RKSIT.TS AND DISCI SSION

In document A Mössbauer study of spin relaxation of ⁵⁷Fe ions (Page 174-176)

Mössbauer spectrometer

RKSIT.TS AND DISCI SSION

The spectra in Fig, 1 were obtained with the Fe'-doped spinel at 295. 77 and 4 2 K with no applied magnetic field. At 295 K a broadened six line magnetic hyperfinc spectrum is seen, indicating that even at this temperature some of the Fe' ions are slowly relaxing. Cooling the

sample to 77 K leads to a sharpening of the lines, and causes some new lines to appear. Further cooling results in changes in the relative intensities of these lines. From these spectra several observations can be made. As the ±5/2 doublet has the longest spin-lattice relaxation time of the three levels[5]. the spectrum at 295 K may be identified as primarily due to this level. Cooling to 77 K produces a second similar 6 line spectrum but with a larger isomer shift and overall splitting, showing two types of ferric ions are present in the spinel. The iron giving this spectrum we shall label as A type and the former B type. On cooling to 4-2 K the B pattern remains, whereas that from the A ions almost disappears. Hence the A type ions have the ±5/2 doublet uppermost, whereas with the B type ions either the separation between the levels is very small or the ±5/2 doublet is the ground state.

The application of a small magnetic field can be used to sharpen the spectra or even produce new lines[4 .7| through the disruption of the small dipolar coupling between the nuclear and electronic spins. The external field polarises the Fe'* electrons by producing an electronic Zeeman interaction that dominates the dipolar coupling between the Fe' ion and any adjacent nuclei having a nuclear magnetic moment and stabilizes in particular the spectra from the ±1/2 doublet. Figure 2 shows the spectra obtained for spinel in fields between 30 and 1000 Oersted. The better resolution in the central region of the spectra is immediately seen and ihese spectra are amenable to comparison with computer generated theoretical spectra.

The spin-Hamiltonian used in producing the theoretical spectra is given by

H = Hr , + ftrß. H S - g„ß„H. f + A I. S+ Hq

with electronic spin S = 5/2. The crystal field splitting of the electronic states is given by

Hr, = D S:: ~ S ( S + I) + ^(S; + SJ).

The other terms in order in the spin-Hamiltonian describe the Zeeman splitting of the electronic and nuclear states in

,,

V -^ 'V

1 ! 1 1 . 1 1— J—L. _ 1 —I__L. 1 _ 1_J

-to o to

S o u r c e V e l o c i t y ( m m / s e c . )

Fig. I. Spectra of ' Fe doped spinel showing temperature dependence of the paramagnetic hyperfine structure.

' / ' " > v - V - 2 9 5 K ■/ W v o ' / - . 51 ■ f \ y * \ ! . ' 4 7 K So u rce Ve loc i t y ( m m / s e c )

Fig. 2. Spectra o f 'Fe doped spinel taken at 4 2K and I 5K in magnetic fields transverse to the y-ray beam. Solid curves are ralculatcd w ith the spin-Maniiltonian parameters described in the

text and using a l.orentzinn linew id th (F W H M )o f 0 4 mm/sec.

an applied magnetic field, the magnetic hyperfine interac­ tion, and the quadrupole interaction. A computer program was used to calculate the spectra for a given set of parameters, averaged over the random orientation of a powder sample to the y-ray direction and applied field|8|. The only added complication here is the need to generate spectra for iron in both sites, and combine them in a

variable ratio before comparing with the observed spectra.

In analysing the spectra certain simplifying assump­ tions were made. The hyperfine interaction tensor A. and the e tensor were assumed isotropic. A value of 2 (KM was

used for g. 1 he best \ alues of the v ariou- parameters were obtained as follows. I he A values for the nuclear ground states were determined to be -2-60 mm/sec for type A Fe’ * and -2-39 mm/sec for type B. These yield effective magnetic fields. I W|. at the type A Fe” nucleus of 222 k()c per unit spin and 204 k()c per spin for tvpe II

The isomer shifts (relative to iron metal at 295K ) and quadrupole splitting found for type A Fe’ - at 4 2 K were 0-43 mm/sec and 0-91 mm/sec respectively, whereas values of 0-36 mm/scc and 0 46 mm/sec were obtained for type B ions, fhe crystal field Hamiltonian parameters obtained for type A ions were

D = 0 50 ± 0 02 cm E = 0 I 30 ± 0 005 cm '

and type B ions

D = - 0 08 ± 0 02 cm "'; E = - 0 012 ± 0 002 cm '.

The electric field gradient asymmetry parameter, rj. could not be determined as it has little effect on the spectra and a value of 3EID was assumed for rj in calculating the theoretical spectra.

The spectra calculated with the values of the various parameters above are shown plotted over the relevant experimental spectra in Fig. 2. The individual contribu­ tions to the spectrum taken at 4 2 K with a 300 Oersted applied field are shown in Fig. 3. As is expected, agreement between the calculated curve and the data improves with increasing field, especially in the central regions of the spectrum where the faster relaxing ±1/2 doublet gives a broad smeared-out pattern at low fields. The improvement in the fit in going to I kOc indicates some polarization of the electronic spins does occur in the 300-1000 Oersted range.

The smaller values of the hyperfine tensor, A. and the isomer shift for the type B ions indicate these ions are more covalently bonded than the tvpe A ions(9). consistent with the former being tetrahedrally coordi­ nated and the latter octahedrally coordinated. The value of A determined here fo r type A Fe’ * is similar to the

S o u r c e V e l o c i t y ( m m / s e c )

Fig 3. Calculated spectra for (a) "F e in the tetrahedral site and (b) ” Fe in the octahedral site in synthetic spinel al 4 2 k in an applied transverse magnetic field of 300 Oe. The spectrum expected from each Kramers doublet is shown.

MössKmcr hvperltnc spectra of dilute Fe' in s \ : ’hetic MpAI-O, spinel 449

value o f 21^ kOc/spin found foi oclahedrally coordinated Fe in i) ■ Al ( )114 1 A value of 20h k( )c/spin was found for

tetinlicclrally cooidinatcd Fe' in I i AI ()„| I0|. very similar to the value of 204 found for Inpe B Fe' . The tetrahedral site in a normal spinel has cubic symmetry, whereas the octahedral site has a trigonal distortion. I he disorder in the spinel w ill lou er both these symmetries hut the small v alue of I) for the type H ions shows these ions to be in a near cubic site and further confirms the assignment of the two types of iron

1 he theoretical spectra are calculated so that |A| - I ' l l )

has its minimum value. The ratio I I I ) for the octa- hcdrally coordinated non is 0 2b. and 0 15 for the tetrahedrally coordinated iron. Thus both sites have large departures from axial symmetry (A = Of with the oc­ tahedral site approaching rhombic (A — 0-33) symmetry. Whilst departures from axial symmetry have been found for (V in the octahedral site in M gAI-0 (A = 0 0 3 3 )|ll| and for AI in the same site in ordered FiAFOv I y] 3A 0-40)[ 121. the si/e of the rhombic distortion observed here suggests that this is due to more than just the disorder in the spinel. The replacement of AI by the larger Fe' could cause some distortion of the surrounding oxygen coordination polyhedra. A recent survey of FPR and NMR asymmetry param eter for Fe’ and A l' in aluminosilicate minerals showed that these can vary quite unpredictable for the two ions in nominally the same sites 11 ^ |. Several examples are also known of Fe' in biological molecules in sites which have been determined b\ \-ra y crystallography to be of trigonal symmetry but for which both the Mossb and I SR data is best represented by an electronic model having rhombic

sy mmetry 114|. Clearly the nuclear levels arc very sensitive to minor distortions in the spatial symmetry around the Fe ions and shows a need for caution in

deducing vttucUual details from impurity studies.

I he best agieement of the calculated and experimental spectra was obtained with equal contributions to the total area from each iron site, implying the spinel has almost equal populations of iion in the two sites. From previous studies the disorder in our sample of spinel is probably around MFT 1111 giving the spinel a composition near (Mg, AI.. >h,„ I Ah Mg,, i|.„.()j. Thus in low concentra­ tions. the iron has a strong preference to enter the tetrahedral site. This is not surprising considering the sim ilarity of the ionic radii (in A) of Mg (0-49) and Fe'" (0 49) in tetrahedral coordination and dilfercncc between the radii of A l' (0 4SI and 1 e (0 CM in octahedral coordination 1151. Certainly, small amounts of I• e' in ordered I.iA M )* go completely into the tetrahedral site| 11. Ih|.

fine effect of the high A value of the octahcdrally coordinated Fe’ is to make the average spectrum of the ±1/2 doublet independent of applied fields above a few' oersteds. The zero-field spectrum of the ±1/2 doublet consists o f I I strong lines (for example see Fig. S. Ref 11"’ ]). The spectrum of the ±1/2 doublet calculated for the spinel sample in an applied field of 5 Oc shows a six line pattern similar to that given in Fig. 3(h). but w ith intensity ratios 3 : 2 : 1 : 1:4:6. The intensities become near those of Fig 3(b). which are calculated for a field of 300 Oe under a

field of l c Oe. The zero field spectrum of spinel taken at 4-2 K shows shaip lines at 5 8 and 8 3 mm/scc. identifiable as arising from the ±1/2 doublet of the A site Fc' . The intensity of the -8-3 mm/sec line shows there is an internal field in the spinel of the order of 10 Oc originating from the nuclear moments of neighbouring AI ions. In contrast for dilute Fc in an axial crystal field where A ~ 0 such a dipolar field would smear out the spectrum from the ±1/2 doublet as is seen in LiAhO«|IO| and Al,0>|4. 7|.

A further interesting feature of the spinel spectra is the large difference in the relaxation rate between the two types of ferric ions. The iron in the tetrahedral site gives a clear spectrum at room temperature, whereas cooling to 77 K is required to see the iron in the octahedral site. The predominant mechanisms for spin-lattice relaxation be­ tween the Kramers doublets are direct two-phonon processcs[51. The spin-lattice relaxation times, rci. are dependent on the effective Debye temperature. fl(>, of the im purity ions. A, the characteristic splitting of the Kramers doublets and the temperature. For T <5 0n.

Ts, - On A T . whereas for T ^ On. r\, 0,,A T |5|. Thus a small value of I) and a high value of 0,, (equivalent to tight bonding) arc required to observe slow spin-lattice relaxation over a wide temperature span. Though the increased covalency of the bonding of the iron in the tetrahedral site over the octahcdrally coordinated iron w ill produce a higher effective value of 0„. the difference by a factor of six in the two D values alone can account for the difference in the relaxation rates seen between the two sites. Similar slow spin relaxation at room temperature has been seen for tetrahedrally coordinated Fe' in l.iA IT M I0| I f ) - - 0 104cm '). in m ullite[ 18| (D = 0-20cm ) and for octahcdrally coordi­ nated iron in alumina1191 ( /) — 0-172 cm '). In contrast. Fe’ * in TiO : with /) = 0-h8cm |20| and in FiScO;

( D = - 0 lb cm ') 1181 do not show sharp relaxation spectra at room temperature. Thus the observation of a sharp relaxation spectrum at room temperature is a way of obtaining an approximate value of I) within the small range o f values of /) that Fc' appears to have when substituted in oxide lattices.

Acknowledgement—The authors would like to thank W. 1 Oosterhuis for the use of his computer program.

In document A Mössbauer study of spin relaxation of ⁵⁷Fe ions (Page 174-176)