EPR study of two Cr3+ sites in MgTiO3 crystal

1. Phys. Chem. Solids Vol. 55, No. 7, pp. 647-650, 1994 0 1994 Elwier Science Ltd Copyright Printed in Great Britain. All rights reserved wJ22-3697194 $7.00 + 0.00

Pergamon

EPR STUDY OF TWO Cr3+ SITES IN MgTiO, CRYSTAL ZHENG WEN-CKEN Department of Material Science, Sichuan Unive~ity, Chengdu 610064, P.R. China? and International Center for Materials Physics, Academia Sinica, Shenyang 1iOOt5, P.R. China (Received 24 August 1993; accepted in revisedform

1 November 1993)

this paper, a simple scheme related to the separation between the impurity and the neighbouring cation in MgTiO, crystal is suggested in the case of charge misfitting substitution. According to the scheme, the impurity ion does not occupy the exact site of host ion, but is displaced along the C, axis. The displacement direction depends upon the charge carried by the impurity. Based on this, two sites of the forms Crkg-Tig for Cr3+ (I) ion and Mgit-Cr&< for Cti* (2) ion in MgTi03:Cr3+ crystal are Abstract-In

proposed by comparing the EPR parameters between calculation and experiment. Keywords:

Electron paramagnetic resonance, impurity environment, crystal field theory, Cr3+ ion,

MgTiO, .

1. INTRODUCTION

For Cf+ in MgTiO, crystai, two sites of Cr3+ (1) and Cr3+ (2) were observed by EPR spectra [I]. By comparing the calculated and observed values of zero-field splitting D, Haider and Edgar [l] suggested that the Cr3+ (1) and Cr’+ (2) ions are located in the sites of the forms Cr3+-Ti4+ and Mg2+-Cr3+, respectively. However, their calculations did not give any firm guide as to whether those are simple substitutional sites (Crzg-Ti$+, Mg&-Cr$+ , where X, denotes the occupancy of Y ion site by X ion) or their mirror images (Ti$-Cr:: , Cr&i-Mg+f )), which is caused by the disorder between the Mg2+ and Ti4+ sublattices in MgTiO, crystal. In this paper, we will recalculate the zero-field splittings D and also the anisotropic g-factor for the two Cr3+ sites by using the Macfarlane’s high-order perturbation formulas [2,3] and the more suitable parameters. In these calculations, the displacements of Cr3+ ions caused by the different electrostatic repulsive force between cation pairs are taken into account. By analyzing the displacement direction of Cr3+ ion, the substitutional sites of Cr3+ (1) and Cr3+ (2) are suggested.

cations [4]. The octahedra are piled along the Cs axis and share common faces. The l/3 octahedral-site vacancies are ordered so as to minimize the cation-sublattice electrostatic repulsive forces. The Coulomb repulsive force between the neighboring MgZ+ and Ti4+ ions displaces these cations from the centers of their octahedra and leads them to closer positions to the distinctive neighboring vacancies (see Fig. 1). So, the separation between these cations depends upon this repulsive force. If the cation is replaced by an impurity having different charge, it can be expected that the impurity ion does not occupy the exact site of the replaced host ion, but is displaced

2. DISPLACEMENT SCHEME

The diamagnetic oxide MgTiO, has the trigonal “ilmenite” structure which consists of a close-packedhexagonal anion sublattice that has 213 of its octahedral sites occupied alternately by Mg2+ and Ti4+ tAddress for correspondence.

Fig. 1. Schematic view of the octahedra stacked along C,-axis in MgTiO, crystal.

ZHENG WEN-CHEN

648

along the C, axis by an amount AZ because the repulsive force acting on the impurity differs from that on the host ion. Generally, when the impurity ion carries extra charge than the replaced host ion, the electrostatic repulsive force acting on the impurity is greater than that on the host ion, the impurity ion should be shifted further away from the

center of the octahedron. Whereas for the impurity having less charge, the displacement direction with respect to the center of the octahedron is opposite because the repulsive force decreases. Obviously, by studying the displacement direction of the impurity ion, some useful information about the lattice site of the impurity ion can be obtained. The displacement scheme will be used in the following studies.

3. CALCULATION

AND DISCUSSION

For d3 ions in trigonal symmetry, the high- order perturbation anisotropic g-factor are as follows [2,3]:

formulae

of zero-field splitting

and

-x), gll =ge-jjj--8&

(1)

25 2(k +g,) + 45 2(k - 2g,) + St 2(k - 2g,) 3022 90; 90:

1

4t ‘k 44 2k -- 3D,D2+ -9D,D,+

Ag =g,, -g,

4ckv

4&fkv

- 4r ‘k

8tkv

3D2D,+9L):--

8&kv 3D,D,

’ ’

(2)

’

(3)

=3o2-D, I

1

4

where g, = 2.0023, t is the spin-orbit coupling coefficient, k is the orbital reduction factor and the zero-order energy separations are [2]: D, =A, D2= 15B+4C, From the point-charge-dipole

U$i=l

-;eq(l

x (1 + Sp/eR)/(r

u’=

i

i= I

JG

D,=A+9B+3C,

D,=A+12B,

D,=2A+38.

model, the trigonal field parameters o and v ’ are:

+3p/eR){r*)(3~0~*8~-

5 1)/R?-&eq

4)(35 cos4 0; - 30 cos2 & + 3)/R 7 - -@18 eq (1 + 5p/eR){r4)sin3

1

0,cos @cos 3#+/R ;’ ,

5Jz eq (1 + 3p)/eR )(r ‘)(3 cos2 f?(- 1)/R?--eeg

X (1 + Sp/eR )(t 4}(35

(4)

COS’ Bi -

30 COS’

8i + 3)/R

: -

$

eq

(1 + 5p/eR){r

4)Sh3

di COS 8i COS 3#i/R i

(5)

1>(6)

where q ( = -2e) is the ligand charge and p the dipole, Ri, Biand & are the structure data of the studied crystal. For MgTiO, , data are not available for the exact atomic positions, we therefore assume that they are the same as those in isomorphous FeTiO, crystal because the hexagonal cell parameters are very close for these compounds [4, S]. Thus, the parameters Ri, 8i and di for Mg*+ and Ti*+ sites of MgTi03 can be obtained and they are shown in Table 1. Utilizing the empirical d-orbit of Cr3 + ion [6] and introducing a parameter N(k = N *) to denote the average covalency reduction effect, we have B = 920.48N 4 cm-‘,

C = 3330.71N4cn-‘,

(r ‘) = 2.4843N ‘(a.u.)*,

4: = 24ON%m-‘,

{r “> = 16.4276N2(a.u.)4.

(7)

649

EPR study of two Cr’+ sites

Table 1. Polar coordinates R, 6, 4 of the six anions surrounding the cation sites in MgTiO,. 19is the angle between the cation-anion distance R and the C, axis. 4 is the polar angle in the plane perpendicular to C, axis. Atomic positions for MgTiO, are taken identical to those in FeTiO,, see text i

4th

‘A

4

Mg site

1,2,3 4,5,6

2.19 2.04

45.2” 2.1”, 122.1”, 242.1” 63.8” 62.8”, 182.8”, 302.8”

Ti site

1,2,3 4,576

2.12 1.89

47.0” 64.1”

2.7”, 122.?“, 242.1” 54.6”, 174.6”, 294.6”

The parameters p and N are determined from the optical absorption spectrum of the studied crystal. no absorption spectrum has For MgTi0,:Cr3+, been reported, we therefore use the parameters N z 0.954 and p z 0.086 eR of MgO:Cr’+ [7] for Cr3+ in Mg*+ site because for both crystals, the cases of charge misfitting substitution are the same and the average M&+-O*- distances R are very close to each other (for MgO, R = 2.101 A and for MgTiOr, R FZ2.115 A). On the basis of the same reasons, the parameters N x 0.938 and p x 0.048 eR of SrTi0,:Cr3+ [8] are applied to the case of Cr3+ in Ti4+ site of MgTiO, (in passing, in the superposition model calculation [l], the parameters obtained from ruby are used. This seems not so suitable because Cr3+ in Al,O, belongs in the case of charge-fitting substitution, but Cr3+ in MgTiO, does not). Substituting the structure data of exact Mg*+ and Ti4+ sites and the distinctive N and p into the above formulae, the calculated D, g,, and Ag for Cr3+ in both sites can be obtained and they are compared with the experimental results in Table 2. It can be seen that the calculated values of D are not in agreement with the observed values. However, in the case of Crr+ (1) site, because the Cr3+ ion carries extra charge than the replaced Mg *+ ion, the Cr3+ should not occupy the exact Mg *+ site, but is displaced further away from the centre of the octahedron in accordance with the above displacement scheme. So, the calculation by using the structure data of the exact Mg*+ site is not

reasonable. By assuming that the Cr3+ (1) ion moves AZ k: -0.06 A (note: the displacement towards the centre of the octahedron is defined as a positive displacement) further away from the centre of the octahedron, one can find that the calculated D and also g,,, Ag are in good agreement with the observed values (see Table 2). We therefore think that the Cr3+ (1) ion replaces Mg’+ ion in MgTiO, and the form of site is Cr&!-Tig . On the other hand, for Cr3+ (2) ion in Ti4+ site, because the difference between the calculated and observed values of D is so large that it can hardly reach a good fit between theory and experiment by assuming the inward displacement of Cr3+ (2) ion. This point is confirmed by the calculation. So, we infer that the Cr3+ (2) ion may not be in the Ti4+ site, but is in a Mg*+ site. In fact, if we assume that Cr3+ (2) ion substitutes for Mgr+ ion and moves AZ NN0.09 A towards the centre of the octahedron, a good agreement between theory and experiment can be obtained (see Table 2). It seems astonishing that the Cr3+ (2) ion is displaced towards the centre site according to the above displacement scheme because. the extra charge is carried by the Cr3+ (2) ion. However, if we consider that there may be some disorder between the Mg*+ and Ti4+ sublattices, the above inward displacement can be understood. In fact, up to 12% disorder between Ni*+ and Ti4+ sublattices in the isomorphous NiTiO, was found [9] and so the disorder may exist in MgTi03. In the case of cation sublattice disorder in MgTiO, crystal, the neighbouring cation of Cr’+ (2) in Mgr+ site may not be a Ti4+ ion, but is a Mgr+ ion. Thus, the form of site related to Cr3+ (2) should be Mg$-Cr$ rather than MgM:-Crc. Obviously, this Mg*+-Cr3+ separation is smaller than the host Mg*+-Ti4+ separation because the electrostatic repulsive force between M$+ and Cr3+ is smaller than that between Mgrf and Ti4+. Thus, the Cr3+ (2) ion should be displaced towards the center of the octahedron so as to give a smaller separation between the cation pair. Of course, the cation sublattice disorder is rare in the general

Table 2. EPR parameters for Cr3+ ions in MgTi03 crystal Cr-‘+ (1) D

Cal.? Ca1.S Ca1.g Cal. 11 Expt.[l]

(cm-‘)

Cr3+ (2)

-0.2319

1.9670

Ag - 0.0008

-0.5023

1.9656

-0.0028

-0.5016 (3)

1.9761 (3)

-0.0011 (5)

gll

D (cm-‘) -0.7535

t Calculated from the 1 Calculated from the 5 Calculated by taking it replaces Mg2+ ion. II Calculated by taking replaces Mg*+ ion.

0.1004 0.1092 (6)

gll

Ag

1.9700

-0.0053

1.9691 1.9752 (5)

0.0019 0.0026 (10)

structure data of exact Mg*+ site. structure data of exact Ti4+ site. into account an outward displacement AZ 2: -0.06 8, of Cr3+ (1) ion when into account an inward displacement AZ z 0.09 A of Cr3+ (2) ion when it

650

ZHENGWEN-CHEN

ilmenite structure. So, the number of Mg$-Ct$ pair should be much smaller than that of the normal Cr3+-Ti4+ r, pair. This point is supported by the fact thaythe intensity of EPR spectrum of the Cr3+ (2) ion is, as pointed out in Ref. [ 11, so much less than that of the Cr3+ (1) ion that it was overlooked in earlier work [lo]. Therefore, our opinion seems reasonable. From the above studies, we suggest that the Cr3+ (1) and Cr3+ (2) ions in MgTi03 crystal are located at sites of structures Cr&-Tit: and respectively. These results are consistMg$-Crcg, ent with, but go a step further than those obtained in Ref. [1], where the C? (1) and Cr3+(2) ions located at the sites of forms Cr3+-Ti4+ and Cr3+-Mg*+ were proposed, but whether these are simple substitutional sites (Crzg-Tit: , Mg$$Crc ) or their mirror images (Ti$-Cr:: , Cr$-Mgg ) is indeterminate. Of course, considering the approximations used in the calculation, particularly, the structure data are not those of MgTi03 crystal, but the values of the isomorphous FeTiO, crystal, our

suggestions should be further experimental methods.

tested

by

other

Acknowledgements-This project was supported by The Science Foundation of National Education Committee of China and The Foundation of ICMP (No. ICMP/92/03/).

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6. Zhao M. G., Xu J. A., Bai G. R. and Xie H. S., Phvs. Rev. B27. 1516 (1983). I. Zheng W. C., j. Phys. Corkens. Matter 1, 8093 (1989). 8. Zhena W. C.. Phvs. Status Solidi (b)lS4. K167 (1989). 9. Shiraie G., Pickart S. J. and Ishikawa Y:, J. Phyi. So;. Japan 14, 1352 (1959).

10. Schimitschek E. J., Phys. Reu. 130, 2199 (1963).