APPARENT LOW A-SITE MOMENT IN Fe3O4

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APPARENT LOW A-SITE MOMENT IN Fe3O4

V. Rakhecha, R. Chakravarthy, N. Satya Murthy

To cite this version:

JOURNAL DE PHYSIQUE Collogue CI, supplement au n° 4, Tome 38, Avril 1977, page Cl-107

APPARENT LOW A-SITE MOMENT IN Fe

3

0

4

V. C. RAKHECHA, R. CHAKRAVARTHY and N. S. SATYA MURTHY Solid State Physics Section, Nuclear Physics Division,

Bhabha Atomic Research Centre. Bombay 400 085, India

Résumé. — En utilisant la technique des neutrons polarisés, on a mesuré jusqu'à des valeurs sin 6/X = 0,83 A~ ' les amplitudes de structure magnétique de 49 réflexions indépendantes dans la zone < 110 > de la magnétite naturelle Fe304. La densité de moment magnétique intégrée sur des surfaces circulaires au voisinage des sites A dans Je plan (110) conduit à une valeur de moment loca-lisé plus faible (3,82 ^ B ) que celle prévue pour les ions Fe3 +. Les points représentatifs des facteurs de

forme magnétique des sites A, obtenus à partir de l'analyse des réflexions sur les sites A seulement, se placent près des valeurs de facteur de forme de l'ion libre F e3' en prenant cette valeur du

moment ; il subsiste toutefois quelque ambiguïté quant au facteur de forme (220). Les facteurs de forme des sites B sont déduits des réflexions restantes. La réduction apparente des moments localisés en site A est considérée comme la conséquence de la covalence dans le cristal. On soutient que le transfert de moments prédominant a lieu par l'intermédiaire des orbitales moléculaires Ti. Une étude de diffraction aux neutrons non polarisés sur le même échantillon en poudre conduit à des valeurs de moment un peu plus élevées pour les sites A et B que les résultats ci-dessus.

Abstract. — Magnetic structure amplitudes of 49 independent reflections in < 110 > zone in

natural magnetite (FejO-i) have been measured upto sin 0//. — 0.83 A- 1 using the polarised neutron technique. The magnetic moment density integrated over circular areas about the A-site in the (110) plane projection leads to a lower value for the localised moment (3.82 HB) than expected for the Fe3 i ions. The A-site magnetic form factor points obtained from an analysis of A-site-only reflections scale closely to Fe3 ; free ion form factor with this value of mo.nent though there is some ambiguity about (220) form factor. The B-site form factors are deduced from the remaining reflections. The apparent reduction of the localised A-site moment is considered to be a conse-quence of covalency in the crystal. It is argued that predominant transfer of moment takes place through T2 molecular orbitals. An unpolarised neutron powder diffraction study of the same specimen leads to little higher moment values for the A and B-sites than from the above analysis.

1. Introduction. — The technique of polarised

neu-tron diffraction has been utilised to measure the magne-tic structure amplitudes of 49 independent reflections in < 110 > zone in a natural crystal of F e304. A relatively thinner crystal (1.2 mm x 0.8 mm x 12.0 mm) was employed in this study than the ones used in a previous investigation [1]. It was hoped in this way to keep down the multiple Bragg scattering in the crystal and to increase the reliability of extinction and depo-larisation corrections to data. Magnetic structure amplitudes were obtained [2] after correction for imperfect neutron polarisation and flipping and extinc-tion and depoiarisaextinc-tion in the sample as discussed elsewhere [2]. The sample used has a saturation magne-tisation of 3.47 IJ.B per F e304 formula, which is about 9 % lower than the reported values. 1-2 % of Ti impurity was found to be the main impurity present in the sample. The magnetic hyperfine fields at the A and B-sites were found from Mossbauer measurements to be close to the reported values (A-site : 492 kOe, B-site : 458 kOe).

2. A and B-site moments and form factors. — The A-site-only reflections, with h + k = 4n + 2, k + I = 4n + 2 and h + 1 = An (and cyclic) have

relatively simple form for the structure amplitude among the various structure amplitude types in this ferrite. For oxygen u parameter equal to 0.25 the structure amplitudes of these reflections depend only on -Asites though there is a small oxygen contribution due to the slight departure of u parameter (0.2551) from the above value. For these reflections, the Debye Waller temperature factor cancells out almost exactly in the ratio of magnetic to nuclear structure amplitudes (M/N). With little or no contamination from other sites, magnetic structure amplitudes of these reflections lead to the A-site magnetic form factor with the least amibuity. For other reflections two or three sites (A, B and oxygen) contribute and hence to get the form factor for any particular site, the other contributions must be correctly substracted out. In the analysis of our data it was assumed a priori that a common Debye Waller factor applies.

The magnetic moment density about A(2), B(2) and B(4)-sites (') in (110) projection was directly integrated out using the magnetic structure amplitudes [3]

(i) The numbers in bracket after the respective sites indicate the number of atoms in projection. A-site with 2 and B-sites with 2 and 4 atoms in projection are seen.

C1-108 V. C. RAKIIECHA, R. CHAKRAVARTY AND N. S. SATYA MURTHY

derived on the basis of the assumed nuclear parame- ters [2]. Foward scattering magnetic structure ampli- tude Moo, was obtained from the saturation magneti- sation value. The A(2)-site moment showed a maxi- mum value of 3.82 p, for 1.2

A

radius of integration. The B(2) and 0(4) site moments found in a similar way were 3.47 and 3.96 p, respectively for radii of integration 1.0 and 1.4

A.

The diffreence in the beha- viour of B(2) and B(4) sites in projection arises for reasons given below. The A(2) and B(2) sites are at a distance of 1.8

A

only in the projection and their overlap results in a reduction in integrated moment beyond

-

I

a

radius. In the case of B(4) sites, which are better resolved in the projection, the moment around oxygen also gets partly included in the inte- gration. In either case, the moment density falls to near zero within a radius of 1

A

and remains small further out ('). The significant density seen away from the cation sites should be attributed to covalency effects if we partition the moment density to belong to different sites (distance between a tetrahedral site and the nearest oxygens is 1.85

A

and between an octahedral site and the nearest oxygens is 2.05 a ) . It must be remarked that the A-site moment as deduced above does not contain in it the ligand density if the same is non-zero. An error analysis was made to assess the significance of density at various points in the (1 10) projection. While this analysis indicated that the observed features are realistic, termination errors and possible multiple Bragg effects could result in some changes in these inferences. In contrast to the moment density analysis which is an integrated effect, a form factor analysis of the magnetic structure ampli- tudes permits a reflection-wise interpretation of data in the framework of an ionic model. A detailed form factor analysis has been carried out and described below.

The A-site only form factors have been derived using the A-site only reflections and an A-site moment of 3.82 p, as obtained above. These are shown in figure 1 alongwith the Fe3 + free ion [4] and the sphe-

rically averaged [5] form factor curves. The open circle is the value for (220) form factor as obtained from unpolarised neutron measurements in

<

11 2

>

zone. The (220) form factor point is taken from an unpolarised neutron measurement since for this reflection (M

--

N) polarised neutrons do not offer a great advantage [ I l l . It is concluded from figure 1 that the A-site form factor, apart from some ambiguity about (220), lies close to the Fe3+ free ion curve but with a significantly lower moment value than the expected free ion value of 4.7 p, at room temperature. Alternatively these conclusions could be stated with respect to the product

~ l f ;

if a full moment is assumed the form factor will have to be highly contracted in comparison to that of Fe3 + free ion. Speaking in terms ( 2 ) In the measurements on YIG by Bonnet et ul. similar

behaviour can be noticed (Fig. 1 of Ref. 9).

A - SITE FORM FACTORS IN Fe,O,

- A SITE SPHERICALLY AVERAGED (R,I 1 2;

- - - F d ' FREE ION

.

EXPERIMENTAL (110) ZONE ( U, : 3 8 2 uB)

0 8 + EXPERIMENTAL ( R E F 1 )

0 FROM UNPOLAHISED NEUTRONS

0 7 fe3' (TETRAHEDRAL) YIG ( R E F 9)

FIG. 1. -- A-site-only form factor points are shown alongwith the spherically averaged ( K A = 1.2 A) and Fe3+ free ion form factors and Fe3-I. (tetrahedral) form factor in YIG. The YIG form

factor has been normalised to (422) form factor.

of the localised moment and allowing for a 9

%

reduction due to lower magnetisation value, the A-site moment is lower by a further 10

%.

Interestingly, in YIG [9] (Yttrium Iron Garnet) the Fe3+ -ions on the tetrahedral (d) and the octahedral (a) sites have the same distance from the nearest oxygens as in Fe304. Also in YIG, the moments are reported to be lower (3.75 p, for the octahedral and 3.70 p, for the tetrahedral sites). I t is seen from figure 1 of ref. [9]

that the octahedral moment has reached an almost maximum at a cube size of 1.0

A

(i. e., cube with an edge 2 A) whereas for the tetrahedral site the moment reaches a value of

-

3.5 p, at 1

A

and rises only slowly further outwards. This behaviour is clearly due to the inclusion of ligand moment density. A large covalency on the A-site has been found res- ponsible for a sharper form factor (due to ligand density) at low sin 0/;1 in (Fe04)-5 complex [lo], as in

YIG, and which in turn is considered responsible for the contraction of the form factor at larger sin

0/;1. But, it should be remarked that this form factor

contains the ligand density as well. In Fe30,, the Fe3+ A-site form factor points or more appropriately the pf values, represent a similar situation, though at lower sin O/I- the behaviour is not clear as yet. The

APPAFUZNT LOW A-SITE MOMENT IN Fe304 C1-109

points and this goes to show that at least for sin

$/A

> 0.3

A-'

the observed tetrahedral Fe3+ form factor in YIG and Fe30, resemble in shape.

The B-site form factors were obtained from the remaining reflections after subtracting out the A-site contribution (but not the oxygen contribution if any) and are shown in figure 2. In the range

8 - SITE FORhl FACTORS IN Fe, 0'

~e)' FREE ION F ~ ' F R E E ION

0 9 ; 8 - SITE EXPERMENTAL (WITH MOMEN? 3.6,~~)

0.8

7

-

FIG. 2. -- B-site form factors are shown alongwith Fe3-+' and Fe*+ free ion form factors. See text for explanation.

0.1 < sin 8/11 < 0.3

A -

I , calculations were done both by assuming the A-site form factor to be like Fe3+ free ion or the YIG tetrahedral form factor [9]. The two choices predominantly affect the (111) form factor. The form factor points in this range are shown by crosses for the free ion case. A 4

%

excess of E- orbital population over the spherical distribution was allowed for in the A-site (3d) form factor and the B-site moment was assumed to be 3.6 p, as suggested from the refinement of M / N values discussed below.

In the same figure, the Fe3+ and Fe2+ free ion form factors are shown for comparison. Some points, parti- cularly (331), (71 1) and (733) show a significant devia- tion from the smooth curve. For these reflections N

value is small and they are particularly sensitive to the value of u-parameter as well as the site scattering

amplitudes. The lack of smooth behaviour of form factor points is expected to be primarily due to the asymmetry of the moment distribution. The devia- tions for pairs of reflections a t the same sin 0111 are

consistent whith an excess E,-orbital population over the spherical distribution.

3. Refinement of M / N values ; covalency conside- rations. - The experimental MIN values were least-

squares refined with magnetic moments of A, B and oxygen sites and nuclear scattering amplitudes for different sites as parameters. Spherically averaged form factors for A and B-sites were employed (cal- culated after each cycle of refinement with an assumed radius for the moment) whereas for oxygen site the 0-' 2p form factor, derived using Clementi's wave- function tables [6], was used. Results of this analysis depend to quite an extent on the weighting of observa- tions. Calculations were done with equal weights as well as with weights based on the estimated standard errors on M J N values. These analyses generally sup-

ported the (lower than expected) values of A- and B-site moments, indicated a small oxygen moment and also provided an estimate of asymmetry of moments at different sites [8]. When the A- and oxygen site nuclear scattering amplitudes were held fixed at 0.951 and 0.575, the value of B-site amplitude was found to be little lower than that assumed in the moment density analysis. The underlying basis for these calculations is briefly summarised below.

The Fe3+(d5) ions on the A-sites are surrounded by four oxygens in a tetrahedral symmetry. The metal 3d-orbitals are presumed to mix with the oxygen 2s and 2p orbitals. The tetrahedral field splits the d-orbi- tals into E(dxZ-y2, dz2) and T,(d,,, d,,, d,,) orbitals. As argued by Hubbard and Marshall [7], we consider antibonding molecular orbitals for the discussion of covalent transfer of moment to oxygens. The required antibonding orbitals for any of the T 2 or E orbitals can be written as

C1-110 V . C. RAKHECHA, R. CHAKRAVARTHY A N D N. S. SATYA MURTHY

The densities are expressed here in terms of four contributions.

First term represents a reduction in moment value by a factor [l - A: - A:

-

A?')~] for T 2 symmetry and [l

-

A?)'] for the E-symmetry. The remaining moment is transferred to the ligands as governed by the fourth term. The overlap terms, second and third, correspond to a net zero moment. The second term has a form factor with a shape exactly that of metal d-orbitals but the third term has a steeper form factor (with opposite sign) due to greater spatial extent of the overlap density (the spherically averaged form factor for this is verified by calculation to almost vanish at sin 8/3.

-

0.4 &I). The net overlap form factor is zero at sin 0 / i = 0. In the region 0

<

sin 8/1< 0.4

A-'

it rises as governed by the difference of form factors due to second and third terms. For sin %/A

-

0.4

A-'

it has the shape essentially that of d-form factor. Net result of the two overlap terms is to produce a slight expansion of overall form factor. The observed scaling of the A-site form factor to Fe3+ form factzr at larger angles (thus ignoring the expansion) should according to above arguments correspond to factors

+ 2 A,

<

d,?

I

$,

>

+ 2 A;~''

<

d~~

1

$LT2'

>]

(5) and

aE = [I - A ~ E ) ~

+

2 A?'

<

d,

I

I//?'

>]

.

₍₆₎ Note that allowing for a slight expansion of the form factor would imply a still lower moment for the A-site than in this case.

The relative population of E and T2 orbitals on

A-site were estimated from the M / N refinement using

the prescription of Weiss and Freeman for E and T 2 form factors [8]. About 4

%

excess of E-population over the spherical moment distribution was indicated, which implies that

0.4 a, 0.44

-- - -

0.6 a,, 0.56 '

With a fractional reduction of 0.1 in the A-site moment we have

0.4 a ,

+

0.6 a,, = 0.9

.

(8) The last two eqs. lead to

a, = 0.993

a,, = 0.84

.

(9)

That is, the moment is transferred predominantly from T2 orbitals with a reduction factor of z 0.16. The admixture coefficient A(,) is indicated to be negli- gibly small from eq. (6). From eq. (5) and using the calculated overlap integral values it is seen that admixture coefficients As, A,, A?') may be as large as

-

0.5, though eq. (9) is not enough to lead to indivi- dual coefficients.

A similar prescription was used for B-sites where a

slight excess of E, population and deficiency of T,, population over the spherical moment distribution was indicated in the refinement. The oxygen moment transferred from the cations was treated to be 2p type and the oxygen form factor was derived using C,,

local symmetry for the oxygens. Contributions due to admixture of oxygen 2s orbitals was considered to be of relatively minor importance and ignored as such. For an oxygen at coordinates ( 4 2 , 2412, u/2) relative to an A-site as origin, the form factors are shown to be

where

and

R(r) is the radial part of the oxygen wave function, j, are the spherical Bessel functions of order n, hkl are the Miller indices and a, is the cell parameter. A, and E are the one and two dimensional representations into which 2p-orbitals split in a C , , field. These res- pectively involve p, and p, orbitals with respect to the A-site. The oxygen contribution was easily included by adding to the A-site contributions an extra term due to four oxygens around the A-site with the C-coeffi- cient in eq. (12) given by C,,,,, Ciil, C$j and Ciki for oxygens at t(uuu), ~ ( U U U ) , t(uuii) and Q(uu17) with reference to the central A-site. In the refinement the oxygen moment was indicated to be about 0.08 p,

with the A, population slightly in excess over the spherical distribution. The A-site moment was seen to be closer to 3.7 p, and the B-site moment to 3.6 p,.

The fit was not entirely satisfactory, possibly due to the inadequacy of the spherically averaged B-site form factor at lower angles and due to more complex nature of covalent moment density in the region between the cations (section 2). Nevertheless, this and the form factor analysis show significant covalency on the A-site and also differences in B-site form factor points in comparison to the free ion case.

4. Powder measurements. - An unpolarised neu-

APPARENT LOW A-SITE MOMENT IN Fe304 C1-l I 1

of the background in the pattern whereas a uniform background was employed in the refinement. This has introduced some inaccuracy in the analysis.

5. Conclusions. - The localised A-site moment is

shown to be lower by about 10

%

than the expected Fe3+ free ion value. The A-site form factor scales closely to the Fe3 + free ion curve and still better to the

Fe3+ tetrahedral form factor in YIG for sin 811 > 0.3

A-'.

Covalency considerations imply a predominant transfer of A-site moment through T,

orbitals. The B-site form factor points indicate the

presence of asymmetric moment density and covalent effects on B-sites as well. There also appears to be a reduction in the localised B-site moment but its magnitude is smaller than for the A-site. Further, the observed reduction is partly due to the Ti impurities going to the B-sites.

Acknowledgment. - Our thanks are due to Dr. M. J. Patni and Prof. C. M. Srivastava of I. I. T., Bombay for making the saturation magnetisation measurements and Dr. S. C. Bhargava for the Moss- bauer measurements.

References [l] SKINIVASAN, R., RAKHECHA, V. C., PARANJPE, S. K., BEGUM,

R. J., MADHAV, L., RAO and SATYA MURTHY, N. S., Proc. Intern. Conf. Magnetism (Moscow, 1973) IV (1973) 246.

[2] RAKHECHA, V. C., CHAKRAVARTHY, R., and SATYA MUR- THY, N. S., Proc. Con/. on Neutron Scattering (Gatlin- burg (vol. 2) 1976) 690.

[3] MOON, R. M., Intern. J. Magnetism 1 (1971) 219.

[4] WATSON, R. E. and FREEMAN, A. J., Acta Cryst. 14 (1961) 27. [5] BROWN, P. J. and WILKINSON, C., Acta Cryst. 18 (1965) 398. [6] CLEMENTI, E., Supplement to IBM J. Res. Develop. 9 (1965)

2.

[7] HUBBARD, J. and MARSHALL, W., Proc. Phys. Soc. 86 (1 965) 562.

[8] WEN, R. J. and FREEMAN, A. J., Phys. Chem. Solids 10

(1959), 147.

[9] BONNET, M., DELAPALME, A., TCHEOU, F. and FUW, F., Proc. Intern. Con/. Magnetism (Moscow, 1973), IV (1974) 251.

[lo] BYROM, E., FREEMAN, A. J. and ELLIS, D. E., Proc. AIP Con$ (1974) (1975) 210.

[ l l ] STEINSVOLL, O., SH~RANE, G., NATHANS, R., BLUME, M., ALPERIN, H. A., and PICKART, S. J., Phys. Rev. 161