Magnetic and structural characterization of the solid solution CdFe2O4NiFe2O4

Mat. Res. Bull., Vol. 15, pp. 969-980, 1980. Printed in the USA. 0025-5408/80/070969-12502.00/0 Copyright (c) 1980 Pergamon Press Ltd.

MAGNETIC AND STRUCTURAL CHARACTERIZATION OF THE SOLID SOLUTION C d F e 2 0 4 - N i F e 2 0 4" 7. F o n t c u b e r t a , +

J. R o d r l g u e z ,

M. Pi + R. R o d n g u e ++ and 7. T e j a d a +

Fac. Fisica, U n i v e r s i t a t B a r c e l o n a , Diagonal 645, B a r c e l o n a - 2 8 , C a t a l u n y a ++ C . S . I . C . , Madrid, Spain (Received May 5, 1980; Communicated by E. F. Bertaut)

AB STRAC r By means of MSssbauer spectroscopy magnetization measurements and powder diagrams, the structural a~d ,na~ netic properties of the isomorphous series Cd,.xNixFe204 has been studied. The cationic distribution depends on the relative concentration of Cd and Ni. The exchange integrals between the two sites in the spinel have been obtained.

Introduction The usual structural formula for the spinels (II, III) is written. (A~BI_~) [ A I _ ~ B I + ~ ] 0 4 where A and B are respectively dlvalent and trival~nt cations occupying tetrahedral (T) or octahedral [0] sites (I). The nature of cations and the last equi librium temperature determine the values of ~ . However several other factors influence the choice of lattice site by a particu l a r cation (1). The Cd 2+ ions present a marked preference forT-sites due to the formation of sp 3 hybrid covalent bonds with the oxyge,~1 anions (2). For this reason CdFe?O A is a normal spi nel with ~ = i. Electrostatic consideration~ like the crystalfield stabilization energies at the T or 0 sites permets us to explain the inverse character of the NiFe204 spinel (i). Therefore makes possible

the continuous substitution of Cd 2+ ions for Ni 2+ the change from a normal to an inverse structure.

The more general

cation distribution

Part of this paper has been accepted ce 1980. 969

in the isomorphous

at the Intermag

se-

Conferen u

970

J . FONTCUBERTA, et al.

ries Cdl_xNix Fe204

can be written

(Cd~ Ni t Fel_~_ ~ ) [Cdl_x_

Vol. 15, No. 7

Nix_ ~Fel+~4~]04

[i]

taking into account the ferrimagnetic behaviour of the spinel structure, the saturation magnetic moment per unit formula is ~J ( ~,~, x ) = (X - 2~ ) ~ ( N i 2 + ) + 2 ( ~ + ~ ) ~ ( F e 3+)

[2]

w h e r e ~ ( N i 2+) and ~ ( F e 3+) are the magnetic moments of Ni 2+ and Fe 3+ respectively. The cation distribution can be deduced from the saturation values of magnetization. The existence of the magnetic moments of the cations and magnetic order in e&ch sublattice create a non-zero hyperfine netic fields in the nuclei (3). One usually assumes a linear lationship between the magnetic hyperfine field (Hhf) and the lattice magnetization (4). The Hhf will vary with the degree substitution of Cd 2+ for Ni 2+ due to the mutual dependence of molecular field H m o n the magnetic moments (3).

the maK resu~ of the

Experimental The Cd~ Ni Fe~O. samples (where 0.2 _L x _L 0.9) were prepaI-~ X Z .4 red by anneallng the mixture of the simple oxides at 9OC°C in air atmosphere during a long period of time. The powder diagrams have shown a single phase correspcnding to the spinel structure. Magnetization measurements were performed at different temperatu res (4.2°K-~ T z-3OO°K) in a vibrating sample magnetometer and in fields up to IOKOe. 57Fe MSssbauer spectra were performed using a constant acceleration spectrometer. The source was 5mCi of 57Co in a Rhodium matrix and the calibration was made via metallic iron and sodium nitroprusside. For structural characterization of the samples we used an X-ray diffractometer with a step scanning device. Chemical analysis have been done in order to check the sam ple composition. I

Results a) M~ssbauer spectroscopy. In Figure I we present a set of M~ssbauer spectra obtained at room temperature for samples differing in the value of x. For x values smaller than 0.2 the high concentration of Cd 2+ cations makes possible the non-magnetic ordering of the spinel at room temperature. For x_~ 0.3 the samples are partially magnetica lly ordered at room temperature. In the case of x = 0.3 the statistical fluctuations in the distribution of magnetic and non-ma~ netic ions produces the coexistence of magnetically ordered re-

Vol. 15, No. 7

CdFe204-NiFe204

971

5

E

2 X=0.1

; X:03 ",. . ,..

3 X:06 0"

....

2

X:04 i i i -8 -4

i

,

0

,

i

,

4

,

8

L

3 X=08

~'z

'

6'

"'

~

v_~

FIG. 1 Room temperature M~ssbauer spectra of Cdl_xNix Fe20 4 for different values of x. gions not coupled to others non magnetically ordered giving rise to the appearance of a quadrupol doublet in the MSssbauer s p e c t r ~ (5). The lines in the spectra of the samples with x > O . 3 are not accurate enoegh, due to the large overlap of the absorption lines, to distinguish the iron cations on the t~o si tes of the lattice• The resolution of the two sextets is only possible for x ~ 0 . 8 . For this reason we define the average of the hyperfine field. av

=

1

~ [ Hh£ (Fe 3+(T) ) + Hhi(Fe3+(O)

)]

[3]

In figure 2 we su~m~srize the calculated values of < H > ~ v = f(x). We can observe a stepped dependence o f < H > on x. In order to explain this result we have calculated a v as a function of ~ and x (see equation [I] ) using the my molecular field approximation (3) The hyperfine magnetic field existing on the iron nL~clei is proportional to the magnetic dipole moment of the atom <~> which depends on the molecular field (4)o The hyperfine fields at room temperature for the samples with x >~ 0.2 can be written in terms of the high temperature approximaeion of Hm (3):

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J. FONTCUBERTA, et al.

Vol. 15, No. 7

2 2 g J A ~ B JA (JA +I) Hhf (A) = k A

HA 3 KT

[4]

2 2 Hhf(B) = kB gJB~B, JB (JB +I) b

3 KX

where A and B represent Fe 3+ cations located in T and O sites. H. and FIB are the molecular f~elds acting or the A and B ca tions, g A' J. and g _ , J_ are ~J fac@ors an~bspins b of t h e Lance the two cations, }Je is the Bohr magneton, K is the Boltzmmn cons tant and k and k_ are the proZ 400I portionali@y constant exi sting between Hhf and H (molecular field), m

500I

3001

For each temperature we can rewrite [3]

FIG. 2 Dependence of the average

Hhf(A) = kAk]H A

[5]

hyperfine magnetic f i e l d OFL X.

Phf(B) : kBk2H B where 2 2 jA(JA+l) gJA ~ B kl = 3~KT~ --

[6]

2 2 gJB }JB JB(JB +'I) k2 . . . . 3KT

taking into account the high preference of the Ni 2+ cations to occupy the O-sites (2), we can suppose that ~=O. Therefore the molecular fields will be HA(X) = ~

'[

]

6Jlx + 6 (1+~-) Jz~Sz(Fo3+)> +4 (1-~)J3
[7] He(X) = ~

6(l"~')Jz+3'xJs+ 3(l+~)J,

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CdFe204-NiFe20 4

973

where and are the temperature dependent average Zalues of the Z-component of the Ni 2+ a~d Fe 3+ atomic spins. Ji (i = 1,5) are the exchange integrals between FeB+(T)-Ni2+(O), FeB+(T) - Fe3+(O), Fe3+(T)-FeB+(T), Fe3+(O) -Fe3+(O) and Fe3+(O)-Ni2+(O) respectively. In the spinel structure the O-T exchange integrals are much larger than the T-T or 0-O exchange (1,3) and [7] can be approximated by: HA(X)= 2____.[ gp~ 6JlX

+6(l+~)j 2 ]

[8] ~ ( x ) = 2---[ 6(l-~)J2gps

]

putting [8] into [3] we finally obtain:

kAKJ where K - gPs ' kl = k2 = K, kA = bkB (6) and Jl = J , J2 =aJ" b is assumed independent of temperature and x ~alue (6). Evidently this function doesn't give us the cation distribution (~,x) but it is a t e s t to verify it. The cation distri bution can be deduced from the M~ssbauer spectra measured above the Neel temperature. We have done it for the samples having TABLE I

Fe3+(O ) Sample

x

l.S.(mm/s)

~ Q(mm/s)

FeB+(T)

T during the M6ssb. measurement

Fe3+(O)

Fe3+ (T)

Fe3+(O)

Fe3+(T)

x = 0.8

-0.22

-0.30

0.59

0

1

800°K

x = 0.6

-O.14

-0.22

O.51

0.4&

1.38

710°K

~= 0.3

-0.09

-0.ii

0.60

0.22

4

603°K

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J. FONTCUBERTA, et al.

Vol. 15, No. 7

x = 0.3, 0.6, 0.9. The results are given in figure 3 and the deduced ca tionic distribution is sunmlarized in Table I. b) Magnetization measurements. We have measured the saturation magnetic moments of our samples and the results are given in figure 4. The obtained values of the saturation mc raent ~s may be fitted using equation [2 ] only when the exchange interac:ion between 0 and T-sites is large enough to produce antiparallel align_ ment of the magnetic moments in the cctahedral and tetrahedral sublattices. In o~r case t'.~,e ferr~-~ag,-et [ C beha~riour appears only at x>wO.5 and the fitted cationic distribution is give~1 in Table I[. c) Powder diagrams. The experimental res~Its of a for the sa:Iples ha vlag x=O (~d.,,e2 0 4 ) and x ~ (Ni Fe~ O,) .are in good agreeraent with those publls,ned (7). The analysis of the correlations shows a clear discrepancy with respect to the law off Vegard (8). The regression line calculated for values of x < 0 . 5 gives a o = 8.33 ~ for x = I. However if the line is i:raced ~:hrough the points ~>/0.7 we obtain a value a o = 8.43 ~ for x = O. These results indLcate a weak change of the lattice parameter for low concentra tion of Cd (see dis.-.ussion a). •

,~

~

O

_

,0-~'" '"""~ '"~'"'"'i

4.

In figure 5, the experimental values -)~= a o are contrasted ~ith the theoretical values calculated supposing that the Vegard law (linear variation of a o ,,,~ith co,~centration) holds.

3

FiG.

Para,.~agaetic t45s sba~er spectra of Cdl_xNixFe204 for: A)x.L~ B)x-u C) x-0.,

!

11

.8

.;,

.6 x

FIG. 4

Saturation magnetic moment as a function of x.

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CdFe204-NiFe20 4

975

YABLE I! x i

Formula [Fe]

(NiFe) 04

Ns (PS ) 2,3

0,9

[Fe]

(Nio,9Cdo,iFe)OL~

2,07

0,8

[Fe]

(Nio, 8Cdo, 2Fe)04

1,84

0,7

[ Feo, 87Cd0, 13 ]

(Nio, 7Cdo, ipFel, 13)O 4

2,91

0,6

[ Feo, 82Cd0,18 ]

(Nio, 6Cdo, 22Fel, 18)04

3,18

0,5

[ Feo, 77Cdo, 23 ]

(Nio, 5Cdo, 27Fel, 23)04

3,45

Discus sion a) Cation distributLon. In order to verify the cation distribu tion deduced from the magnetization measurements, M~ssbauer spectra of the s~nples differing in x above TN (see Table I) . were obtained. In figure 6 the occupancy degree of Cd-9 + in each site is known. For small values of x the Cd 2+ ions r6main in T-sites and the Fe 3+ ions are dLstributed on the two sLtes. For larger x, the Cd 2+ cations are going into the T and 0 sites. For x>~0.8 the Cd 2+ are only situated at the 0 sites (table II). A similar behaviour in Nickel ferrLte-aluminates has been found by Bara (9). This selective dLstribution of the Cd 2+ ions produces, as a consequence, the abnormal variation of the lattice constant a o varying x. This abnormal behaviour for ao (x) has not been found by G l o ~ s et al. (iO). Spontaneous magnetostriction which can appear with the magnetic order cannot explain the found values of ao (x) (II). For high concentrations of Ni 2+ the inverse structure of the spinel is maintained making possible the concentration of thc Cd 2+ cations cn O-sites, which produces a weak variation in ao. Lowering the Ni 2+ concentration the Cx]2+ enters the T-sites;this is reflected by a high variation of a o. Taking into account this dependence of a o on x we are able to explain our results for )J = f(x) a n d < H > = f'(x) when x>~O.5 as a consequence of the cationic distribution, neglecting "the canting of spins".

976

J. FONTCUBERTA, et al.

o

Vol. 15, No. 7

o

a,,,A

ao, A 87

8.~

8t

86 I

8~

85 t

i

8z

8.4

8~

83

X:0 .'dFe,O,

2

4

6

.8

10 NiFe,0.

Fig. 5 Dependence of ao on x. The line represents the theoretical values

°Io 100

80~

..~. T-site-"'"""'~

60

if_--iI---

/,"'

20 1

.8

.6

.4

2

0 X

Fig. 6 Occupancy degree of Cd 2+ in each sublattice

KOel measured values . theoretical values 400 [

3 0 0 ~ 2 0 0 ~ 1 0 0 ~ i

0

100

200

300

400

500 T(°C)

Fig. 7 Temperature dependence of < H > a v

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CdFe204-NiFe20 4

977

b) Exchange integrals. The aim of the present paper is to obtain the average value of each exchange integrals and their dependence on the substitution of non-magnetic (Cd 2+) for magnetic (Ni 2+) ions. The exchange energy between two cations i,j in the lattice can be written (3) H ::-2 J...S..S. Lj l j

[i0]

where J.. is the negative exchange integral between the two cations ~ Si, S. are the cationic spins (S = ~ for Fe 3+) J In the molecular field approximation and considering only the antiferromagnetic exchange coupling A-B the Neel temperature is given by (3) 2

S~+I)

TN = -

Zn J~B (n)

3 K

[ii]

rl

~nere Z(n) represents the nearest magnetic neighbours corresponding to the integral exchange JAB(n) and a represents the numbrer of different A-B couplings. For our s~mples, which corr~:spond to the formula (Cd~ Fel_ ~ ) [Cdl_x.~N[x Fel+~] 0 4 we can define ~ = (I-~)_[ 6x+6~I_+~)]+Ii___+ ~) (I-~)

6(i- ~) + 6 x ~

[12]

+ x + (I+~)

and TN

2 S IS+l) =---B--K----

- Z JAB

the average Jing being A to the Fe3+(T)

[13]

value of the exchange integrals corresponNi2+(O) and Fe3+(T) - Fe3+(O) magnetic cou pling and Z the average value of the n~nber of paramagnetic nearest nelghbours.° The J._AD and Z values for samples having x = 0.8, 0.6, 0.3 are sun~narized in the table III.

B

Using the exact expression of the e,~uat[on [ii] we can calculate the exchange integrals between Fe3+(T) - Fe3+(O) --- J2 and FeB+(T) - Ni2+(O) =- Jl TN(X) = -

2S(S+!)" 1 2 x ( l - = ~[) 3 K

2Jl + + x 1 2 ( l - ~ ) ( l + c ~ ) J 2 ]

[l&]

978

J. FONTCUBERTA,

et al.

Vol. 15, No. 7

this expression cm% be written 3 TN (x) K (2+x) 24 S(S+I) .... = ( i - ~ )

x Jl + (i-o~ 2) J2

[15]

determining the Neel temperatures corresponding to two smnples differing in x we can obtain the value of Jl ~ d Jg. This has been done ~-ith the samples having x = 0.8 and x = 0.6 which cation distribution have been determined by means of M~ssbauer m%d magnetization measurements. The results are given in Table III. The average value obtained for the exchange coupling in this solid solution decreases by decreasino the Ni 2+ concentration (12). This is due to the fact that also the degree of inversion decreases by decreasing the Ni 2+ concentration. Consequently the average number of par~magnetic nearest-neighbours decreases, l~lis fact can also be explained in terms of the covalent transfer process (6). Decreasing Z, the supertransferred hyperfine interaction STHI will vary due to its dependence on the angles between the spins of the iron cations on different sublattices. For x~0,5 our results f o r < H > = f(x) can be interpreted neglecting the "canting of spins": the reduction in the number of par&magnetic neighbours Z produces a decrease in the STHI whithout appearance of the Yafet-Kittel angles in the magnetic structure. For x ~<0.5 we assume that the reduction in the STHI is due not only to the reduction in Z but also to the appearance of the Yafet-Kitte! angles in the magnetic structure. This fact explains the non-linear behaviour o f ~ = f(x) a n d < H > = f(x) for x~0.5. The STHI decreases as the Yafet-Ki~tel angles appear in the magnetic structure. The obtained values for Jl m%d J2 are in good agreement with those published for other spinels (13). The temperature dependence o f < H > has been well fitted by a Brillouin function with $ = 25-- (seeav fig. 7 ) reflecLing ~ ~he same spin state for the iron situated in the two sites. Even in the high temperature range, it may be concluded, that the electronic relaxation in the i~- ~5 > electronic crystal field levels of s~12 57Fe 3+ ions is large enough compared to the nuclear Lar mor precession time.

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CdFe204-NiFe20 4

979

TABLE III

x 0.8

7.71

0.6

6.73

0.3

3.88

-Jl (OK)

-J2 ¢ ~

-J (OK)

-K--

--f-

i-

13.06

23.7

Tn(°K )

17.78

800

16.63

653

16.03

363

Conclusion ~ d s s b ~ e r paramagnetic spectra together ~ith magnetization ~easurements have been performed in Cdl_xNixFe204. For large x, the crystal lattice corresponds to that of NiFe204, he~ ce the Cd 2+ ions occupy only O-sites. As x decreases the ~ 2 + ions can enter into the two sites of the spinel, the crystal lattice being that of CdFe~O~. For x~O, Cd 2+ ions occupy only T-sltes. Thls fact is reflected in the abnormal variation of the lattice par~neter with x. The MSssbm~er data have been used to measure the Neel temperature and to calculate the exchange couplin~ integrals between Fe3+(T) - Fe 3+ (0) and Fe 3+ (T) --Ni2~(O). Our results are in agreement with those p~ blished. The average exchange coupling is very sensitive to the diamagnetic cation concentration. References I. S. Krupicka, Physik der Ferrite und der verwandten magneti,~ chen Oxyde (T. Vieweg. Braunschweig (1973)). 2. J.H. Vecnick in: Treatise on Solid St=ate Chemistry. Vol~ne I. The chemical structure of solids, pag. 202. Ed. N.B. HanJ~ay Plen~mm Press 1975. 3. A. Herpin. ce 1978).

Theorie du nagnetisme

(Ed. Press.

Univ. de Fran

4. T.C. Gibb. Principles of M~ssbauer spectroscopy, Chapman and Hall, London 1976. 5. F. Basile, P. Poix, Phys. Stat.

p. 112.

Sol (a) 3__5, 153 (1976).

6. C.M. Srivastava, S.N. Shringi and R.G. Srivastava. B. 1 4 , 20.41 ( 1 9 7 5 ) .

Phys. Rev.

980

J . F O N T C U B E R T A , et al.

Vol. 15, No. 7

7. ASTM card. 8. M. Van Meersche and J. Feneau-l>apont. tallographie 2 iem Edition 1976.

Introduction N la Cris

9. J.J. Bara, Phys. S~at. Sol (a) 44, 737 (1977). i0. A° Globus, H. P~scard and V. Cagan, J. Phys. 4, CI-163 (1977). II. V.A. Gorcienko, V.J. Nikolaev and S.S. Yakimov. JETP 39, 551 (1974).

Sov. Phys.

12. N.A. Eissa, A.A. Bahgat and M.K. Fayet, Hyp. Int. 5 (2) 137 (1978). 13. G.A. Sawatzky, F. Van der Woude and A.H. Morrish. 187 ~ 747 (1969).

Phys. Rev.