ON THE LINESHAPE OF SPIN RELAXATION BROADENED MÖSSBAUER SPECTRA OF SOLID POTASSIUM TRIOXALATOFERRATE (III)

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ON THE LINESHAPE OF SPIN RELAXATION

BROADENED MÖSSBAUER SPECTRA OF SOLID

POTASSIUM TRIOXALATOFERRATE (III)

D. Barb, L. Diamandescu, D. Tărăbăsan

To cite this version:

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JOURNAL DE PHYSIQUE Colloque C6, supplément au n° 12, Tome 37, Décembre 1976, page C6-113

ON THE LINESHAPE OF SPIN RELAXATION BROADENED

MOSSBAUER SPECTRA OF SOLID POTASSIUM TRIOXALATOFERRATE (US)

D. BARB, L. DIAMANDESCU and D. TARABASAN Institute of Atomic Physics, P. O. B. 5206 Bucharest, Romania

Résumé. — Les spectres Môssbauer du trioxalatoferrate de potassium (enrichi de 25 % en

57Fe), élargis en présence de la relaxation électronique, ont été obtenus dans l'intervalle de

tempé-rature de 77 à 300 K. Les spectres ont été analysés à l'aide des théories pour la forme de la ligne, notamment celle d'Afanas'ev et la théorie stochastique de Blume. La meilleure concordance avec les données expérimentales a été obtenue pour le cas de la relaxation isotrope. Le paramètre de relaxation y est approximativement de 0,012 s/mm et le temps de relaxation spin-spin, donné par la théorie de Blume, de « 2 x 10"» s.

Abstract. — Relaxation broadened Mossbauer spectra of solid potassium trioxalatoferrate (25 % enriched in 57Fe) have been obtained within the temperature range of 77-300 K. The spectra were

analysed by means of Afanas'ev theory as well as with Blume stochastic theory for the lineshape. The best fit with experimental data was obtained in the case of isotropic relaxation. The relaxa-tion parameter y is about 0.012 s/mm and the spin-spin relaxarelaxa-tion time given by Blume theory is « 2 x 10-9 s.

1. Introduction. — Recoilless absorption of y-rays can be used to determine the dynamical properties of the electronic spin system if the fluctuation rate is comparable to the nuclear precession frequency. Such fluctuations change the shape of the hyperfine spectrum by broadening and shifting the position of the absorp-tion lines. In the past few years this phenomenon has been extensively investigated theoretically as well as experimentally [1-14].

The high-spin F e3 + compounds are very suitable for

the study of relaxation effects in Mossbauer spectra. Because of the strength of the spin-spin relaxation the F e3 + ions have to be apart at least about 5 A to cause

an observable effect in the spectrum. This can be attained using crystal hydrates rather than water-free compounds.

Resonance absorption spectra of 57Fe in

K3[ F e ( C204)3] . 3 HzO show strongly broadened lines

over a large temperature range indicating the presence of electronic spin relaxation effects.

The spectra were simulated and fitted by considering Afanas'ev [13] and Blume [6] expression for the lineshape in the presence of electronic relaxation. 2. Experimental results. — The absorbers were prepared by grinding single crystals. In order to obtain good spectra the sample was 25 % enriched in 5 7Fe.

The absorber thickness was 3 mg/cm2 natural iron.

An ELRON type Mossbauer spectrometer with 10 mCi

57Co(Cu) source was used. All the spectra consist of a

broadened single line (half width « 2.2 mm/s).

The crystal structure of K3[Fe(C204)3].3 H20 is

monoclinic with four formula units in a cell [15]. The three oxalato groups in a complex ion are planar, their inner oxygen atoms form a slightly distorted octa-hedron round the central iron atom (Fig. 1).

Q 0 Carbon

O Oxygen

FIG. 1. — Diagrammatic sketch of the complex ion F e ^ C t h .

The measured spectra were fitted by using of pro-grams based on a conventional least squares fitting procedure extending them with the resulting formulas of the theoretical calculation given in [6] and [13]. The transmission scale of the theoretical and experimental spectra were adjusted by multiplying the theoretical

8

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C6-114 D. BARB, L. DIAMANDESCU AND D. TARABASAN

results with a scale factor computed in the least square fits,

3. Discussion.

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Mossbauer line broadening can be caused by many different factors.

In order to determine the mechanism of the broadening in a particular case, it is important that the broadening behaviour be studied experimentally under as many different conditions as possible, in the hope of establish- ing the correct mechanism by aprocess of elimination. First of all, it is possible to eliminate instrumental broadening effects as the cause of the systematic behaviour found experimentally. The numerous cali- bration experiments indicate that the instrumental

noise due to extraneous vibration, electrical pickup, etc., is less than two natural linewidths. Another instrumental effect is the broadening due to finite absorber thickness ; in the absorber used the amount of 57Fe was in the range 0.6-0.7 mg/cm2 which would correspond to a maximum broadening of only two linewidths, too small to explain the observed effects (2.2 mm/s half width).

Broadening due to diffusion or other types of net atomic motions is ruled out by the fact that the material studied is crystal with well-known structure (Fig. 1). Lattice-vibration effects could in principle cause a broadening of the Mossbauer line if there were a high localized mode (e. g., an internal molecular vibration) associated with the 57Fe atom [16,17]. The broadening would then be a measure of the rate of decay of the phonons associated with the localized mode. Our observation disagrees with a mechanism of this type because the broadening decreases slightly and does not increase strongly with temperature.

The behaviour of spectra suggests that the electronic spin relaxation is responsible for the broadening In potassium trioxalatoferrate (111) the Fe3+ ion is in a 6S5/2 ground state. When there is no relaxation, Fe3+ ions would show fully resolved hyperfine structure resulting from core polarization of each of the ionic states. In the fast relaxation limit, Mossbauer spectra with broadened lines appear.

It was shown [I31 that for fast relaxation a simple description in terms of certain physical parameters can be obtained for the Mossbauer line shape. The shape of the absorption line depends on a tensor yij the elements of which are closely related to the self corre- lation function of the electronic spin. One obtains for the line shape a sum of Lorentzians whose intensities and widths can be analytically given for special hypothesis concerning spin relaxation process (longitudinal, transverse, isotropic transverse, isotropic).

We performed the computer fits in the supposition of isotropic, isotropic transverse and longitudinal relaxation. For all the spectra obtained the best fit corres- ponds to the isotropic relaxation model (Fig. 2).

In figure 3 the single components of isotropic relaxa- tion fit are displayed. In the case of isotropic relaxation

FIG. 2. - Mossbauer spectrum of ~ 3 [ F e ( C ~ 0 4 ) 3 ] . 3 Hz0 at

300 K (Bl-ack points). Computer fits made by supposition of longitudinal (- x -), isotropic transverse (-0-) and isotropic

(-) relaxation.

FIG. 3. - Isotropic relaxation fits of 300 K and 77 K spectra of Ks[Fe(C204)3]. 3 H20. The single components are displayed,

too.

the Mossbauer spectrum is a sum of three Lorentzian with the following parameters [I31 :

Position Line width Intensity

- - -

3 a + $ y ( 5 A : - 2 A , A g + A:) 1

- 3 a + & y ( 1 5 ~ f - l O A , A , + 3 ~ ; )

3

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Temp. Relax.

6 )

model

-

- 300 IR ITR 148 IR ITR 77 IR ITR

Parameters of analysis of the spectra discussed in the text

The hyperfine coupling constants were evaluated pro- ceding from the hyperfine field H, = 535 f 5 kOe, a value characteristic [18] for the S, = f 512 states of Fe+3 in an octahedral oxygen environment. The Moss- bauer line width was assumed to be 0.36 mm/s. The results of fits assuming isotropic relaxation (IR) and isotropic transverse relaxation (ITR) are collected in table I.

Here the center shift (CS) is given relative to the 57Co(C~) source. A Misfit is the difference of the Misfit parameter introduced by Ruby [19], for the fits with the isotropic transverse and isotropic relaxation model, respectively.

Therefore, the best fit with the experimental points is given by isotropic relaxation model taking into account a small quadrupolar interaction. This result seems to be in agreement with a very small deviation from cubic symmetry of the iron environment.

If we assume zero quadrupolar splitting and perform a fit with a single Lorentzian line we obtain a wrong

x2

((X 3).

Y

A Misfit (s/mm) -

x2

- - (

%)

0.010 f 0.001 1.02 0.68 0.026 f 0.003 3.14 0.012 f 0.001 1.09 0.45 0.021 f 0.003 2.42 0.012 f 0.001 1.06 0.36 0.019 f 0.003 1.54

We performed also a fit (Fig. 4) with Blume stochastic theory 161, considering the electronic relaxation as being represented by the truncated Hamiltonian [20] :

x,,

=

C

(ABi

+

JBi)

[sf

S:

+

SL

+

S! s:)]

i

where ABi and JBi are the dipolar and exchange cons- tants respectively.

The transition rate between

I

M,

>

and

1

M,,

>

electronic states was written as

where N ( M , , ) is the normalized Boltzmann distribu- tion for electronic eigenstate

I

M,,

>,

and K is a constant.

The best

x2

value (M 3.5) was obtained for a constant K = 7.3 x lo6 Hz. If we renormalize K by weight- ing with the average of the multiplying factors

I

<

I

S + -

I

>

l4

we find a mean relaxation time

References -

-

A o 9 - %

-

[I] AFANAS'EV, A. M. and KAGAN, Yu., Zh. Eksp. Teor. Fiz. 45 [4] WEGENER, H., Z. Phys. 186 (1965) 498.

(1963) 1660. [5] WICKMAN, H. H., KLEIN, M. P. and SHIRLEY, D. A., Phys.

[2] BLUME, M., Phys. Rev. Lett. 14 (1965) 1108. Rev. 152 (1966) 345.

[3] VAN DER WOUDE, F. and DEKKER, A. J., Phys. Stat. Soi. 9 [6] BLUME, M. and TJON, J . A., Phys. Rev. 165 (1968) 446. (1965) 775. [7] LEVINSON, L. M. and LUBAN, M., Phys. Rev. 172 (1968) 268.

- 4 -3 - - 2 -1 o I 2 3 L agreement with observation ; the only temperature

Velocity I ~ ~ I S I _{sensitive changes in shape expected are those due to}

FIG. 4. - Computer fit with Blume stochastic theory for the populations the various ~~ystalline-field room temperature spectrum. states or to the onset of spin-lattice relaxation.

- -. .

<.

....

. . ..

.

V-

..'.

.. .. .. : .. .:....

I

-.

..

_.._{...- ...-}_- We have applied here a model with six electronic

-,.

...

.

fx;-2236L- ... . levels [20]. This model applies rigorously if a polarizing

..-=-.+

%*

4

field Hex, is present so that Zeeman interaction be greater than hyperfine interaction. The high

x2

value

5 ) .

,

can be a measure of error appearing when one consi-

i:

'r

i ders a paramagnet in Hex, = 0 with this model.

. ,/

I

In spite of these, the broadening of Mossbauer

,d

spectra obtained is in good agreement with the above

I hypothesis of spin-spin relaxation mechanism. The

I I I I I I I I I

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C6-116 D . BARB, L. DIAMANDESCU A N D D. TARABASAN

[8] BRADFORD, E. and MARSHALL, W., Proc. Phys. Soc. 87 (1966) 1141 BARB, D . and DIAMANDESCU, L., Rev. Roum. Phys. 20 (1975)

731. 259.

191 SVETOZAROV. V. V.. Fiz. Tverd. Tela 12 (1970) 1054. [I51 HEIDRICH, W., Z . Phys. 230 (1970) 418.

. -

.

,

[lo] GABRIEL, H., Phys. Stat. Sol. 23 (1967) 195. [I61 LAX, M. and WALLER, I., Phys. Rev. 138 (1965) A 523. [17] SNYDER, H. S. and WICK, G. C., Phys. Rev. 120 (1960) 128. [ l l ] SCHWEGLER, H., Fortsch. Phys. 20 (1972) 251. _[18]_WERTHEIM,_G._K._and_REMEIKA,_J._P.,_{Phys. Lett. 10}_{(1964) 14.} [I21 Mer~up, S., in : Miissbauer Effect Methodology, ed. 1. J. Gru- _{[l9] RUBY,}_S._{L., in}: Miissbauer Effect Methodology, ed. b y verman (Plenum Press, New York-London) 1974, vol. 9. _I._J._{Gruverman lPlenum Press. New York-London)} [13] AFANAS'EV, A. M. and GOROBCHENKO, V. D., Zh. Eksp. Teor. 1973, vol. 8.