ANOMALOUS LINESHAPES IN PARAMAGNETIC HF SPLIT MÖSSBAUER SPECTRA OF HIGH SPIN Fe (III) IONS IN AMORPHOUS FROZEN SOLUTION

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ANOMALOUS LINESHAPES IN PARAMAGNETIC

HF SPLIT MÖSSBAUER SPECTRA OF HIGH SPIN

Fe (III) IONS IN AMORPHOUS FROZEN SOLUTION

J. Knudsen

To cite this version:

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ANOMALOUS LINESHAPES IN PARAMAGNETIC HF SPLIT

MOSSBAUER SPECTRA OF HIGH SPIN Fe (111) IONS IN

AMORPHOUS FROZEN SOLUTION

J. E. KNUDSEN Laboratory of Applied Physics I1

Technical University of Denmark

-

DK 2800 Lyngby, Denmark

Rhumb.

-

Le complexe hexaquo-ferrique [Fe(H20)6] 3-1 a et6 Btudie par spectroscopie Mossbauer sous forme d'une solution aqueuse, dilde magnetiquement, et congelke en un etat vitreux homogkne. Les spectres sont enregistres a 4,s K sous champs magnetiques allant jusqu'a 6 200 G . 11s montrent une structure hyperfine paramagnktique, bien rksolue. En presence des champs magnetiques faibles les raies ont une forme anormale, non symetrique. En comparant les spectres obtenus en champs faibles et forts on conclut, que la forme anormale des raies n'est pas, cornrne on le pensait, due & l'orientation au hasard des axes du champ cristallin, par rapport a la direction du champ applique. La forme des raies est attribuke aux variations des paramktres du champ cristallin du complexe dans la matrice vitreuse.

Abstract.

-

By means of Mossbauer spectroscopy tne ferric hexaquo complex [Fe(H20)6]3+ has been investigated in a magnetically dilute aqueous solution, frozen to a homogeneous glass. Spectra obtained with various applied magnetic fields up to 6 200 G at 4.5 K show a well resolved paramagnetic hyperfine structure. With small applied fields the lines have an anomalous, asymmetric shape. By comparison of the spectra obtained in small and strong fields it is concluded, that the anomalous shape is not, as hitherto assumed, caused only by the random orientation of the crystal field axes relative to the applied field direction. The shape is ascribed to variations in the crystal field parameters among the complexes in the glass matrix.

1. Introduction.

-

Mossbauer spectra of paramagnetic ferric complexes may show a well resolved magnetic hyperfine (hf) splitting, if the relaxation of the electronic spin is suppressed by dilution of the magnetic ions and the use of low temperatures.

This work presents a Mossbauer investigation of the ferric hexaquo complex, [F~(H,o),]~+, in a magnetically dilute, aqueous solution. frozen to a homogeneous glass. In this complex the ferric ion is found in the high spin state with the six water ligands coordinated in an -approximately octahedral arrangement [l, 21. The Mossbauer spectra obtained at 4.5 K show a well resolved magnetic hf structure. With small applied magnetic fields the lines have a characteristic asymmetric, non-Lorentzian shape. Spectra of the same complex in a similar frozen aqueous solution (fas) have been obtained by Afanas'ev et al. [3] in a small applied field (200 G), with the same anomalous lineshape. The authors interprete their spectra in terms of a definite crystal field spin Hamiltonian, and attribute the asymmetric lineshape to the random orientation of the local crystal field axes relative to the applied field. From a comparison of their experimental data and model- parameters a saturation value of the hf field as high as H,, W 610 kG can be deduced. However, from a later Mossbauer investigation by Sontheimer et al. [4] of a

similar fas at 4.2 K in a strong applied field of 80 kGY where the electronic spin is nearly polarized, a saturation field H,

x

580 kG is found.

The present work supplies the experimental material and offers a new interpretation related to the amorphous structure of the fas, that consistently accounts for the positions as well as the anomalous shapes of the absorption lines.

2. Experimental.

-

The absorber investigated was frozen from an aqueous solution of composition 0.030 M Fe(N0,),(90

%

57Fe), 0.5 M HNO,, 5.4 M LiNO,, where the iron is present as the complex [Fe(H20),I3 + [l, 2, 51. After quick-freezing in liquid

N, the absorber had a clear, transparent (but cracked) appearance, which indicates that a homogeneous glass had formed during the cooling [6, 71. A He cryostat of

the cold finger type was used for cooling the absorber during the Mossbauer measurements. Magnetic fields up to 6.2 kG could be applied perpendicularly to the y-ray beam by means of an electromagnet with iron pole shoes. The spectra were obtained in transmission geometry with a movable source of "CO in Pd. The spectrometer was of the conventional constant accele- ration type with a multichannel analyser operated in the time mode. A thin iron foil was used for the

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C6-736 J. E. KNUDSEN velocity calibration. The line width was 0.23 mm/s with

this absorber. AI1 velocities (and isomer shifts) are given relative to the centroid of the spectrum of this foil at room temperature.

Data obtained at 4.5 K are shown in figure 1 with the applied field specified. The spectra have a well resolved

magnetic hf structure. They are symmetric, indicating a vanishing quadrupole interaction. At 250 G the main impression is two magnetic split, six-line spectra of different area, corresponding to hf fields H,

a

573 kG and 250 kG, respectively. The lines are rather broad

(z

0.8 mm/s) with an anomalous asymmetric shape. In a strong field (6 200 G) the lines are nearly Lorent- zian and the width has decreased to z 0.5 mm/s for the outer lines.

VELOCITY (MM/S)

FIG. 1.

-

Mossbauer spectra obtained at 4.5 K in transverse magnetic fields. The full curves show the fits calculated from the spin Hamiltonian model by admitting some variation of

the crystal field parameters.

3. Model considerations.

-

The electronic state of the ferric ion depends on the crystal field and the applied magnetic field The splitting of the 6S ground level is often adequately described by means of a spin Hamiltonian 181 :

S being the full electronic spin, S =

3.

In the present case the hf splitting of the electronic levels is decoupled by the applied field, and the six electronic eigenstates follow from (l) without consideration of the nuclear states. Then,the Mossbauer spectrum can be described by means of effective fields

acting on the nucleus, one field for each electronic state. Here H, is the saturation value of the hf field, equiva- lent to the hf coupling constant A (assumed isotropic for an S-state ion), H, = - AS/g,

P,.

In a small applied field (250 G) the electronic levels may be considered as three well separated, but individually weakly Zeeman split Kramers doublets with a total separation A,, 9 2 pH. Each doublet gives rise to a six-line Mossbauer spectrum with a hf field

-

He = (Hex, Hey, He,) given by 131 :

Here xyz are the principal axes of the gyromagnetic tensor of the Kramers doublet in question, with corresponding principal values g,, g,, g, [8] and

-

H = (H,, H,, H,) is the external field.

The hf field (2) depends heavily on the direction of the (local) magnetic axes xyz relative to the applied field. In an amorphous sample this will in general lead to a smearing of the hf splitting. However, if the doublet in question has a high magnetic anisotropy, say g, p g,, g,, a well resolved hf splitting will result also in a glass. Then the hf field takes a maximum value H, = (g,/lO). H, directed along the longitudinal axis z, when the external field is applied in this direction. The applied field must be inclined at a large angle to this direction to cause an appreciable lowering of the hf field below H,. In an axial case, g, = g, = gL (-g g,),

it can be shown from (2) that the probability is

3

to find the hf field He in the range H,-AH< He< H,,

where

and with a direction that deviates less than

from one of the longitudinal directions -L z. Thus a six- line spectrum results, corresponding to a hf field near H,, and with line intensities in the ratio

but with broadened, non-Lorentzian line shapes, that reflect the distribution (2). This shape will resemble the anomalous shape of the outer lines of the experimental spectrum at 250 G shown in figure 1.

For a Kramers doublet with an isotropic gyromagnetic tensor, g, = g, = g, = g, a well resolved six- line spectrum will be observed also in an amorphous sample. The spectrum will correspond to a hf field He = (gll0). H,, directed along the applied field, and the lines will be narrow Lorentzians in the ideal case. For a transverse applied field the intensity ratio

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In a strong applied field the electronic Zeeman interaction dominates the Hamiltonian (l), 2 p H % A,,. In a first approximation the electronic eigenstates are then the states with definite spin projection,

along the applied field

f?,

to which correspond the effective fields H

+

H,, H

+

3 Ho/5, H & H0/5, with direction along

p.

Thus a spectrum composed of six magnetic split, six-line spectra of narrow Lorentzians is expected, whether the sample is amorphous, single- or polycrystalline.

4. Discussion.

-

From the detailed resolution of the hf structure it is concluded that the spectra are determined mainly by a static spin Hamiltonian (l) of an isolated ferric hexaquo ion as described in the preceding section, the spin relaxation time ze is long compared to the period a(lL1 2 ns of the nuclear Larmor precession in the hf field. According to the relaxation model of Blume and Tjon [g] (which does not

apply rigorously to the present case) the relaxation will appear in the spectra chiefly as a broadening A T = 2 h/z, of the lines if re b o l l . A value ze

,

50 ns is estimated

from the experimental width of the outer lines. In the approximation set by this model the relaxation will then influence neither the Lorentzian shape nor the positions of the lines significantly, the separation of the outermost lines will be affected only 0.1

%.

A quantitative interpretation of the spectra in terms of a crystaI field spin '~amiltonian rests on a determination of the saturation value H, of the hf field. Ignoring the crystal field interaction in the strong field spectrum (H = 6 200 G) a value H, = 580 (& 2) kG can be deduced from the separation of the outermost lines, with due regard to the thermal population

P(M,) cc exp(- 2 PHM,/kT) of the electronic levels M, =

+

5

contributing the effective fields H

+

H,. This value of H, was also found by Sontheimer et al.as mentioned in the introduction.

~ o l l o w i n ~ a suggestion originally formulated by Afanas'ev et al. [3] the 250 G spectrum is interpreted as composed of three six-line spectra of (nearly) the same area, one spectrum for each of the three Kramers doublets. Two of the doublets have highly anisotropic and nearly identical gyromagnetic tensors (He

x

573 kG), whereas the third doublet has a nearly isotropic g-tensor (H,

z

250 kG). The spectra are indicated by the bar diagram above the experimental data in figure 1. These circumstances are met for a spin Hamiltonian with a dominating quadratic spin term (D 9 a) with

A

near the fully rhombic value, A

3

[3].

With the hf coupling constant known, the gyromagnetic factors of the doublets can be deduced. The longitudinal g-factors, say g,, of the two anisotropic doublets correspond to hf fields H,,,

-

573 kG, i. e.

The finite values- of ..the transversal .g.factors, g,, g,,

contribute to the asymmetric line shapes according to the discussion of eq. (2). If this effect is fully responsible for the shape of the outer lines, a width AHIH,,,

--

5

%

of the hf field distribution is necessary. For the anisotropic doublets, transversal g-factors g,

2

1.5 are thus estimated. For the isotropic doublet a g-factor g N 10.250/580 = 4.3 is estimated from the six-line spectrum with He 250 kG. However, the width of the lines indicates a departure from ideal magnetic isotropy, a set of g-factors, g,, g,, g,, near 4.3, but individually deviating

--

1, is more feasible.

The valuation of the g-factors facilitates the ultimate determination of the crystal field spin Hamiltonian. For this purpose a computer program was written, which calculates and diagonalizes the three g-tensors of a given crystal field spin Hamiltonian (1). This is defined by the splitting parameters D, 1, a and the orientation aj?y of the principal axes xyz of the quadratic spin terms relative to the cubic axes tql, o l f i being the Euler

angles of the xyz axes relative to the &l-system (a is the azimuth and

p

is the polar angle of the z-axis in the tql-system, and n-y is the azimuth of the c-axis in the xyz-system). By means of this program the values of the crystal field parameters consistent with the estimated g-factors could be limited to a few ranges. Another program simulates the corresponding Mossbauer spectrum in the effective field approximation (taking the thermal population of the electronic levels into consideration). To simulate the random orientation of the crystal field axes in the glass the final spectrum is generated as an average over 450 spectra with different orientations of the axes. Despite of great efforts spent in a systematic search it was not possible to find a spin Hamiltonian that accounts for the anomalous line shapes in the low field spectra as well as the experimental line positions in both the low field and the strong field spectra (the spin Hamiltonian proposed by Afanas'ev et al. [3] must be renounced also, as it corresponds to longitudinal g-factors 9.52 and 9.19 of the anisotropic doublets, much lower than the value 9.87 determined in this work).

Figure 2 shows the best approach to the experimental spectra obtained in this way with nearly correct line positions. The spectra are calculated from a spin Hamiltonian (1) with parameters D = 0.10 cm-',

A

= 0.26, a = 0.017 cm-', and with the orientation a j l y = 00 n/4 of the principal axes xyz of the quadratic

spin term relative to the cubic axes tqc (X = [110], y = [ilo], z = [OOl], with =

<

100

>).

The hf parameters H, = 585 kG, AEQ = 0, and 6 = 0.50 mm/s were used. All the spectra were calculated with the same width

r

= 0.50 mm/s of the fundamental Lorentzians. It appears clearly that the anomalous asymmetric line shape as well as the relative line intensities of the 250 G spectrum are not correctly reproduced, the transversal g-factors are much too small to account for the asym- metry of the experimental - line shape.

The conclusion is that the spin Hamiltonian model

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C6-738 J. E. KNUDSEN

average values,

<

D

>, <

1

>,

<

p

>,

and standard deviations, a,, a,, cp. In the special case of interest here,

<

p

>

= 0, it is felt less meaningful to vary a and y independently of each other. Instead the value of a is chosen at random (a, = CO), and then the value

of y is chosen such that cl

+

y has a prefixed average value,

<

a

+

y

>,

and standard deviation a,+,.

The full curves shown in figure 1 with the data points represent the best fit obtained in this way. The corresponding set of parameters is :

Crystal field parameters (D

>

0 is assumed) : 0

<

_D

>

₌_{0.10 cm-'} _a, ₌_{0.02 cm-'} 2 .. 4 .

<

1

>

= 0.20 a, = 0.10 6 a = 0.017 cm-' o, = 0 8 .

< p > = o ,

a, = 4 6 10 ..

<

a + y > = n / 4 aa

+

7 nI6

<

X

>

= [iio],

<

Y

>

= [iio],

<

z

>

= [ooi],

-16 -12 -8 -4 o 4 8 12 16 Hypefine parameters : VELOCITY (MM/S)

H, = 585 kG

,

AEp = 0 , B = 0.50 mm/s

.

RG. 2.

-

Simulated Mossbauer spectra, calculated for trans-

versely applied fields from the spin Hamiltonian model with Width of fundamental Lorentzians :

fixed crystal field parameters.

_r

= 0.34 mm/s

expressed by eq. (1) is insufficient to account consistently for both the experimental line shape and the correct line positions. A new feature must be introduced into the model. It turns out that the spectra can be reasona- bly reproduced if the crystal field parameters are admitted some stochastic variation from one iron complex to another in the glass matrix. Due to the narrow line width seen in the strong field spectrum it can be concluded, that the hf coupling constant has a well defined value, which does not vary from one iron complex to the next. The cubic splitting factor a, that is connected with the underlying cubic symmetry of the water octahedron, is kept fixed too, whereas the parameters Dlapy, attached to the quadratic spin terms, which account for the distortion of the cubic symmetry, are given a stochastic variation.

With the fit shown in figure 2 as starting point the final spectrum is calculated in the following way : For each of the 450 different orientations of the crystal field axes

&I[,

a Mossbauer spectrum is calculated with the values of D, 1 and chosen at random from (independent) Gaussian distributions with prefixed

(Kramers levels : 0.35 cm-',

-

0.05 cm-',

-

0.29 cm-').

It is apparent from figure 1 that the allowance for some variation of the crystal field from one ion to another in the glass can explain at the same time the line positions as well as the broad, asymmetric, non- Lorentzian line shapes in the low field spectrum, and the narrow Lorentzians in the strong field spectrum, together with the main features in the intermediate field range. But the actual method used to simulate these variations is of course questionable. The fundamental assumption of the mutually independent Gaussian dis- tributions of the crystal field parameters is quite ad hoc, the values given for the standard deviations can serve only as an indication of the variations of the parameters, which presumably reflect a corresponding variation in the structure of the water octahedron. In contrast to the crystal field spin Hamiltonian, the hf coupling constant seems rather insensitive to these variations.

Acknowledgement.

-

It is a pleasure to thank

S. M ~ r u p for stimulating discussions on the subject.

References [l] MULAY, L. N. and SELWOOD, P. W., J. Am. Chem. Soc. 77

(1955) 2693.

[2] COITON, F. A. and WILKINSON, G., Advanced Inorganic

Chemistry, 2 ed. Qnterscience Publishers, London

and N. Y.) 1968.

131 AFANAS'EV, A. M., GOROBCHENKO, V. D., DEZSI, I., LUKAS-

HEVICH, I.. I., and F n r ~ ~ o v , N . I., Zh. Eksp. Teor.

Fiz. 62 (1972) 673 [Sov. Phys. JETP 35 (1972) 3551. 141 SONTHEIMER, F., -NAGY, D. L., DEZSI, I., LOHNER, T., R ~ ~ T E R , G., SEYBOTH, D., and WEGENER, H., J. Phy-

sique Colloq. 35 (1974) C 6-443.

SHARMA, S. K., J. Znorg. Nucl. Chem. 35 (1973) 3831.

MBRUP, S., KNUDSEN, J. E., NIELSEN, M. K. and TRUMPY, G.,

J. Chem. Phys. 65 (1976) 536.

KNUDSEN, S. E., Investigations of Frozen Aqueous Solutions of Fe QII) Ions by Mossbauer Spectroscopy (thesis), L. T. F. I1 Report N o 1,1975.

ABRAGAM, A . and BLEANEY, B., Electron Paramagnetic

Resonance of the Transition Ions (Clarendon, Oxford)

1970.