Debye temperatures from ESR

V&me 10, number 1

1 July 1971

CHEMICAL PHYSICS LETTERS

DEBYE ‘II’EMPERATURES FROM ESR

J. S. M. HARVEY Department of Physics, University of Toronto, Toronto 5, Cam&

Received 10 November I970

A recent letter by Shrivastava, entitled “Evaluation of Debye Temperatures as a New Application of ElectronSpin Resonances” is discussed. it is argued that this letter may give tie to unwarran ted optimism regarding this method, which is probably more useful for the investigation of the substitutional process.

In a recent letter entitled “Evaluation of Debye temperature as a new application of ESK’ [ 11, Shrivastava raises the interesting pcssibility

that the

Debye temperature of solids may be determined from the splitting of ionic states by the electron-phonon interaction (called SETI). As a resuit of investigations into the origins of the splitting of ionic states by crystalline environments, we have largely discarded this method for determining the Debye 8. We therefore feel that it is necessary to clarify some of the implications of Shrivastava’s letter. The points that we wish to make are the following: fatly, that values for 0 have been obtained from ZSR for several crystals, secondly, that the presence of a substitutional pammagnetic impurity ion alters the apparent value of 6 in a largeIy unknown way; and thirdly, that the theory for SEPl must be considered speculative as it lacks experimental confirmation. Regarding the first of these, values of 8 were deduced from ESR measurements as early as 1967. Credit should be given to Kiel and Mims [2] who found that their relaxation data for (non S-state) rare-earth ion in CaWO, was consistent with 8 = 140°K, and to Rosenthal et al. [3] who fitted their measurements of the hype&me constant A for Mn2+ in CaO with 8 =65O”K. As far as we know, the fist attempt to evaluate 8 from the splitting of ionic states was made by Harvey and Kiefte [4], although the mechanism was there assumed to bc thermal expansion. Regarding the second, it is probably sufficient

to

L

0

I

I

100

200

I 300

T (WI

Fig. 1. Temperature dependence oi the cubic field

splitting of

ionic states (of b$ in noncubic CaWO& The dashed lines rep

resent the implicit (thermal expansion) dependence derived from pressure meatiements. When the necessary two parameter fit to Shrivastava’s equation is carried out, small differences in curvature, such as those-shown for different substituent ions, represetitrelatively large changes io 0.

Volume 10, number

1

I July 1971

CHEMICAL PHYSICS LETTERS

call attention to difierences in the functional dependence on temperature of the ionic state splittings for different pammagnetic ions in the ame host lattice. Exampies for Mn2+ and Fe3+ in MgO [S 1, and Eu*+ and Gd3+ in CaWO, [4,6] are reproduced in fig. 1. Because of size or charge distrepancies, the substitutional impurity will influence the localized force constants. As the ion-lattice interactions are short range, the apparent value of B will not therefore be charzcteristic’of the host lattice. This argument applies for a temperature dependence arising from either thermal expansion (implicir dependence) or SEPI (explicit dependence). Elaboration of our third point requires a brief description of the SEPI theory. The perturbation mechanisms responsible for the splitting of ionic states in S-state ions are complex and not well understood [7] _ Thus the changes in these splittings arising from lattice vibrations cannot be predicted with certainty and a theory must be regarded as speculative until confirmed by experiment. The Debye integral used by Shrivastava is obtained, in the long wavelength approximation, for an iron-group ion in an ionic lattice with octahedral coordination. This approximation and the short wavelength one [S] have been tested rather extensively in connecticn with the explicit temperature variation of the A constant. The state function here required is simple, needing only the admixture of states with spherical symmetry, but good functional agreement is not often obtained. For example, Zdansky [9] found it necessary to postulate the existence of a large amplitude local impurity mode. Some values of 0 obtained by this method are listed in table 1 and are compared, where possible, with values obtained from other methods. We note that if 8 is not kilown, a two parameter fit to the experimental curve is required and that this fit is relstively insensitive to the value of 0 used [3,4]. Recently, Menne [lo] has generalized the k-space averaging and fmds that the optical modes make a significant contribution. The ionic S-states are split by the orbit-!attice interaction only if’ their symmetry is reduced. Thus the state function is more complicated and the possibility exists for strong coupling to specific phonon modes. It would be surprising if the long wavelength approximation were equally valid here. To the best of our knowledge, the example chosen by Shrivastava,

Table I Debye temperatures

obtained by various methods

Substance

Method a)

0 (%)

Ref.

MgO:hfn*

1 4

850 750

131 t31

BaO:Mn%

1

56 (loti mode)

191

4

173

c91

CaO:Mn*

1

650

131

Sro:Mn~

1

131 (local mode)

CdF#&+

1

350

VI

CaW04:EuN

1 2 3

150 140 250

141 [21 t41

CaWO&GF+

3

3.50

[61

a)

1 ESR, temperature dependence of.4. 2 ESR, spin relaxation. 3 ESR. splitting of ionic states (thermal expansion). 4 Specific heat.

ZnS:M$+, is the only one for which this theory is functionally in agreement with the obsrved explicit temperature dependence. Parenthetically, ihis success of the ionic model occurs for a compound in which appreciable delocalization is known to occur. We conclude that the SEPI theory must be considered speculative in the absence of further experimental confirmation ar.d that further theoretical development is required. For the preser.t, it is our belief, based on our own studies of experimental curves such as those in fig. 1, that ESR measurements of the spI.itting of ionic states can be more profitably applied to an investigation of the localized thermodynamic changes caused by the substituent ion.

References [l J K.N.Shrivastava, Chem. Phys. Letters 6 (L9701545. [2] A.Kiel and W.B.Mims, Phys. Rev. 161 (1967) 386. 131 J.Rosenthal. L.Yannusand R.H.Bartrarn, Phys. Rev. 153 (1967) 407. [4) J.S.M.Harvey and H.Kiefte, Can. I. Phys. 47 (L969) 1505. IS] W.M.W&h Jr., J.Jeener and N.Blaen;bergen. phys. Rev. 139 (1965) A1338. (6) J.S.M.Harvey and HXiefre, to 5-e published.

63

Vahime 10,numba 1 ._. 171 Iamh4A6mham, --cr, .

fsj

CLkFmch, EJ.Lee and LA.

Wah. I. Pbyn Chela. S43L2Q Il!X% 81c.-~.Flua~~, FXachford, J.kLock and M.A.Mostrom. 3. *ys.

64

CHEMlCALPHYSICS

chti.

SOL 31(1970)

871.

LET~RS [91 K-y, [lo]

-

Ph)s,

1 July 1971

St& Sit 28 119681181.

-r.~.~cnne, phys. Rev. B 1 (19?0) 4496.