HYPERFINE INTERACTION OF THE Fe2+ ION IN Fe(H2O)6·(ClO4)2

HAL Id: jpa-00215786

https://hal.archives-ouvertes.fr/jpa-00215786

Submitted on 1 Jan 1974

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

HYPERFINE INTERACTION OF THE Fe2+ ION IN Fe(H2O)6 × (ClO4)2

H. Spiering, D. Nagy, R. Zimmermann

To cite this version:

H. Spiering, D. Nagy, R. Zimmermann. HYPERFINE INTERACTION OF THE Fe2+ ION IN Fe(H2O)6 × (ClO4)2. Journal de Physique Colloques, 1974, 35 (C6), pp.C6-231-C6-234.

�10.1051/jphyscol:1974629�. �jpa-00215786�

IN INSULA TORS.

HYPERFINE INTERACTION OF THE Fe2+ ION IN Fe(H2O),.(C1O4),

H. SPIERING, D. L. NAGY (*) and R. ZIMMERMANN

Physikalisches Institut I1 der Universitat Erlangen-Niirnberg, D 8520 Erlangen, Germany

RBsurnB.

Les spectres Mossbauer de Fe(H20)6(C104)2 ont ete releves A 4,2 K en presence d'un champ magnetique externe longitudinal allant jusqu'a 50 kG et ont 6th analysCs dans l'approxima- tion du champ de ligands (T2g). La symetrie du champ de ligands est principalement

avec une faible distorsion C2h. Le comportement des molecules Fe(H20)6 dans le perchlorate et le fluo- silicate ferreux Ctant presque identique (meme deplacement isomerique et mdme symetrie du champ de ligands) nous supposons que la covalence et les constantes hyperfines sont aussi les mdmes. Nous avons pu analyser les spectres de Fe(H20)6(C104)2 a l'aide des paramktres connus du fluosilicate ferreux. En outre, il est possible de faire la distinction entre la covalence des Ctats orbitaux (~=0,96) et l'expansion radiale de la distribution des electrons 3d par I'intermediaire de la reduction de la .constante de couplage spin-orbite (l

- 95 cm-1).

Abstract. - Mossbauer spectra of Fe(Hz0) 6. (C104)~ have been measured at 4.2 K in longitu- dinal external magnetic fields up to 50 kG and fitted in the ligand field (Tzg) approximation. The symmetry of the ligand field is mainly

with a small distortion Caa. Because of the almost iden- tical behaviour of the Fe(H20)6 molecules in the compounds ferrousperchlorate and ferrous- fluosilicate (same isomer shift and ligand field symmetry) it is assumed that the covalency and hyper- fine constants are the same too. The attempt to fit the Fe(H~0)6.(C104)2 spectra with the known parameters of ferrousfluosilicate has been successful. Moreover, it can be differentiated between the covalency of the orbital states (a

0.96) and the radial expansion of the 3d-electron distribution via the reduction of the spin-orbit coupling constant (1

- 95 cm-1).

1. Introduction. - The hyperfine interaction of the high-spin Fe2+ ions have been studied in many compounds to solve the appropriate ligand field pro- blem. The usual methods, susceptibility and Moss- bauer measurements, are not sufficient to determine the ligand field, covalency parameter and hyperfine constants uniquely. In every case some reasonable suggestions have been made to limit the number of independent parameters. Especially covalency para- meters and hyperfine constants are choosen with quali- tative arguments. ^I11 the present work another concept will be used.

The compounds, hexahydrated ferrousperchlorate and ferrousfluosilicate, have the following properties.

The crystals are build up of the complexes Fe(H,O),, C10, and SiF,, respectively. The Fe(H20), molecules are known from Mossbauer measurements to behave similarly in both lattices at 4.2 K. First of all the isomer shifts are almost equal which indicate, following the arguements of Hazony [I], the same charge distri- bution of the Fe2+ ion. Coey et al. [2] and Reiff et al. [3]

have shown that the orbital ground state of ferrous- perchlorate is the singlet state dZ2 = t;, implied tri-

(*) Onleave of absence from the Central Research Institute

for Physics, Budapest, Hungary.

gonal symmetry of the ligand field, which is the same situation in ferrousfluosilicate. The trigonal field splitting 6 between the singlet ti, and the higher doublet { ti,, t2p ) of the cubic T,, ground state are of the same magnitude because of nearly the same qua- drupole splitting at 4.2 K.

Generally Fe(H20), molecules have similar isomer shifts [ l ] due to the fact that in these crystals the mole- cule itself determines the chemical binding to the iron atom. The small differences are caused by the different environments giving rise to different ligand fields at the iron atom. In this case the ligand field is essentially the same too, so that the whole state of the molecules can be assumed to be very similar and to result in equal covalency paramtters and hyperfine constants. There- fore the conception is to fit the ligand field and hyper- fine parameters of Fe(H,O), in both lattices with the additional equations obtained by equating the cova- lency parameter and hyperfine constants.

2. Ligand field and hyperfine parameters. -The ligand field Hamiltonian X is described in terms of CZh symmetry parameterized in

subspace of the Fe2' high-spin state 5D. The eigenvalues are expressed as

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1974629

C6-232 H. SPIERING, D. L. NAGY AND R. ZIMMERMANN

and correspond to the orbital eigenstates q 0 = cos et;, - sin et& , q - = t~ , q + = sin et;, + cos et& .

The t:i0 states are as used in [4]. The equations define two energy splittings 6, a and one mixing angle 8. The total Hamiltonian with applied magnetic field H is given by

3 % + ILS + p B ( L + 2 S ) H , (1)

where the orbital momentum L is reduced by a2 due to a covalent mixing of the states of the free ion and the ligands. A reduction of the spin-orbit coupling constant 1 is taken into account by a factor k : A = k l , (A, = - 103 cm-I), which is caused by a radial expansion (k < 1) of the 3d-electron distribution.

k = 1 and k = a2 will be discussed.

The effective magnetic field at the nucleus in the case of fast relaxation

requires two parameters HL = 2 pB < r i > and the Fermi contact field Hc. The constant

is related to the spin dipole operator O,,. The expecta- tion values < ^{r 6 3} > and < ^rsd3 > are assumed to be equal.

The dependence of the EFG tensor

on the magnetic field H is neglected. The lattice contri- bution (1 - y,) V,,, is assumed to be small and pro- portional to ( 1 - RQ) V,,,, the EGF produced by the 3d electrons [5]. Since the quadrupole splitting

is taken from the zero field spectrum and the asym- metry parameter r] = (VXX - V,)/V,, results from the Hamiltonian X + ILS, no further parameter is neces- sary.

Therefore in the 5T2g approximation with C,, sym- metry seven parameters

determine the Mossbauer spectra in external magnetic fields.

3. Experimental results and interpretation. - Figure I shows the powder Mossbauer spectra at 4.2 K in longi- tudinal magnetic fields up to 50 kG. The isomer shift

6,, = 1.398 $ 0.008 mm/s has been evaluated from least-squares analysis related to natural iron at 298 K.

Velocity (mmls 1

FIG. 1. - 57Fe Mossbauer spectra of the polycrystalline speci- men Fe(H20)6.(C104)2 at 4.2 K (10 mg natural iron/cm2) in longitudinal magnetic fields up to 50 kG. The dashed lines are

calculated spectra (cf. text).

The shift of ferrousfluosilicate has been measured once more. The obtained value a,,

1.41 I + 0.008 mm/s slightly differs from 1.428 mmls 161. The measured difference of the isomer shifts of the two compounds is very small : 0.013 + 0.008 mm/s.

The shape of the powder spectra in applied magnetic fields is typical for an almost axial ligand field sym- metry which generates a susceptibility tensor x with

xL $- XI, at low temperatures [6]. Similar spectra were measured for ferrousfluosilicate. In this case a detailed analysis of susceptibility, proton resonance and Mossbauer data results in the plot of figure 2 [7] which shows the dependence of the hyperfine parameters H,

and Hc from a 2 and k until 1 Hc I < I ~ , f " ~ ~ ~ ~ I. Using

FIG. 3. - The shape of the absorption lines on the left hand side at 50 kG calculated with 0

+ 6 O and a2

0.94 are shown for

k

1 and k

(cf. text).

FIG. 2.

The parameter sets compatible with Mossbauer measurements of ferrousfluosilicate [7] are shown. The hyperfine constant HL

2

< ^{r i 3} > divided by k, the reduction factor of the spin-orbit coupling constant A

klo, and the covalency parameter a2 are plotted versus the Fermi contact field Hc. k is assumed to be k

1 and k

given in brackets. H L / ~ is within less than 1 % independent of k. He is limited by a2

1

tree ion

and 1 Hc I

I H , I

275 kG. The values of these para- meters are taken over for fitting the Mossbauer spectra of

ferrousperchlorate (cf. text).

this plot the parameters 6, a, 8, a2, k have been left for fitting the Mossbauer powder spectra of the Fe(H,O), molecule in ferrousperchlorate. This problem can be further simplified because a16 and 8 are small and there- fore influence the shape of the spectra almost inde- pendently. As described in [7] fl determines the line shape of the H = 50 kG spectrum of the two lines at negative velocities and a16 the line broadening of the lines at positive velocities in addition to the broadening from powder-averaging.

To adjust the line positions as a function of the applied magnetic fields H = 10, 30, 50 kG only the energy splitting 6 is relevant with fixed a2 and k. If a2 < 0.95 values of 6 can be found which reproduce the line positions for all fields H better than 0.05 mm/s.

In the case of ferrousfluosilicate k = 1 and k = a2 could not be differentiated whereas the better approxi- mation for k now can be found. In figure 3 the shape of the line at - 2 mm/s of the 50 kG spectrum with 8 = + 60 and a2 = 0.94 is shown fork = 1 and k = a2.

Obviously k = a2 fits better. The measured line shape is most accurately reproduced at the lower limit a2 = 0.92. This fact may be a hint at the reduction of 1 which is possibly greater than given by k = a'.

The dashed lines in figure 1 are calculated spectra with the parameters :

The intensities are not very well fitted. This is assumed to be caused by texture obvious from the

H = 0 kG quadrupole split spectrum, which shows different intensities for the two transitions.

Provided that the reduction of 1 is the same for

< r~~ >, the quotient HL/k = 575 kG = 4.7 a. u.

represents an extrapolation to the free ion value. HL/k and H, agree very well with the theoretical free ion values [8] already mentioned in [7].

AE, = A E ~ / ~ ~ F, where the factor F(6, a, a2 1, _T) reduces the quadrupole splitting by the spin-orbit coupling, is called the bar quadrupole splitting. The difference of AE, in ferrousperchlorate (4.35 mm/s) and ferrousfluosilicate (4.60 mm/s) is 0.25 mm/s, a reasonable value to be related to the lattice contribu- tions in both compounds.

The quadrupole moment Q = AE,/ (7 2 e2 < ^r; >)

becomes Q = 0.19 barn if AE, is taken to be 4.6 mm/s and < ro3 > isequated to < r~~ > = 4.4ai3.

4. Conclusion. - In this Mossbauer study of Fe(H20), . (CIO,), results of the previous investigation of ferrousfluosilicate hexahydrate are involved. This concept is suggested because of the similar behaviour of the two Fe(H20), molecules indicated by almost the same isomer shift at 4.2 K and nearly the same axial distortion of the ligand field. The advantage of this procedure is the possibility to fit all the seven parame- ters used in T,, approximation and C,, symmetry, the ligand field parameters 6, a, 8, the covalency para- meter a, the spin-orbit coupling constant 1, and the hyperfine constants HL, H,. The perchlorate spectra can only be understood by an eight per cent reduction of A relative to the free ion value. The total reduction of the spin-orbit coupling ILS then is ka2 = a4 = 0.85.

Susceptibility data are not available for the present.

Single crystal measurements would proof the crystal field data and therefore the concept used.

It would be more reasonable to compare Fe(H,O), molecules dissolved in compounds of isomorphes series like M(H20),. SiF, with M = Mg, Co, Ni, Zn.

The binding of Fe(H20), to the environment is the

same and the small differences of the ligand field para-

C6-234 H. SPIERING, D. L. NAGY AND R. ZIMMERMANN

meter of one per cent relative to the cubic splitting will Acknowledgments. - Financial support of the not be accompanied by a remarkable change of the Bundesministerium fiir Forschung und Technologie molecular orbitals which determine the covalency, the and the Deutsche Forschungsgemeinschaft is much spin-orbit coupling, and hyperfine constants. Such appreciated. The authors are grateful to Prof. H. Wege- measurements are in progress. ner and Dr. G. Ritter for stimulating discussions.

References

[ I ] HAZONY, Y., in MiiSSbauer Effect Methodology (Ed. Gruver- [4] BALLHAUSEN, C. J., Introduction to Ligand Field Theory mann I. J.).

Vol. 7.

v. - 147. (Mc Graw Hill, New York) 1962, p. 68.

[2] COEY, J. M. D., DEZSI, I., THOMAS, P. M., OUSEPH, P. J., ^[5] INGALLS, R., Phys. Rev. 133 (1963) A 787.

[6] JOHNSON, C. E., Proc. Phys. Soc. 92 (1967) 748.

Phys. Lett. 41A (1972) 125. 171 - - SPIERING. H.. ZIMMERMANN.

R., RITTER.

G..

Phvs. Stat. Sol.

[3] REIFF, W. M., FRANKEL, R. B., ABELEDO, C. R., Chem. Phys. b 62 (1 974) 123.

Lett. 22 (1973) 124. [8] FREEMAN, A. J., WATSON, R. E., Phys. Rev. 131 (1963) 2566.