An EPR study of solid solutions ZnAl2O4ZnCr2O4

CHEMICAL PHYSICS 4 (1974) 307-313.

Q NORTH-HOLLAND

PUBLISHING COMPANY

AN EPR STUDY OF SOLID SOLUTIONS ZnA1204-ZnCrtOq F. GESMUNDO and C. DE ASMUNDIS Cenrro Studi di Chimim

e Chimica Firica Applicata alle Caratreristiche di Impiego deiMareriaU Pkzale Kennedy, Pad. D. Geneva, truly

de1 C.N.R..

Received 6 December 1973

We studied the EPR spctra of ZnAl20~-ZnCr204 solid solutions. The changes observed in the spectrum with increasing chromium concentration are altributed lo the gradual development of magnetic interactions between wagnetic ions in the solid solution. From the concentration dependence of the intensity of the isolated ions spectrum an approximate value of the range of the exchange interactions is deduced. The spectrum observed at high chromium concentrations is attributed to clusters of chromium ions coupled by exchange: the temperature dependence of its intenrity indicates an antiferromagnetic character of the concentraled solid solutions.

1. Introduction The spinels containing transition-metal ions show interesting magnetic properties [ 1,2] depending on the values of the exchange interaction constants between the magnetic ions [3,4]. Among the different ways to measure the interaction constants, the study of the EPR spectrum of pairs of magnetic ions in solution in isomorphous diamagnetic compounds is powerThis method reful and increasingly used [5-IO]. quires the use of single crystals with a concentration of l-5 at.% of magnetic ions and is very delicate since the spectra of the various levels of the different pairs are weak and overlap partly each other and the much stronger spectrum of isolated ions. Useful indicatilins on the exchange interactions between paramagnetic ions in solution in diamagnetic compounds can however be obtained also from the EPR spectra of powders, though many details of the spectra are lost because of their anisotropy [ 1 l-l 51. In fact it will be shown that the largest distance to which the exchange interactions between chromium ions in the spine1 ZnA1204 are transmitted, and the kind of magnetic behaviour of the solid solutions can he deduced from the EPR spectrum of powder samples of these solid solutions. In this paper we report an electron paramagnetic resonance study of solid solutions ZnA1204-ZnCr204.

Both pure spinels have a normal structure [16, 171, with the Zn*+ ions in the A sites and the trivalent ions in the B sites. Because of the high preference for the octahedral coordination of the Cr3+ ions [IS. 191, it seems reasonable to assume that also solid solutions have the normal structure. Therefore the magnetic interactions in pdre ZnCr204 and in its solid solutions with ZnAl,O, will only be of the B-B kind. The geometric arrangement of the B-B pairs at short distance in spinels is shown in fig. 1, and the corresponding parameters are reported in table 1. The neaZest neighbouts

Fig. 1. Geometric arrangement of B sires md oxygen atoms in the Ipine lattice.

308 Table 1 B-B pairs

F. Gesmundo and C. de Asmundis, EPR study of solid solutions ZnA1#4-ZnCr204

in spine1

Bo-BI

6

Bo-Bi

12

Bo-B3

6

taJi_ ’ i

$06 )a&

Bo-B4

6

Bo-BS

12

+a& %am

Bo-B6

24

+afi

l) Notation of Baker e taL[Zl] susedinthiswork. *) “i = number of neighboun. 3) rJ2 =CI-Cr SpmtiOn: 0 = 8.086 A for %&04.

ofa generical

ion B. ire called B,. The interactions between nearest neighbours can be both direct through an overlap of their clxu orbitals and indirect at right angles via the intermediate oxygen ions [20]. While the first effect is strongly dependent on the Bo-B, distance, and has a magnitude and sign which cannot be predicted, the second is of ferromagnetic kind [ZO]. Theretore the value of the exchange interaction constant for nn pairs may be positive (antiferromagnetic interaction) as well as negative (ferromagnetic interaction). The interaction with more distant neighbours occur only through the intermediate anions. Among these, the Bo-B,, E&,-B4 and Bu-B, interactions can be considered of the same strength, since they are transmitted along the same superexchange way Bu-0-A-0-Bj. while the Bu-B, interactions are more complex [21;. Even though the strongest interactions are the Bo-B,, also those with more distant B ions are important. In fact it has been shown that a long range order of the B sites cannot be obtained when the indirect interactions between non nearest neighbours are irrelevant [22].

2. Experimental

mium referred to the trivalent ions. The phase purity and homogeneity of the samples was checked by X-ray diffraction. The samples showed a single phase in the ranges 0 Q f < 0.25 and 0.75 SfG 1. In the range 0.25
results

Solid solutions ZnA1204-ZnCr204 were prepared by mixing together the weighted quantities of the pure oxides, grinding the mixture and firing at 8OOOCfor 24h, then at 1200°C for 24h after intermediate grinding. The sample composition is given in the form ZnfAL IT ICr&O~. _,.L ~-VI where fis the mole fraction of chro-

=-l Ii*

Fig. 2. EPR spectra (a)f= 0.001; (b)f=

of

r-

c

4id SO~U~~OIS hAl2O4-ZnCr~04: O.OS;(c)f= 0.25.

F. Gesmzdo and C. de Asmumiis, EPR study of 00lid solutions ZrtAl,04-Zn0204

- \ .

0

b

Fig. 3. Relative intensity at room temperature of the EPR spectra CI(0) and 0 (0) in function of the chromium concentration.

The EPR spectrum of the chromium ions in solid solution in ZnAl,O,changes with the chromium concentration. In fig. 2 the spectra of some samples with increasing chromium concentration are shown. The spectrum of the dilute sample cf= 0.001, curve a) snows a strong absorption centered at 1790 G and a weak one at about 3400 G. In more concentrated samples cf= 0.05, curve b) in addition to the low-field absorption a strong symmetrical absorption centered at 3413 G is present. Finally in the most concentrated sample cf= 0.25, curve c) only the strong central signal is left. We call a the spectrum of dilute samples and @ the strong absorption at 3413 C of concentrated samples. The intensity at room temperature of the two spectra has been measured as function off. The intensity has been obtained computing the first moment of the spectrum [23], using for the a spectrum only the lowfield absorption. The values obtained, normalized to unity, are shown in fig. 3. For the @ spectrum the value of IT,being I the relative intensity and T the absolute temperature, has been measured as function of T for some samples. The results are shown in fig. 4.

Fig. 4. Dependence of IT on temperature for different samples: (o)f= 0.05;(m)/= (0) f = 0.20.

of the Q spectrum O.lO;(r)l= 0.15;

3. Discussion 3. I. a spectrum The a spectrum is the only absorption shown oy dilute samples, it is present along with the Q spectrum in more concentrated samples and dkapsears at high chromium concentrations. Therefore it must be produced by chromium ions isolated in the ZnAl,O,. This spectrum has already been studied in single crystals [24] : the powder spectrum is irrgood agreement with that expected on the grounds of the spin-hamiltonian parameters obtained in the previous study. In fact the axial zero field splitting parameter D of the Cr3+ ions in the B sites of ZnAl,O, is D = 0.9304 cm -i, and so one has D > hu,working at X-band frequency. In these conditions the powder spectrum should present a strong absorption at the magnetic field value H/HO = 0.52 [25] (Ho = /W/&I) and a much weaker one close to Ho [26], as actually found in the a spectrum. In addition to these two absorptions. two other ones are predicted at high magnetic fields [26], which cannot be obtained with our instrument. However the assignment of the a

310

F. Gesmundo and C. de Astttundis. EPR study

spectrum to the isolated chromium ions is certain. An interesting feature of the 0 spectrum is its in. tensity dependence, as measured at room temperature, on the chromium concentration f,as shown in fig. 3 (rune a). The curve shows a maximum at f= 0.015; the subsequent decrease of I is due to the decrease of the isolated ions concentration because the presence of groups of two or more ions coupled by strong exchange interactions becomes more and more probable asfincreases. The chromium ions coupled by exchange do not give the EPR spectrum of the isolated ions. The f value corresponding to the maximum intensity of the 4: spectrum can be used to measure the distance to which exchange interactions strong enough to modify the EPR spectrum of the isolated ions are transmitted in the spinel. In fact a paramagnetic ion in solution in a diamagnetic compound gives the spectrum of isolated ions only if it is not coupled to a paramagnetic neighbour with an exchange interaction such that the condition J % &3H holds [27]. This condition requires a number m of cationic sites around a given ion free from paramagnetic ions. Since in the solid solutions studied here the trivalent ions are only in the B sites, the probability that a B site is occupied by a chromium ion in a sample with a mole fraction f is f, while the probability that a B site is occupied by an Al+3 ion is (I -f). The mole fraction jc of isolated chromium ions, i.e., of Cr+3 ions without chromium neighbours among the tint m cationic sites around it, is then given by ;2!3] :

f0 =f(1 -jy . The function f 0 reaches its msximum when df O/d/ = 0. that is when f = l/(m + 1). If we introduce into this last equation the experimental value offcorresponding to the maximum intensity of the aspectrum v= 0.015). we obtain m = 66. From the distribution of B sites in the spine1 lattice, we obtain that each B site has 66 cationic sites B within the distance r. = 0.935 a (where o is the cubic cell edge), including the neigh. hours up to B,. Since in the ZnAIZ0,4 P = 8.086 A [ 161, we conclude that the exchange interactions between chromium ions in this spine1 are strong up to a distance r. = 7.56 A. This result is in agreement with the study of the EPR spectra of chromium pairs in the spine1 ZnGaz04, which showed that the exchange interaction constant J is greater than microwave quantum

of solid wlutions ZttAl~O~-Zn&O. used in our measurements (hv e 0.3 cm-t) at least up to the distance 0.79 II, including the B, neighbours [29]. We find that In the spine1 ZnAl,O4 even the Bo-Bs interactions must be considered strong. 3.2. @ spectnrm

The symmetrical absorption centered at 3413 C with a nearly lorentzian shape appears in the EPR spectra of samples with a chromium concentration f = 0.02 and its intensity increases regularly with f (fig. 3, curve b). Itsg value is 1.99, very close to that of the isolated ions [24]. This spectrum is attributed to chromium ions taking part of clusters coupled by exchange interactions. In fact when the chromium concentration increases, the formation of clusters of ions close together becomes more and more probable, so that the concentration of associated chromium ions will increase with f. Moreover groups of many ions coupled by exchange are expected to give an EPR spectrum with a g value close to that of the isolated ions in the same matrix [30]. As a source of the Cpspectrum any kind of groups of two or more chromium ions can be considered. Actually the strong symmetrical spectrum with a nearly lorentzian shape shown by concentrated solid solutions of magnetic ions in diamagnetic compounds has often been assigned to pairs of magnetic ions [ 12, 14,31,32]. We think on the contrary that the pairs of magnetic ions cannot give an important contribution to the @ spectrum on the following grounds. First of all the concentration of ions taking part of pairs is always small, and tends rapidly to zero when f > 0.015. This can be shown by considering the dependence of the mole fraction of chromium in isolated pairs on f. For isolated pairs we mean systems of two chromium ions with a distance r < ro, where r. is the range of action of the exchange forces defined in the previous section, and with no other chromium neighbour at a distance less than fo. In order that a pair is isolated all the other cationic B sites inside the volume of the two spheres of radius r. centered at the two chromium ions must be occupied by Al+3 ions. Considering an isolated pair formed by an ion in a B. site with another in one of the rri equivalent Bi sites, the mole fraction of chromium making pairs of the kind i ir. a sample of mole fraction f will be [28] : f; =n#.f2(1

-fl’,

(2)

F. Cesmundo atzd C. de Asmundis,

EPR study

of did solutions ZnA120.,-Zn0204

311

dicting the EPR spectra of the pairs, The spin hamikonian of a pair of ions with a spin s is (ref. [30], p- 533) Q=gLlfSSt~J[S(S+

l)-2S(s+

I)]

where J is the exchange interaction constant of the. pair,S is the total spin of the pair, taking the integer values between 2.r and zero, and DS and Es the zero field splitting parameters of the levels of the pair, having the form (ref. [30], p. 533) DS=3asD,+4$,,

Fig. 5. Values of the mole fraction of the isolated ions f. (curve a) and of ions in isolated pairs Fr (curve b) as function of the chromium concentrationf.

where mi is the number of cationic sites inside the volume of the two spheres, and is function of the distance between the ions ri. The number mi is related to m, as defmed in the previous section, by the equation: mi = m(l +

+ri/ro- j&/r:).

(3)

The total mole fraction of chromium ions in isolated pairs with ‘id r. (F,) is obtained adding the4 for all the possible pairs with ri G ro. The discussion of the previous section shows that for this system all the sites up to Be must be included. Therefore one obtains:

(4) In fig. 5 the valuesof lo (curvea) and Ft (curve b) are reported as function off, taking m = 66. The function F, has a maximum at f = 0.02 and in any case is always smaller thanfo.Where the 9 spectrum due to the pairs, its intensity should be very small. In the second place a significant contribution to Cp spectrum deriving from the pairs can be excluded pre-

ES=osE,+B$c.

(6)

In the eq. (6) D, and Ec are the usual zero field splitting parameters of the isolated ion, D, represents the contribution of the magnetic interaction both dipolar and of exchange to CS, and, since the dipolar term usually prevails, De = D, = -g2p216, r being the distance of the two ions [5,9]. E, represents the contribution of the magnetic interacti’ons to ES and is usually small enough to be neglected [9] . as and flS are two parameters function of the spin s of the isolated ion and the spin S of the pair [S] . The previous expression for the spin hamiltonian of a pair is only correct when the principal axes of the crystal field of the two ions are parallel, and the pair axis is along one of them [S] . For pairs of ions having a crystal field of axial symmetry with the two symmetry axes not parallel to each other and to the pair axis, the pair hamiltonian as function of the total spin S has a different expression [33] : sY=g/?H*St+JS(S + I) +S-DS,

(7)

if the g tensor is isotropic, and the hyperfme interaction terms are neglected. The zero field splitting tensor D has now the form 133) :

where Dt and D, are the zero field splitting tensors of the ions 1 and 2,D,, is the magnetic interaction tensor, and C, and C, are coefficients expressed as function of the spin of the pair S and the spins of the isolated ions sl and s2. Since the rhombic term of the tensor Deti is usually irrelevant [9] , we assume that the magnetic

312

F. Cesmundo and C. de Asmundis, EPR stu& of solid svlutkmr ZnA120&MhO~

interaction tensor is axially symmetrical along the pair axis, while the crystal field tensors D, and Di of the two ions have axial symmetry along the local diagonal of the cubic cell [29]. Therefore the principal axes of the three tensors Dt , D2 and De are in general not parallel, and to evaluate G it is necessary to express them in a unique set of axes, chosen along the cubic cell edges, add the terms of eq. (8) together, and then diagonalize the resulting tensor in order to find its principal values. These are then transformed into the usual D and E terms in the normal way [34]. The values of D, and Es so obtained are then used to predict the position of the strongest absorptions in the EPR spectra of the pairs Bo-Bi by the method already described in a previous work [35]. The results obtained show th3t the main absorptions due to the S = 1 and S = 3 levels in the powder spectrum are well separated from the position of the @ spectrum, while S = 2 levels which have the lowest values of D and E may give a contribution to the wings of the @ spectrum. as it can also be deduced from the plots of the resonance fields for systems with S = 2 [36]. The previous results rule out a significant contribution of the pairs of chromium ions to the @ spectrum. Therefore attributed

we conclude that this spectrum has to be to groups of more than two ions coupled

by exchange, as we already proposed for similar systems [28,3S]. An other interesting feature of the 9 spectrum is the dep‘,&nce oflT on the temperature, as shown in !?g. 4 for some samples. While for dilute samplesIT is nears ly independent on T, for concentrated samples there is a clear decrease of fT at low temperature. For an isolated ion ofspin s = a without low energy excited states IT is independent on T if hu 4 k9’ [37]. For systems containing associated ions the decrease of IT at low temperature is an indication of an antiferromagnetic behaviour of the sample [ 11,121. The behaviour shown in fig. 4 by the concentrated samples indicates the presence of antiferromagnetic interactions in the clusters of the chromium ions. This finding is in agreement with the fact that the pure spine1 ZnCr204 is an antiferromagnetic compound with a very low NCel temperature, between 16% [38] and 9S”K [39]. Even if the strongest interaction with the six B, neighhours in ZnCr204 are of ferromagnetic kind (J = 14.7”K), the antiferromagnetic interactions with the 30 B2, Bq and B, sites (.I = - 7.3OK) prevail, producing an anti-

ferromagnetic order at low temperatures 1391. Also in the solid solutions studied here the antiferromagnetic interactions prevail, probably because of the higher number of B2, B4 and B5 chromium neighbours compared with B, chromium neighbours in the various groups of ions producing the Cpspectrum.

Acknowledgement The authors wish to thank Professor V. Lorenzelli for his kind interest in the present work.

References

Ill J. Smit and H.P.J. Wijn, Fenites (Wiley, New York, 1959). 121 P.J. Wojtowicz. IEEE Trans. Magnetism 5 (1970) 40. I31 J.B. Goodenough, Magnetism and the chemical bond (Interscience, New York, 1963) p. 193. I41 A.H. Morrish, The physical principles of magnetism (Wiley, New York, 1965) p. 503. I51 J. Owen, J. Appl. Phys. Suppl. 32 (1961) 2131.

1’51R.L. Carifullin~, h1.M.Zaripov and V.G. Stepmav, Sov. Phys. Solid State 12 (1970) 43. 171 S.R.P. Smith and J. Owen, J. Phys. Solid State Phys. c4 (1971) 1339. ISI A.J.B. Codling and B. Henderson, J. Phys. Solid State Phys. c4 (1971) 1409. 191 E.A. Harris, J. Phys. Solid State Phys. C5 (1972) 338. IlO1 J.C.M. Henning, J.H. den Boef and G.G.P. van Gorkom, Phys. Rev. B7 (1973) 1825. IllI C.P. Poole, Jr, and J.F. Itzel, Jr., J. Chem. Phys. 41 (1964) 287. I121 F.S. Stone and J.C. Vickerman, Trans. Farad. Sot. 67 (1971) 316. I131 J.C. Wickerman.Trans. Farad. Sot. 67 (1971) 665. 1141 J.T. Foumier. R.J. Landry and R.H. Bartman, J. Chem. Phys 55 (1971) 2522. I151 F.P. Classer, F.W.D. Woodhams. R.E. Meads and W.G.. Parker, J. Solid State Chem. 5 (1972) 255. F.C. Romeijn. Philips Res. Repts. 8 (1953) 304. 1::; E. Whipple and A. Weld. J. Inorg. Nucl. Chem. 24 (1962) 23. 1181 D. Dunia and LB. Orgel. J. Phys. Chem. Solids 3 (1957) 318. 1191 D.S. McClure. J. Phys.Chem. Solids 3 (1957) 311. 1201 P.W. Anderson, in: Solid state physirs. Vol. 14, eds. F. Seitz and D. Turnbull (Academic Press, New York, 1963) p. 203. WI P.K. Baltzer, PJ. Wojtoaicz, M. Robbins and E. Lopatin. Pbyn Rev. 151 (1966) 367.

;::;

P.W. Anderson, Phyn Rev. 102 (1956) 1008. SJ. Wyard, J. Sci. Instr. 42 (1965) 769.

F. Gesmundo and C. de Asmundis, EPR study of solid wlurions ZnA1204-Znct204 124) P. Schimiler, P. Gerber and F. Waldner. Helv. Phys Acta 43 (1970) 583. 1251 T.I. Barty, J. Mat. Sci.4 (1969) 485. i26j L.L. v%n Reijen, Thesis, Technological University, Eind-

hoven (1964).

131) CJ. Carman and W.J. Kroenke. I. Phys Chem 72 (1968) 2562. [32] W. Gunsser. W. HiBe and A. Knappwost. Z. Phyr Chem. (Neue Folg) 65 (1969) 326. 1331 Chien-ChungChao. J. Magn. Rer 10 (1973) 1. [341 J.W. Orron, Electron paramagnetic resonance. (lliffe.

1271 H. Statz, L. Rimai, M.J. Webe; and GA. de Mars; J. AppL 1 Phys. Suppl. 32 (1961) 218s. I281F. Gsmundo and C. de Asntundis. J. Phys. Chcm. Solids 33 (1972) 1961. ‘4A (1971) 215. 1291J.C.M. Henning. Phyr Lett

34 (1973) 637. 1361 R.D. Dowsing, J. Mqn.

I301 A. Abngam and B. Bleaney.

[37j

‘ton paramagnetic resonance of transition ions (Ck... Ion F’ress.Oxford, 1970) p. 518.

313

London, 1968) p. 52.

[ 351 F. Gesmundo and C. de Asmundis, J. Phys. Chem. Solids Rer 2 (1970) 332. J.H.E.Criffiths, J.Owen, J.G.P~kandhl.F. Partridge, Rot. Roy. Sot. A250 (1959) 84. (381 G. Blasse and J.F. Fast. Philips Res. Rep& 28 (1963) 393. 1391 Y. Kino and B. Uithi, Solid St&z Commun. 9 (1971) 805.