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A FURTHER EXAMPLE OF SLOW RELAXATION IN HIGH-SPIN IRON (II) COMPOUNDS : Fe(papt)2 .
C6H6
R. Zimmermann, G. Ritter, H. Spiering, D. Nagy
To cite this version:
R. Zimmermann, G. Ritter, H. Spiering, D. Nagy. A FURTHER EXAMPLE OF SLOW RELAX- ATION IN HIGH-SPIN IRON (II) COMPOUNDS : Fe(papt)2 . C6H6. Journal de Physique Colloques, 1974, 35 (C6), pp.C6-439-C6-442. �10.1051/jphyscol:1974689�. �jpa-00215846�
A FURTHER EXAMPLE OF SLOW RELAXATION IN HIGH-SPIN IRON (11) COMPOUNDS : Fe(papt),
.
C,H,R. ZIMMERMANN, G. RITTER, H. SPIERING and D. L. NAGY (*) Physikalisches Institut I1 der Universitat Erlangen-Niirnberg, 852 Erlangen, BRD
RBsum6. - Les spectres Mossbauer de Fe(papt);?C~Hs ont kt6 mesurks a 4,2 K dans des champs magnktiques longitudinaux allant jusqu'a 40 kG. Les spectres sont caractkristiques d'un ktat fonda- mental spin-fort (ST$ du fer (11). Cependant la valeur a saturation du champ magnktique interne apparait deja dans un champ magnktique externe de 5 kG. Ce comportement est expliquk en admet- tant que la relaxation est lente et que l'ktat fondamental est un doublet de spin kciatk de moins de 1 cm-1. La relaxation lente est due la faible probabilitk des transitions spin-rkseau pour des 6tats fondamentaux doublet de spin.
Abstract. - Mossbauer spectra of Fe(papt)~. CGHG have been measured at 4.2 K in longitudinal fields up to 40 kG. The spectra are typical for the high-spin (5T2) ground state of iron (11). However, the saturation value of the internal magnetic field is already evident in an external field of 5 kG. This behaviour is explained by assuming slow relaxation and a spin doublet ground state being split to an extent less than 1 cm-1. The reason for slow relaxation lies in the smallness of the transition probabilities of spin-lattice relaxation for spin doublet ground states.
1 . Introduction. - The compound Fe(papt),
.
C6H6is one of the solvates of Fe(papt), where (papt) denotes the tridendate deprotonated ligand 2-(2-pyridy1amino)- 4-(2-pyridyl) thiazole. The Fe(papt), compounds show a thermally induced high-spin ('T,) s low-spin ('A,) transition over a range x 300 K to x 100 K and no abrupt phase change is evident. The transition is incomplete in that a fraction of complexes remains in the 5T, ground state even at cryogenic tempera- tures [I]. Particularly in the case of Fe(papt),.C,H, the area fraction A('T,) is 0.81 at 4.2 K. Due to the relatively low contribution of the 'A, ground state the compound may be used to obtain additional informa- tion concerning the electronic structure of the 5T2 ground state by a study of simultaneous magnetic and electric hyperfine interactions.
2. Experimental. - The substance was prepared by the methods described earlier [2] and was checked for chemical purity by elemental analysis. 57Fe Mijssbauer spectra at 4.2 K in longitudinal magnetic fields up to 40 kG were obtained using the same equipment as described previously [3]. The polycristalline absorber of Fe(papt), . C6H6 contained 0.075 mg/cm2 57Fe and the source was 5 7 ~ o in copper.
3. Experimental results. - At 4.2 K and He,, = 0 the Mossbauer spectrum of Fe(papt), .C6H, consists
(*) On leave from the Central Research Institute for Physics, Budapest, Hungary.
of two quadrupole doublets arising from high-spin ('T,) iron (11) and from low-spin ('A,) iron (11). The doublets are characterized by AEQ(5T,) = 2.27 mmls, 6(5T,) = 0.91 mm/s and AEQ('A,) = 1.55 mmls, 6('A1) = 0.33 mm/s, respectively (cf. Fig. 1). Isomer shifts 6 are relative to natural iron at 298 K.
The area fractions of the two ground states are A(5T,) : A('A,) = 0.81 : 0.19 for Fe(papt), . C,H,. It has been shown previously that the Mossbauer spectra of Fe(papt),.C,H, and Fe(papt), at 4.2 K and He,, = 0 are identical within the uncertainty of measu- rement except for the area ratio A ( 5 ~ 2 ) : A('A,) which is 0.17 : 0.83 for Fe(papt), [4]. Due to the relatively low contribution of the 5T, ground state the spectrum of Fe(papt), is typical for the 'A, state. In addition, it was demonstrated [4] that the low-spin part of the spectra of Fe(papt), at 4.2 K in applied fields up to 40 kG may be reproduced by a calculation following the method of Collins and Travis [5]. This result may be used to correct the magnetic hyperfine spectra of Fe(papt), . C,H, in figure 1 for the small 'A, contri- bution.
By application of a magnetic field on high-spin Fe(papt), . C6H, internal magnetic fields at the nucleus are produced as indicated by the overall splitting of the spectra in figure 1. The spectra look similar to those measured for Tetrakis-(l,8-naphthyridine) iron (11) per- chlorate [6, 71. An empirical evaluation shows that the sign of the quadrupole splitting is positive, that the internal magnetic field is mainly parallel to the prin- cipal axis V,, of the electric field gradient and that its
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1974689
C6-440 R. ZIMMERMANN, G. RITTER, H. SPIERING AND D. L. NAGY
I I I I I I
-6 -4 -2 0 42 +4 +6
Velocity (rnrnlsl
FIG. 1 . - Mossbauer spectra of a powder sample of Fe(papt)z.CsHs at 4.2 K in longitudinal external fields up to
40 kG.
amount is about 150 kG. The observed broadening of the lines is due to the statistical orientations of the microcrystals relative to the external magnetic field. The positions of the lines at the right hand side of the spectra in figure 1 are a rough measure of the effective magnetic field at the nucleus. The ljehaviour of these lines indi- cates that the maximum internal field is already evident in applied fields of 5 kG at least for a fraction of the statistical orientations of the microcrystals (cf. the corresponding intensities in Fig. 1). This experimental result is very important for the following discussion of the Mossbauer spectra. Particularly it leads to the evidence of slow relaxation in high-spin iron (11).
4. Discussion. - Mossbauer spectra of high-spin iron (11) can be successfully interpreted within the framework of ligand field theory. In this model the orbital states of the 5D ground multiplet of the iron are split by an arbitrary electrostatic ligand field with Hamiltonian X,. The spin degeneracy is removed by the spin-orbit coupling IL.S and by the external magnetic field H. Thus the total Hamiltonian is given by
where 1 is the spin-orbit coupling constant, L the orbital angular momentum, S the spin and pB the Bohr magneton. Covalency is taken into account by cova- lency factors. These factors are not known when using ligand field theory but may be obtained by a mole- cular orbital approach.
The electron shell of the Mossbauer atom produces an electric field gradient (EFG) tensor Vpq (p, q = x, y, z) and additionally an internal magnetic field Hint if an external magnetic field is applied. The correspond- ing operators are expressed as
where
All the other quantities have their usual meaning. To the valence EFG a small lattice EFG may contribute.
The effective magnetic field at the nucleus is the vector sum
In the limit of slow or fast relaxation the Mossbauer spectra do not depend on the time evolution of the EFG and the effective magnetic field. In the case of slow relaxation the spectra are obtained from the expectation values < 'Up, > and < X: > for each populated state. In the case of fast relaxation the spectra depend on the thermal averages < WPq > T and < X? > T
of the EFG and the effective field.
At low temperatures only a few states of the whole energy level scheme of the 'D multiplet are populated.
Then it is often possible to use the spin Hamiltonian formalism for the discussion of the spectra. The small- ness of the quadrupole splitting ( A E ~ = 2.27 mm/s at 4.2 K for high-spin Fe(papt), . C6H6) indicates that the excited orbital states mix strongly to the ground state via spin-orbit coupling. Since the saturation value of the internal field is already obtained in very small
external fields (5 kG) the ground state of the spin Hamiltonian should be the doublet
If 2 E is the splitting of the doublet the matrix of X, + 1L. S is expressed as
(X, + lL.S) =
be 3 -
The interaction with the magnetic field can be described by
where pz is the magnetic moment of the doublet. If the doublet states originate from states with L, = f 2 and S, = f 2, pz has the value 6 pB. This is the maximum value for any doublet state of 5D.
The operator of the internal field has a form similar to the magnetic moment
Thereby H;' is the saturation value of the internal magnetic field of the doublet state.
The expectation values of the internal field for the eigenstates I a, > and 1 b, > of the Hamiltonian X, + lL.S + p,(L + 2 S).H are obtained by diago- nalization of the corresponding matrices
The energies of the eigenstates I a, >, I bH > are
Figure 2 shows the expectation value of
as a function of the external magnetic field H. It is seen that in the slow relaxation limit the internal field satu- rates even for very small applied fields if the zero field splitting 2 E is small.
The thermal average of the internal field < 32:' > T
contains additionally Boltzmann factors
- - Pz H z tanh (JE'
+
~ 2 2 H : / K T )J E Z
+
p,2 H:Applied Field H z in kG
FIG. 2. - The expectation value of the internal field operator divided by the saturation field, < a H I Xbnt I a H >/Hgat(p = x, y,
z) as a function of the applied field Hz for the doublet model
bZ = 6 p ~ ) . The numbers at the curves give the value of E (in cm-1) which is one half of the splitting of the doublet.
Applied Field HZ in kG
FIG. 3. - The thermal average of the internal field divided by the saturation field, < Xpt > T/Hgat ( p = x, y, z) as a function of the applied field Hz for the doublet model ( T = 4.2 K, pa = 6 PB).
The numbers at the curves give the value of e which is one half of the splitting of the doublet b in cm-1).
Figure 3 shows the thermal average of the internal field as a function of the external field for T = 4.2 K and p, = 6 pB. The curve for vanishing zero field splitting (2 = 0) lies above the curves with E > 0. For a doublet ground state the thermal average of the internal field approaches the saturation limit at lower external fields
C6-442 R. ZIMMERMANN, G. RITTER, H. SPIERING AND D. L. NAGY than for doublets which are split. Thus in the case of
fast relaxation 95 % of the saturation value of the internal field can be achieved only at 4.2 K with external fields above 20 kG. In an external field of 5 kG the internal field has at most 50 % of its saturation value.
This in strong contrast to the Mossbauer spectra of Fe(papt),
.
C6H6 where saturation is already achieved in external fields of 5 kG.The saturation behaviour of the internal magnetic field in Fe(papt), .C,H6 can be explained by the assumption of slow relaxation. In the slow relaxation limit the Mossbauer spectra are determined by the expectation values of the internal magnetic field and thus figure 2 has to be applied. Taking into account that in an external field of 5 kG the internal field has reached at least 95 % of its saturation value it follows from figure 2 that the splitting 2 E of the ground state should be less than 1 cm-I.
5. Conclusion. - The Mossbauer spectra of high- spin iron (11) can be usually interpreted with the assump tion of fast relaxation. An exception has been found to be the eight coordinated complex Tetrakis-(l,&
naphthyridine) iron (11) perchlorate [6, 71. In the pre- sent context another exception has been discussed.
Both substances have a spin-doublet ground state which is split to an extent less than 1 cm-l. The reason for slow relaxation lies in the smallness of the transition probabilities of spin-lattice relaxation for doublet ground states as discussed in [6].
Acknowledgment. - The authors wish to thank Dr. H. A. Goodwin for a gift of the compound and Prof. H. Wegener for helpful discussions. Additionally the Deutsche Forschungsgemeinschaft and the Bundes- ministerium fiir Forschung und Technologie are grate- fully acknowledged for financial assistance.
References
[I] KONIG, E., RITTER, G. and GOODWIN, H. A., Chem. Phys., 5 (1974) 211.
[2] SYLVA, R. N. and GOODWIN, H. A., Austr. J . Chem. 21 (1968) 1081.
131 KONIG, E., RITTER, G. and GOODWIN, H. A., Chem. Phys. 1 (1973) 17.
[4] KONIG, E., RITTER, G., ZIMMERMANN, R. and GOOD- WIN, H. A., J. Chem. Phys., in the press.
[5] COLLINS, R. L. and TRAVIS, J. C., MiiSSbauer Effect Methodo- logy 3 123, I . J. Gruverman Ed. (Plenum Press New York) 1967.
[6] ZIMMERMANN, R., SPIERING, H. and RITTER, G., Chem.
Phys. 4 (1974) 133.
[7] ZIMMERMANN, R., SPIERING, H. and RITTER, G., Abstracts of the 5th International Conference on Mossbauer Spectrometry, Bratislava, Czechoslovakia 1973 p. 123.
