SPIN RELAXATION IN DISORDERED NICKEL-ZINC FERRITES USING MÖSSBAUER EFFECT

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SPIN RELAXATION IN DISORDERED

NICKEL-ZINC FERRITES USING MÖSSBAUER EFFECT

S. Bhargava, P. Iyengar

To cite this version:

S. Bhargava, P. Iyengar. SPIN RELAXATION IN DISORDERED NICKEL-ZINC FERRITES US- ING MÖSSBAUER EFFECT. Journal de Physique Colloques, 1974, 35 (C6), pp.C6-669-C6-674.

�10.1051/jphyscol:19746147�. �jpa-00215762�

JOURNAL DE PHYSIQUE Colloque C6, suppliment au no 12, Tome 35, DCcembre 1974, page C6-669

SPIN RELAXATION IN DISORDERED NICKEL-ZINC PERRITES USING MOSSBAUER EFFECT

S. C. BHARGAVA and P. K. IYENGAR

Nuclear Physics Division, Bhabha Atomic Research Centre Trombay, Bombay400 085, India

R6umB. - Des effets de fluctuation ont ete observes dans un large domaine de temperature en dessous de TN dans les spectres des ferrites mixtes avec x

0,25,0,5 et 0,75. Les formes theoriques des spectres generkes sur ordinateur B l'aide du modele stochastique de relaxation de spin ionique sont en bon accord avec les spectres expkrimentaux pour les 3 ferrites. Le temps de relaxation ( r )

ainsi determine depend faiblement de la temperature en dessous de TN. AUX environs de TN, il d6croPt rapidement. z augmente avec la concentration en ions Zn". Un tel comportement a kt6 expli- qu6

comme provenant d'un dksordre dans la distribution des ions Niz+ et Fe3+ sur les sites A et B ainsi que de la presence d'ions Znz+.

Abstract. - Fluctuation effects have been observed in the spectra of the mixed ferrites Ni,Znl-ZFe~04 (x

0.25, 0.5 and 0.75) over wide range of temperatures below their magnetic transition temperatures. Theoretical line shapes, computed using the stochastic model of ionic spin relaxation show good agreement with the experimental spectra of all the three ferrites. The relaxa- tion time (z), thus determined, is weakly dependent on temperature below TN. Around TN it decreases rapidly. r increases with increase in the concentration of Zn2+ ions. Such a behaviour has been explained earlier to arise from the presence of disorder in the distribution of Niz+ and Fe3+

ions at A and B sites as well as from the presence of Znz+ ions.

I. Introduction. - A large number of investiga- tions [l] of the properties of mixed ferrites, using Mossbauer Spectroscopy, have been carried out with a view to understanding the composition dependences of their magnetic properties. These studies, however, revealed that the magnetically split spectra at higher temperatures are generally characterised by line broadenings which render the determination of hyper- fine interaction constants difficult. Line broadening in Mossbauer spectrum can arise from any of the following three reasons :

A. A change in the near neighbour environment can produce a change in hyperfine interactions. In mixed ferrites the environment can be different even for ions at otherwise equivalent crystal sites and thus may result in broadening of the spectra corresponding t o ions at these sites.

B. It is well known that in particles with physical dimensions smaller than 150 a (radius), the direction of magnetisation changes rapidly due to thermal energy. This modulates Mossbauer spectrum if the rate becomes comparable to the nuclear precession frequency v,.

C. When the ionic spin flip frequency becomes comparable with v,, line shape modulation takes place.

In most of the investigations referred to above, attempts were made to explain the broadening quanti-

tatively by fitting the observed line shape with a set of magnetically split spectra, assuming the first of the three causes mentioned above to be responsible for broadening. Two aspects have to be considered.

Firstly, a change in the nature of bonding, due to a change in the nearest neighbour environment, may result in a significant change in hyperfine magnetic field. This will then effect the value of saturation ma- gnetic field also [2]. Information about such an effect can be obtained from low temperature (TITN < 0.1) spectra of substituted garnets and ferrites. In earlier investigations on substituted garnets, changes in the value of internal magnetic field (H), at low tempera- tures, due t o diamagnetic ion substitution have indeed been observed but it has been found that hyperfine fields at both types of sites (a-and d-sites) decrease similarly even though the substitution occurs in the neighbourhood of one type of site only [3-51. Another important observation is that although in mixed ferrites containing appreciable concentrations of Zn2' ions, the near neighbour environment of ions at equivalent lattice sites differ considerably, but the spectra of cobalt-zinc ferrites and nickel zinc ferrites, at low temperatures (TITN < 0.1), show presence of narrow absorption lines only [6-81, implying absence of significant distribution in values of hyperfine fields.

At higher temperatures, another source of line broadening due t o changes in near neighbour envi- ronment exist, even if the magnetic field H(T) is depen-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19746147

C6-670 S. C. BHARGAVA AND P. K. IYENGAR

dent on the moment of the parent atom alone. The temperature dependence of < ^S, >, and consequently of H ( T ) , of ions at equivalent lattice sites but with different near neighbour environment, may be different if Weiss molecular field experienced by them differ.

The extent of broadening in the spectra of the oxides with large concentration of diamagnetic ions can be large. (Here, it has been assumed that z < l/v, otherwise the shape of the spectrum depends on 6, s and t only). If this is the source of broadening at higher temperatures, it should be possible to simulate the observed line shapes with a reasonable number of magnetically split spectra. Earlier investigations, however, revealed that the temperature dependences of internal magnetic fields at higher temperature (TITN > 0.4), thus obtained, show anomalous beha- viour [9], mainly due to the fact that the intensity of the central pair of lines increases considerably at higher temperatures. Some authors have attempted to avoid this difficulty by assuming the presence of super- paramagnetic effects also [3, 61 even at temperatures well below T,. The theoretically simulated spectra obtained by incorporating this assumption also did not show good agreement with the experimentally observed line shapes [3, 61, mainly because the central lines do not form a paramagnetic doublet (as the present study show) but they are a part of the magne- tically split spectrum, and its characteristics like line widths, line separations, etc. change significantly with temperature unlike the usual behaviour of a parama- gnetic spectrum. Furthermore, in mixed ferrites containing large concentrations of Zn2' ions, there is a large variation in the environment of B site ions, in comparison to the environment of A-site ions, yet the shape of the spectra of ions at the two sites have been found to be similar at all temperatures (present measurement 10, 11). In none of the spectra of mixed ferrites, broadened lines showed structure which is more than the statistical spread in the total counts.

In the present measurements, broadened spectra of the three compositions of Ni,Zn, -,Fe,O, have been observed at several temperatures. There are unambi- gous features which show the presence of fluctuation effects. The presence of superparamagnetic effects has been ruled out due to several reasons. The relaxation time of the direction of magnetisation is given by (Neel's model),

z = z, exp(XV/kT) (1)

where ^7, is in the range 10-9-10-11 ^S. The effects of superparamagnetism are observable when either K or V is small such that anisotropy energy barrier KV becomes comparable to kT. The fact that similar effects have been observed in Co,Znl-,Fe204 and Ni,Zn, -,Fe,04 shows the insensitiveness of the effect t o large changes in K (due to replacement of cobalt with nickel). The exponentional dependence of z on (KVIkT) shows that the effects should be obser- vable in a narrow range of temperature only [12-141

unless the distribution in particle sizes is large [15]. In cobalt-zinc ferrites and Nickel-Zinc ferrites, on the other hand, fluctuation effects exist over a wide range of temperature below TN (shown by the temperature dependences of A , ,/A ,, and A, ,/A3,). The physical sizes of the particles in the present investigations, as well as in investigations referred to above, are not small. Ishikawa [16] proposed formation of small size magnetic clusters, isolated magnetically from the rest of the matrix by diamagnetic ions, in mixed ferrites with large concentrations of diamagnetic ions, which could explain the nonlinear behaviour of saturation magnetisation vs. x curve obtained for Ni,Zn, -,Fe,04 using magnetisation measurements. (An alternative explanation for this non linear behaviour, i. e., the formation of non collinear spin arrangements, has been experimentally confirmed beyond doubt.) But this cluster formation cannot take place in composi- tions with x = 0.5 and 0.75 due to insufficient concen- trations of Zn2+ ions. Furthermore, if a large dis- tribution in particle size exist, in a certain range of temperature the following three types of spectra should coexist :

(a) a paramagnetic peak, due t o small size particles which have z < llv, ;

(b) a magnetically split spectrum, arising from par- ticles with large sizes for which z % I/v, ;

(c) a modulated spectrum due to particle for which z x l/v,.

With increase in temperature, the intensity of (a) should increase at the expense of (b). Such features have been observed in a number of studies on super- paramagnetic particles [17]. Theoretical spectra with such features have been shown in [I81 also. Spectra with such features have not been observed at any temperature and in any of the compositions of the mixed ferrites studied.

On the other hand, the present study shows that experimental spectra of the three ferrites at all tempera- tures can be fitted with theoretical spectra, computed using the stochastic model of ionic spin relaxation. It has been found that the broadenings and line shapes at all temperatures can be completely accounted for to be due to ionic spin relaxation effects.

2. Experimental. - The method of preparation of

these ferrites is the usual sintering process and has

been described earlier 1191. Neutron diffraction

study [19] showed that Zinc and Nickel occupy A

and B sites respectively in all the compositions. The

Mossbauer spectra of these samples have been

recorded using a spectrometer operated in the constant

acceleration mode and a 400-channel analyser operated

in the time mode. The source of 14.4 keV y-rays, used

in the present measurements, consists of CoS7 in chro-

mium metal. The absorber powder was in the form of

circular pellet enclosed between two aluminium foils.

SPIN RELAXATION IN DISORDERED NICKEL-ZINC FERRITES USING MOSSBAUER EFFECT C6-671

The heating and the cooling of the pellet has been done in vacuum and the temperature has been controlled to within f 0.50, using proportional temperature controller.

The resonance absorption spectra of the three compositions ( x = 0.75, 0.5 and 0.25) of the mixed ferrites, at several temperatures below their Nee1 temperatures, have been shown in figures la, 2a and 3a. The temperature dependence of A ,,/A ,, ^and

A2,/A3, have been shown in figure 4, which clearly show the presence of fluctuation effects in the spectra of all the three ferrites [20]. In absence of fluctuation effects, these ratios are independent of temperature.

Another important experimental evidence of the pre- sence of fluctuation effects has been provided by Daniel and Rosencwaig [18]. Relative intensities of outer and inner lines in the spectrum of Ni, ,,Zn, ,,Fe204, at room temperature, changed considerably on appli- cation of an external magnetic field. Such a change cannot occur, if the shape is due to the presence of a number of magnetically split spectra (reason A listed above). Mossbauer spectra of Nio.,,ZnO.,,Fe2O4 show the interesting feature that the magnetic split- ting disappears slowly as the temperature is increased.

Even at 257 K, magnetic splitting is observable, though fluctuation effects strongly modify the spectrum.

I I I I I

0 50 100 150 ZOO 250

CHANNEL ---r

FIG. 1.

a) Mossbauer spectra of Ni0.75Zn0.2sFe204. b) The theoretical spectra which fit best the experimental spectra are shown on the right hand side. The spectrum at 139 K has been fitted with two six finger spectra with intensity ratio 3 : 5 using least squares method. The curve thus obtained is shown with

solid line.

( 6 1 - 1 I I 1 . I

,,

0 50 101 150 200 2 5 0

CHANNEL

-

FIG. 2. - a ) Mossbauer spectra of Nio.~Zno.~Fe204. b) The theoretical line shapes which fit best these spectra are shown on the

right hand side.

I I I I I I <

0 50 100 1 5 0 2 0 0 2 5 0

CHANNEL --r

FIG. 3. - a) Mossbauer spectra of Ni0.25Zno.~~Fe204. b) The theoretical line shapes which fit these spectra are shown on the

right hand side.

C6-672 S. C. BHARGAVA AND P. K. IYENGAR

0 ~ 2 5 1 ~ 3 ~ Al6/A3&

A Raj 8Kulshrcshtha

L

I

0 100 200 300 600 500 600 700 800

T E M P E R A T U R E

FIG. 4. - The temperature dependences of A 16/A

and A2s/A

determined from the spectra of the three compositions of the ferrites. The values of

determined by Raj and Kulshresh-

tha [5] for the composition x

0.5 are also shown here.

3. Comparison with theoretically computed line shapes and results. - The theory of line shape, using the stochastic model, when the parent atom has spin 2 and is in magnetically ordered environment, has been described earlier [20-221. The expression of the line shape depends on the following quantities :

(A) Line widths and relative line intensities in absence of relaxation effects.

(B) Separation of the outermost lines, A , , , in the Mossbauer spectrum when the ion is in state, M, = 9.

It is denoted bv 10 6.

(C) Ratio of population of successive ionic Zeeman levels, denoted by

Here p and Ha represent Bohr magneton and Weiss molecular field respectively.

(D) The relaxation time z. n. p. Ni, ,,,Zn, ,,,Fe,04 : The spectrum at 139 K has little broadening due to fluctuation effect due to two reasons : (1). This temperature corresponds to TITN z 0.2 and (2). The

Nio Temperature (K) - 293 47 1 523 573 625 645 661 671

relaxation rates are sufficiently fast ( z lo-" s).

Thus the values of line widths, relative line intensities, in absence of fluctuation effects, and 6 have been determined from the spectrum at this temperature, by resolving it into two six finger spectra with relative intensities 3 : 5, using least squares method. This analysis revealed that 6, z 6,. There is a small centre shift between the two spectra, resulting in uniform broadening of all the lines. The combined relative intensities of the three pairs of lines have been found to be 3 : 2 : 1. In the computation of the theoretical spectra, it has been assumed that the line widths of all lines are equal, 6, = dB, and the relative intensities of the three pairs of lines are 3 : 2 : 1. Small differences in centre shifts have been neglected.

The assumption of equal line widths has its bad effect only in the fitting of the spectrum at room temperature because at this temperature the line broadening due to relaxation effects are not appre- ciable compared to the natural line widths. Line sepa- rations help in determining the value of s but, compa- rison of line depths give wrong value of z if line widths are assumed to be equal. Assuming the value of line widths determined from the spectrum at 139 K, give relaxation time as z = 12.6 x 10-lo s. At higher temperatures the broadening due to relaxation effects become significant compared to natural line width, and the above assumption about line width do not effect line depths significantly.

The computed spectra which fit the experimental line shape at various temperatures have been shown in figure lb. The values of s and z thus determined are given in table 1. The values of < S, > determined using the relation

have been plotted in figure 5. For comparison the temperature dependence of A-sublattice magnetisation, determined using the neutron diffraction method [19], is also shown in this figure. The agreement is very good except at one point which perhaps leads to the discrepency between the transition temperatures deter- mined using the two methods. Comparison with the

Nio.sZno. sFez04

Temperature z

(K)

- - ( 4

-

92 0.07 4.17 x ^10-9

293 0.38 3.23 x ^10-9

337 0.47 2.55 x 10-9 377 0.55 2.63 x 10-9 418 0.65 2.05 x 10-9 458 0.75 2.15 x 10-9

474

-

490 1.0 -

Nio.zsZn0.75Fe204

Temperature z

(K)

- - (s)

- 87 0.61 4.93 x 10-9 103 0.63 4.87 x ^10-9

136 0.71 4.64 x 10-9 156 0.74 4.46 x 10-9 176 0.78 3,82 x ^10-9

202 0.82 3.41 x 10-9

230 - -

257 -

SPIN RELAXATION IN DISORDERED NICKEI ,ZINC FERRITES USING MOSSBAUER EFFECT C6-673

0 PRESENT WORK 0 SATYAMURTHY c t a l

T E M P E R A T U R E ( O K )

FIG. 5. - The temperature dependence of < SZ > of the Fe3+

ions, determined from the values of s given in table 1, for the compositions ^x

0.75 and 0.5, are shown. As described in the text, it has been assumed that < Sz >

< Sz >

The temperature dependence of A-sublattice magnetisation of Ni0.75Zn0.25Fe204 determined using neutron diffraction method [19], normalised to value 2.5 at 0 K, are also shown here.

temperature dependence of B-sublattice magnetisation has not been made because it has contributions from the moments of Ni2+ ions also. n. p. Nio,,Zno,5Fez04 : Mossbauer spectra at 7 K, observed by Leung e t al. [7]

show that 6, w 6, for this composition. Relative areas of the three pairs of lines in the spectrum at 92 K, determined using least squares method, provided values of the relative line intensities needed for computation of theoretical line shapes. It has also been assumed that the line widths of all the lines are equal. The presence of significant relaxation broa- dening in the spectrum at 92 K also, makes this assumption satisfactory even for this temperature.

Theoretical line shapes which fit best the experi- mental spectra at higher temperatures have been shown in figure 2b. The values of z and s, thus deter- mined, have been given in table I. The temperature dependence of < S, > determined using eq. (2) has been shown in figure 5. At 479.5 K it is not possible to compare computed line shapes with experimental spectrum unless, quadrupole interaction is also included.

Nio~,5Zno,,,Fe20, : Theoretical spectra have been computed assuming that the line widths of all the lines are equal, the relative intensities of the three pairs of lines are 1 : 2. 1 : 2. 48, and 6, = 6,. The spectrum of the ferrite with x = 0.3 at 4.2 K, observed by J. Piekoszewski e t al. 161, supports the assumption of equal line widths and 6, = 6,. The value of 6 used corresponds to a magnetic field of 502 kOe. The

value of s and z, characterising the spectra which fit the experimental spectra, are given in table I. The interest- ing feature is the slow decrease of s with increase of temperature. It is not possible to correctly estimate the temperature at which magnetic splitting disappears completely but the temperature dependence of s shows that it occurs at temperature above 250 K.

4. Discussion. - The present investigation shows that spin relaxation effects are present in the spectra of the mixed ferrites. The presence of relaxation effect masks the features of hyperfine interactions and the shape of the spectrum depends on 6, s and z only.

It occurs at all temperatures below the magnetic transition temperature. The effect is insignificant at TITN w 0.2 for larger concentrations of nickel ions.

But as x decreases, the broadening becomes significant at low values of TITN also. For example, in

the line shape is highly modified even at TITN w 0.35.

The relaxation effects appear to be present even at 7 K in the spectra of ferrites with x < 0.3 [7], although these authors interpreted the broadening to be due to large difference in the values of HA and HB. I t is possible to determine the properties like the hyperfine interactions, Yafet-Kittle angles, etc. only if the relaxa- tion effects are insignificant. At higher temperatures the fluctuation effects masks these features.

The value of z is weakly dependent on temperature below TN. Around TN it starts decreasing rapidly giving rise to the collapse of the magnetic splitting. The value of z increases with increase in the concentration of ZnZ+ ions. These results are consistent with the interpretation given earlier [I]. In the mixed ferrite lattice, due to random distribution of cations and the presence of Zn2+ ions, the long range coherent motions of spins are not present. The magnetic interactions between ions can be resolved into two parts :

(a) The component of the field in the Z-direction which gives rise to ionic Zeeman splitting. The 6S state of Fe3+ ion, for example, splits into six levels due to this field. The value of splitting (AE) between any two levels depends on the strength of interactions with the environment. In ideal case, when all ions have identical environment, the value of AE is same for all the ions, but this is not true in mixed ferrites. A and B sites ions have different number of ions as near neighbours.

Even for ions at crystallographically equivalent sites, the environment differs.

(b) The transverse part of the interaction which has the form

for exchange interaction between ions i and j. Dipolar

interaction also possesses similar transverse part but

the strength of this interaction is much weaker and

C6-674 S. C. BHARGAVA AND P. K. IYENGAR depends on distance between the ions. The operator

in the bracket cause mutual spin flip of ions i and j provided the energy is conserved in the process. Neigh- bouring ions in the mixed ferrites, however, do not have equal splittings AE, for the reason mentioned above, and thus mutual spin flip of neighbouring ions, which have significant exchange coupling, are not energy conserving. The relaxation time ^z refers to the rate at which ion flips from one Zeeman state to ano- ther due to exchange of energy with other spins. This rate thus depends on the strength of dipolar interac- tions between ions with identical Zeeman splitting

AE in disordered magnetic substances. The other mode in which ion can exchange energy with neighbours is spin-lattice relaxation but this possibility can be ruled out for the following reasons. Firstly, Fe3+ ion is in S-state. Secondly, spin-lattice relaxation times are dependent on temperatures, contrary to the behaviour of z observed in the present measurements.

It also follows from the interpretation given above that in amorphous substances also spin-spin relaxation times should be large. Thus fluctuation effect should be observable provided spin lattice relaxation rates are also low.

References

[I] BHARGAVA, S. C., Ph. D. thesis (1974), Bombay University, India, gives an extensive list of these references.

[2] VAN

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[4] LYUBUTIN, I. S., Proceedings of the Conference on the application of the Mossbauer Effect, Tihany (1969) 467.

[S] NOWIK, I. and OEER, S., Phys. Rev. 153 (1967) 409.

[6] PIEKOSZEWSKI, J., SUWALSKI, J. and DABROWSKI, L., Proceedings,of the Conference on Mossbauer Spec- troscopy, Dresden (1971) 427.

[7] LEUNG, L. K., EVANS, B. J. and MORRISH, A. H. B 8 (1973) 29.

181 PETITT, G. A. and FORESTER, D. W., Phys. Rev. B 4 (1971) 3912.

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[16] ISHIKAWA, Y., J. Appl. Phys. 35 (1964) 1054.

[17] COLLINS, D. W., DEHN, J. T. and MULAY, L. N., Mossbauer Effect Methodology (Plenum Press) 3 (1967) 103.

[18] DANIEL, J. M. and ROSENCWAIG, A., Can. J. Phys. 48 (1970) 381.

[19] SATYA MURTHY, N. S., NATERA, M. G., YOUSSEF, S. I., BEGUM, R. J. and SRIVASTAVA, C. M., Phys. Rev. 181 (1969) 969.

[20] VAN

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[21] BLUME, M., in Hypefine Structure and Nuclear Radiation Eds. Matthias E. and Shirley D. (North Holland Publ.

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