the F6 quartet one should be able to show whether the I = 4,6 terms are important. We have made measurements on Dy3+ in CaF2 at X band (-SkHz), where EPR is observable in both the l? ground state and the r, doublet at 7.35 cm -1\5]. Although experimental difficulties have so far frustrated a complete determination of the parameters the measurements we have made so far, which are summarised in table 1, do lead to some definite conclusions. Table 1 represents the average of several measurements for each direction and the last two columns have been checked in different crystals. These are compared in row 6 with the point charge model, where I = 2 terms dominate in each case. In row 7 we have used the model of Sroubek et al. This gives a better prediction of the g shifts but does not improve the discrepancy between the F7 g shift and the second order shift of the F6 line for ~(001). Row 6 uses a third model in which 1 = 4,6 terms are ignored and the 1 = 2 parameters
736
10 March
LETTERS
r8 (001) (100) Quadratic mG/ (kg cm-2)2 - 1.19 - 12.2 - 16.4 - 33.6
are chosen to fit the g shifts; its predictions are equally poor. In fact the two measurements for P(OO1) can only be reconciled by using much larger sixth order terms. In this connection it is interesting that calculations of the change of covalent contributions indicate that sixth order terms may vary much more rapidly than fourth order terms [6]. Thus these measurements indicate both that the point charge model is poor and that there are sizeable contributions from 1 = 4 and 1 = 6 components.
References Canad. J. Phys. 40 (1962) 1670. 1. H.A.Buckmaster, 2. B. Bleaney, Proc Roy. Sot. A 277 (1964) 289. 3. J. D. Axe and G. Burns, Phys. Rev. 152 (1966) 331. R. E. Watson and R. A. Freeman, Phys. Rev. 156 (1967) 251; M. M. Ellis and D. J. Newman, J. Chem. Phys. 47 (1967) 1968. 4. Z. Sroubek, M. Tachiki, P. H. Zimmermann and R. Orbach, Phys. Rev. 165 (1968) 435; M. M. Zaitov and L. Ya. Shekun, Zh. Eksp i Teor. Fiz. 26 (1968) 8’76; T. D. Black and P. L. Donoho, Phys. Rev. 170 (1968) 462. Phys. Rev. 132 (1963) 5. R. W. Bierig and M. J.Weber, 164; W. Low, Phys. Rev. 134 (1964) A1479. 6. J.M. Baker, J. Phys. C. 1 (1968) 1670.