ON THE LINESHAPE OF SPIN RELAXATION
BROADENED MÖSSBAUER SPECTRA OF SOLID
POTASSIUM TRIOXALATOFERRATE (III)
D. Barb, L. Diamandescu, D. Tărăbăsan
To cite this version:
D. Barb, L. Diamandescu, D. Tărăbăsan.
ON THE LINESHAPE OF SPIN RELAXATION BROADENED MÖSSBAUER SPECTRA OF SOLID POTASSIUM TRIOXALATOFERRATE (III). Journal de Physique Colloques, 1976, 37 (C6), pp.C6-113-C6-116.
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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
Fe), élargis en présence de la relaxation électronique, ont été obtenus dans l'intervalle de température 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.
57
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 relaxation parameter y is about 0.012 s/mm and the spin-spin relaxation 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 absorption lines. In the past few years this phenomenon has
been extensively investigated theoretically as well as
experimentally [1-14].
The high-spin Fe 3 + compounds are very suitable for
the study of relaxation effects in Mossbauer spectra.
Because of the strength of the spin-spin relaxation the
F e 3 + 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 57 Fe in
K 3 [Fe(C 2 0 4 ) 3 ]. 3 H z O 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 7 Fe.
The absorber thickness was 3 mg/cm2 natural iron.
An ELRON type Mossbauer spectrometer with 10 mCi
57
Co(Cu) source was used. All the spectra consist of a
broadened single line (half width « 2.2 mm/s).
The crystal structure of K 3 [Fe(C 2 0 4 ) 3 ].3 H 2 0 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 octahedron 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 programs 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
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1976626
C6-114
D. BARB, L. DIAMANDESCU AND D.
TARABASAN
results with a scale factor computed in the least square
fits,
3. Discussion. - 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 establishing 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 calibration 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 57Fewas 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 57Featom [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 6S5/2ground 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 correlation 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 corresponds to the isotropic relaxation model (Fig. 2).
In figure 3 the single components of isotropic relaxation 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
-
3a
-3a
Line width
Intensity
-
+$y(5A:-2A,Ag+
-
A:)
+&y(15~f-lOA,A,+3~;)
1
3
where A, and A, are the hyperfine coupling constants of
the excited and ground state, respectively, y is the trace
of y i j and
Parameters of analysis of the spectra discussed in the text
Temp.
6)
-
Relax.
model
(s/mm)
-
-
IR
ITR
IR
ITR
IR
ITR
0.010 f 0.001
0.026 f 0.003
0.012 f 0.001
0.021 f 0.003
0.012 f 0.001
0.019 f 0.003
1.02
3.14
1.09
2.42
1.06
1.54
Y
-
300
148
77
The hyperfine coupling constants were evaluated proceding from the hyperfine field H, = 535 f 5 kOe,
a value characteristic [18] for the S, = f 512 states of
Fe+3in an octahedral oxygen environment. The Mossbauer 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).
--..
I.-..
. ... .
....
V..'...... :...:..
<.
...,-
-
-
........
. ...- -
fx;-2236L-
.-=-.+
A
%*
o
i:
,i
,d
I
4
5
9
-
) .
'r
-
%
.
--
,/
I
I
-4
I
-3
I
I
--2
-1
I
o
I
I
I
2
Velocity
I
3
I
L
I ~ ~ I S I
FIG.4. - Computer fit with Blume stochastic theory for the
room temperature spectrum.
A Misfit
x2
( %)
-
0.68
0.45
0.36
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: +
i
SL
+ S!
s:)]
where ABi and JBi are the dipolar and exchange constants respectively.
The transition rate between I M, > and 1 M,, >
electronic states was written as
where N(M,,) is the normalized Boltzmann distribution 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 weighting with the average of the multiplying factors
< I S + - I > we find a mean relaxation time
I
l4
We have applied here a model with six electronic
levels [20]. This model applies rigorously if a polarizing
field Hex, is present so that Zeeman interaction be
greater than hyperfine interaction. The high x2 value
can be a measure of error appearing when one considers a paramagnet in Hex, = 0 with this model.
In spite of these, the broadening of Mossbauer
spectra obtained is in good agreement with the above
hypothesis of spin-spin relaxation mechanism. The
spin-spin interactions are temperature independent in
agreement with observation ; the only temperature
sensitive changes in shape expected are those due to
populations
the various ~~ystalline-field
states or to the onset of spin-lattice relaxation.
References
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A. M. and KAGAN,
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(1963) 1660.
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A. J., Phys. Stat. Soi. 9
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H. H., KLEIN,
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J . A., Phys. Rev. 165 (1968) 446.
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