Electron-Nuclear Hyperfine Interactions of 53 Cr 3+ in Mg2Si04 (Forsterite)

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1 Electron-Nuclear Hyperfine Interactions of 53 Cr 3 in Mg2Si04 (Forsterite) H. Rager Department of Geoscienees, University of Marburg Z. Naturforsch. 35a, (1980); received October 25, 1980 The magnetic hyperfine interaction between the electron and nuclear spin system of 33 Cr 3 was studied at the Mg sites, Ml and M2, in Mg2>Si04. The study was undertaken at room temperature and 9.52 GHz. The hyperfine structure data exhibit a covalent Cr-0 bonding of approximately 10% indicating a mainly but not purely ionic bonding. Including the corresponding results obtained for 57 Fe 3 [1] and 55 Mn 2 [2] in Mg2Si04, this is interpreted such that the bonding of transition metal ions is mainly dominated by the oxygen sublattice in Mg2Si04 and less by the properties of the transition metal ions themselves. The small variation of the hyperfine splitting parameters found for 53 Cr 3 f at Ml and M2, and also for 57 Fe 3 at these positions indicates that the hyperfine interaction varies also with varying average metal oxygen distances as well as with changes in the oxygen coordination size. I. Introduction Electron spin resonance (ESR) investigations of the paramagnetic impurity ions, Fe 3 [1], Mn 2 [2], and Cr 3 [3] in forsterite, Mg2SiC>4, have primarily dealt with the fine structure (FS) terms, Bk m, which can be obtained by fitting an appropriate effective spin Hamiltonian operator to the observed ESR transitions. The hyperfine interaction between the electron and nuclear spin system of the isotopes 57 Fe, 55 Mn, and 53 Cr was also measured. However, there is so far no general discussion of the hyperfine structure (HFS) data with respect to the properties of the positions substituted by the above ions in Mg2SiC>4. Therefore, in this paper we present our investigation of the 53 Cr 3 -HFS-interaction. The results will be compared with corresponding studies of 57Fe 3 [1] and 55Mn 2 [2] in the forsterite crystal. The two Mg sites differ in point symmetry which is 1 at 4a(Ml) and m at 4c(M2), and in the sixfold oxygen coordination where the average Ml-0 and M2-0 distance is Ä and Ä, respectively. Silicon occurs at 4c (Si) and oxygen at positions 4c(01 and 02) and 8d(03) where at 8d the point symmetry is 1. M(1) 25 <; (75 II. Crystal Structure The well known structure of Mg2Si04 [4] is illustrated in Figure 1. It can be described as being based on an approximately hexagonal, tightlypacked array of oxygens with silicon in the fourfold and Mg in the sixfold oxygen coordinated sites. The unit cell belongs to the space group Pbnm and contains two inequivalent Mg sites, 4a and 4c, which are designated as Ml and M2, respectively. Reprint requests to Dr. H. Rager, Fachbereich Geowissenschaften, Philipps-Universität Marburg, Lahnberge, D-3550 Marburg. u Fig. 1. Crystal structure of forsterite. The representation of the space group is Pbnm. The numbers give the «-coordinate in percent of the lattice constant a (after [1]). III. Theory The spin Hamiltonian operator which describes the ground state energy levels of the paramagnetic impurities 57 Fe 3, 55 Mn 2, and 53Qr3 jn a crystalline environment with an external magnetic field H $ Please order a reprint rather than making your own copy. Download Date :33 PM

2 H. Rager Electron-Nuclear Hyperfine Interactions of is [5] fi = ßHgS 2 2 Bz7" 02m m= 2 -r 4 2 «;= 4 53 Cr 3 in MgjSiO«(Forsterite) BmOm S A *. (1) T h e first term describes the Zeeman interaction between the effective electron spin S and the applied magnetic field H. T h e second and third terms depend o n the second and fourth derivatives, respectively, o f the crystal field potential at the substitutional site. T h e y are called fine structure (FS) terms a n d stand f o r the interaction o f the effective electron spin S w i t h the electric field derivatives at the paramagnetic center. In the fourth term the tensor A represents the hyperfine interaction between the electron (S) and the nuclear (I) spin o f the paramagnetic ion. F o r a predominantly orthorhombic e n v i r o n m e n t the fourth term can be written [6] as S A = A Sz Iz B (Sx Ix Sy Iy). (2) A and B will, in general, be m a d e u p of contributions f r o m the orbital, spin dipolar, and Fermi contact interactions. T h e y depend on the ion itself and in particular o n the ground state o f the ion under investigation. T h e electron configuration o f F e 3 and M n 2 is [ A r ] 3 d 5 and o f C r 3 [ A r ] 3 d 3 where [Ar] denotes the electron configuration of the noble gas argon. I n the high spin state these configurations result in an orbital singlet i.e., the orbital m o m e n t u m L o f F e 3, M n 2, and C r 3 is quenched or, in other words, the e x p e c t a t i o n value o f L is zero. Then, the ground state hyperfine interactions are almost entirely due t o the c o n t a c t and spin-dipolar terms. H o w e v e r, spin-orbit coupling either b y itself or in conjunction with l o w - s y m m e t r y crystal field matrix elements mixes in e x c i t e d states, thereby reintroducing an orbital contribution into A and B. T h e same mixing carries the electron g shift from , and o n e can often write the orbital hyperfine terms [6] as Aorl, = gi juo Ag<r-3>, 0 r b = giuoui Ag±<r_3> Ag and Agj_ arc the parallel and (3.1). (3.2) perpendicular electron g shifts, uo and are the B o h r and nuclear * For brevity the interaction of the nuclear spin I with the external magnetic field H as well as the quadrupole interaction have been omitted in Equation (1) magnetons, gi is the nuclear spectroscopic splitting factor and <V -3 > refers t o the 3 d orbitals o f the paramagnetic ion under investigation. Provided there are n o contributions which arise f r o m electron transfer or high order effects, (3.1) and (3.2) will supply accurate estimates o f the orbital hyperfine contribution t o A and B. I f the hyperfine interaction is assumed to be mainly isotropic, i.e. A > B, the relation HF = ASgiui (4) approximately determines the magnetic hyperfine field H F at the nuclear site [7]. Experimental and theoretical estimates s h o w that for 3 d w ions the normalized hyperfine field i H F 2 $ is roughly constant for ions o f c o m m o n v a l e n c y in c o m m o n environments. Significant deviations f r o m the constancy are assigned t o covalent contributions in the metal-ligand bonding. Therefore, the investigation o f the hyperfine interaction is one m e t h o d t o obtain information on the c o v a l e n c y o f the metal-ligand bonding [8]. IV. Experimental Results and Discussion D u e t o the hyperfine interaction, the E S R fine structure lines o f F e 3 and C r 3 are centered b y 2 1 -j-1 a p p r o x i m a t e l y equally spaced hyperfine structure ( H F S ) lines (Fig. 2) where I is the nuclear spin o f the isotopes 5 7 F e and 5 3 Cr. T h e intensity o f the H F S lines results f r o m the a b u n d a n t transition metal isotopes with a nuclear spin I. F o r example, in the case o f the c h r o m i u m d o p e d forsterite the Cr-HFS-intensity is roughly 1 0 % according t o the % natural abundant 5 3 Cr isotope with 7 = 32. F o r M n 2 o n l y H F S lines exist (Fig. 2 a) because o f the % a b u n d a n t 55Mn isotope. T h e H F S lines o f 5 7 F e 3, 5 5 M n 2, and 53Cr3 in M g 2 S i 0 4 are well resolved. Their overall splitting ranges f r o m 450 G for 5 5 M n 2 via 60 G for 53(> 3 t o o n l y 13 G for 57p e 3 as shown in Figures 2 a c. T h e hyperfine interaction between the nuclear spin (1=32) and the effective electron spin ( = 3 2 ) of 53Qr3 j n forsterite was studied at r o o m temperature and 9.52 G H z. T h e four hyperfine lines are well resolved (Fig. 2 c) and their splitting, AH, depends o n the crystal orientation with respect t o the applied external magnetic field (Figure 3). A t M2 positions the angle dependence o f A H is small, whereas at M l positions it is v e r y distinct. Thus, Download Date :33 PM

3 1298 H. Rager Electron Nuclear Hyperfine Interactions of ^Cr 3 * in Mg2Si04 (Forsterite) Fig. 2 a. Hyperfine splitting of 55 Mn 2 in chromium doped forsterite. The spectrum was taken at room temperature and GHz. The crystal was oriented with a HQ , ,00 MAGNETIC FIELD [GAUSS] J ivh# Fig. 2b. Hyperfine splitting of 57 Fe 3 in iron doped forsterite enriched with approximately 90% 57 Fe. The spectrum was taken at room temperature and GHz. The small central lines are due to the ESR transitions of 56 Fe 3 with 7=0. The crystal was oriented with A HQ U00 _l I I I MAGNETIC FIELD [GAUSS1 Fig. 2 c. Hyperfine splitting of natural abundant 53 Cr at Ml and M2 positions in Cr doped forsterite. AH denotes the total HF splitting. The notations (1 2) and (3 4) indicate the Cr 3 -fine structure transitions MA = 32 -». M3 = 12 and Ms = - 12 MS = - 32, respectively. The crystal was oriented with a_[_ho and ch (see Fig. 4). MAGNETIC FIELD (GAUSS) Download Date :33 PM

4 The notations (1 2) and (3 4) are as in Figure 2c. Fig. 4. Angle dependence of the Cr 3 fine structure ESRtransitions at Ml and M2. The notation is the same as in Fig. 2 c and Figure 3. Download Date :33 PM

5 1300 H. Rager Electron-Nuclear Hyperfine Interactions of 53Cr3 in MgjSiO«(Forsterite) 1300 in the following we will discuss the hyperfine split- at the Cr ( M l ) site (Table 2). Plotting both axes ting o f 53Qr3 systems together in a sterographic projection, f r o m at M l positions in more detail. Comparing the rotation pattern o f AH in Fig. 3 Fig. 5 and Table 2, it can easily be seen that at the with that o f the E S R fine structure transitions in distinct crystal orientation < (b, Hres) Fig. 4, it is apparent that the angles for the maxi- c o m p o n e n t o f the applied magnetic resonance field na 39 the z- m u m magnetic resonance fields, res, max, agree runs through zero in the principal axes system, well with the angles for the minimum I^perfine whereas in the crystal axes system r e s runs through splitting zltmin- T h e angles refer t o the crystal a maximum. axes system and are listed in Table 1. T o understand the reason for this we transformed, b y example o f the C r 3 ( 1 2 ) E S R transitions, the magnetic resonance field r e s f r o m the crystal axes system into the principal axes system o f the crystal field tensor Table 1. Angles between the applied magnetic resonance field res and one crystal axis at which HTes for the Cr 3 (M1) ESR transition is at a maximum and the respective 53(^r3 hyperfine splitting AH at a minimum, a J_ b Ilo, and c _L Ho are the different crystal orientations. (1 2) and (3 4) denote the ESR fine structure transitions as in Figs. 2 c, 3 and 4. Crystal orientation Angles between the applied maximum magnetic resonance fields, IITCs,max of the Cr 3 (Ml) ESR transitions and one crystal axis Transition a ± H0 bj_h0 c J_ Ho a ± Ho b±h0 C Ilo (1-2) (3-4) Angles of the corresponding hyperfine splitting AIImjn minimum Fig. 5. Stereographic projection of the applied magnetic resonance field Hres in the crystal axes system a, b, c and of the 2-eomponent of r e s in the principal axes system, Y, Z, of the Cr (Ml) crystal field tensor (see also Table 2). F o r a constant magnetic field of Ho = 1980 G, the F S energy levels EFS(1) an d 1?FS(2) were calculated b y solving the corresponding energy matrix of E q u a Table 2. Angle dependence of the normalized components of the applied magnetic resonance field, Hres, in the principal axes system, Y, Z of the Cr3 crystal field tensor at Ml. The crystal orientation was a J_ Ho. Angle Normalized components of the applied magnetic resonance field, IIrcs, for the Cr3 ( 1-2 ) ESR transitions in the principal axes system, Y, Z of the C'r3 crystal field tensor at Ml. Y Z o o 3 O o 3 c* a- -i a Ox a n d ZFS(2) runs through a minimum at the same orientation <%(b, Ho)s»39. This is shown in Figure 6. Therefore, it is plausible that at this particular crystal orientation, with respect t o the applied magnetic field vector, the magnetic resonance field must be raised in order t o fulfill the resonance condition for the used microwave frequency of G H z. T h e HF-splitting, A EN F, o f the F S - E S R levels, -E'FS(I) and?fs(2), is also angle dependent and at a m i n i m u m at the special angle setting of approximately 39. This is shown in Figure 7. Thus, the hyperfine-split 53Cr3 (1 2)-ESR-transitions oc- cur near 39 v e r y close t o the h y p o t h e t i c fine structure tion (1) [3]. T h e difference between -EFSU) 53Cr3(l 2)-ESR-transitions yielding a mini- m u m hyperfine splitting in accordance with the experimental results. Discussing the C r 3 ( 3 4 ) - E S R - Download Date :33 PM

6 H. Rager Electron-Nuclear Hyperfine Interactions of M Cr 3 in MgjSiO«(Forsterite) = ^ 90ize= H b * H 0 09ie= H h hv«91527 GHz l o i" i 2 o. O-J «O O o. Z r> < UJ u J ", o I Download Date :33 PM

7 1302 H. Rager Electron-Nuclear Hyperfine Interactions of 53 Cr 3 in M g 2 S i 0 4 (Forsterite) transitions the same results will be obtained. Thus, accordance with the average metal o x y g e n distances the tensors g and A in E q. (1) can be considered t o at these positions (see Table 3 a n d Section I I ). b e collinear [9] and it is justified t o calculate the Because the dipolar contribution t o the magnetic hyperfine constants b y solving the energy matrix hyperfine field at the c h r o m i u m site is negligible, which was constructed o f E q s. (1) and (2). the difference b e t w e e n the experimental magnetic T h e hyperfine constants, A and B, thus obtained f o r 53C!r3 at M l and M2 positions revealed A > B in accordance with the assumed collinearity o f the hyperfine field ( E q. (4)) and the orbital H F zation H F field tensors g and A which means that the electron and TJ H F cp = ~ nuclear m o m e n t s are aligned along the main symm e t r y axis o f the crystal field tensor. Therefore, the 5 3 Cr hyperfine interaction is denoted b y the hyperfine splitting parameter A, which is listed in T a b l e 3. T h e limit o f error o f A at M l and M2 is relatively large. This is due t o the experimental ina c c u r a c y in determining the magnetic resonance fields f o r the hyperfine transitions. T h e contributions t o the C r 3 H F field are mainly due t o the orbital and core polarization H F fields. A c c o r d i n g t o the experimental result A > B the crystalline field m a y be assumed t o be nearly cubic and, thus, the dipolar contribution t o the H F field should be negligible [5]. T h e orbital H F field can b e estimated b y the relation (5) if Ag is entirely due t o orbital effects and isotropic. 3d3 ions the AS IT H F ^orb (*>) I n contrast t o the orbital the core polarization hyperfine field has been observed t o b e independent f r o m the a t o m i c distances within the host lattice. Regarding the limits o f error o f the parameters A at M l and M2, this is in qualitative agreement with the values obtained for H ^ F (Table 3) at these positions. F r o m Table 3 it can be n o t e d t h a t the parameter A seems t o be slightly smaller at M l than at M2. This m a y be interpreted such t h a t the covalency of the C r - 0 b o n d at M l is slightly larger than at M2, in accordance with the average M l - 0 and M 2-0 distances in forsterite. T o estimate t h e covalent contribution to the C r - 0 b o n d in forsterite, Paulings # 5 b = f i B S A g & v { r - 3 y For field ( E q. (5)) m a y then b e attributed t o the core polari- normalized orbital HF field is small in comparison t o the H F field prod u c e d b y the core polarization effect [5]. I t varies with the m e t a l - o x y g e n distance in such a wray that the orbital H F field increases with increasing M - 0 distance. Assuming an isotropic gr-shift f r o m , w e m a y estimate f r o m the eigenvalues o f the Cr 3 - definition of the c o v a l e n c y, c, is used [10]. A c c o r d ing t o that, the definition contains t w o assumptions: i) A general relationship exists between the electronegativity difference A B lency of an A-B and the c o v a - bond. ii) T h e gauge curve can be constructed b y taking the electric dipole m o m e n t s o f the hydrogen halides as representative f o r t h e ionic character (i = 1 c) in these c o m p o u n d s. gr-tensor at M l and M2 [3] that A g & v & and T h e gauge curve proposed b y H a n n a y and Smith Ag&x ^ 0.041, respectively. F r o m E q. (5) we then [11] obtain a larger orbital field at M2 than at M l in B)2 (7) Table 3. Hyperfine splitting parameter A deduced magnetic hyperfine fields of 55 Mn 2, 55Fe3" and 53 Cr 3 Ml and M2 positions in Mg2Si04. The signs of the magnetic HF fields were not experimentally determined. at Center 55 Mn 2 57pe3 5 7 Fe 3 53Cr3 53 Cr 3 a c Position ^ 10-4 c m - 1!12 Ml M2 Ml M a ergg ± 0.4 b ± 0.2 b ± 1.7 ± S c = 1- MML kg , [A - B) - kg , (A - kg c c c ( - ) b Values taken from Niebuhr [1]. Value taken from Gaite [2]. The deviation of the F e 3 ± and M n 2 ± ^-values from is negligible [5]. Download Date :33 PM kg ( ) ( ) ( )

8 H. Rager Electron-Nuclear Hyperfine Interactions of 53 Cr 3 in MgjSiO«(Forsterite) can then be used t o calculate the degree o f covalency. Taking the electronegativities A,B from G o r d y and T h o m a s [12], f r o m E q. (7) an average c o v a l e n c y o f apparently 1 0 % was o b t a i n e d f o r the C r - 0 b o n d in forsterite E q u a t i o n (7). H o w e v e r, the gauge curves are also based on the relation (7) o f H a n n a y and Smith [11]. Conclusions 10%. In summary, we establish that the ions F e 3, M n 2, and Cr 3 in their sixfold o x y g e n coordination in forsterite exhibit a covalent b o n d i n g of 10 t o 1 5 %, i.e. the bonding of these transition metal ions is not purely but mainly ionic. This m a y be interpreted such that the covalent contribution t o the metal o x y g e n bonding is mainly d o m i n a t e d b y the oxygens and less b y properties o f the transition metal ions themselves, like ionic radius and electron configuration. Further, the small variation o f the HF-splitting parameters f o u n d for 5 3 C r 3 at M l and M2, and also for 5 7 F e 3 at these positions [1] indicates that the HF-interaction varies with varying metal o x y g e n distances. Likewise, the hyperfine constants o f 5 7 F e 3 at M l, M 2 and the silicon position in forsterite have already been discussed b y Niebuhr [1]. Their values for an octahedral and tetrahedral coordination agree with corresponding literature [13]. F o r the t w o octahedrally coordinated M l and M2 sites o n e obtains a covalent contribution t o the F e - 0 b o n d o f roughly 1 3 %. H o w e v e r, as f o u n d f o r the C r - 0 b o n d s, the c o v a l e n c y o f the F e - 0 b o n d s also seems t o increase slightly with decreasing metal o x y g e n distance. Actually, the covalent contributions f o r the M n - 0 and F e - 0 bonds in forsterite were d e d u c e d f r o m gauge curves given b y Simanek and Müller [7] and Henning [13], respectively, and not calculated f r o m There are a series o f methods like E S R, N M R, C o m p t o n scattering, Mössbauer and photoelectron spectroscopy t o investigate c o v a l e n c y effects. H o w ever, t o date it is still a problem t o e x t r a c t detailed information about the spin and charge distribution in the investigated c o m p l e x f r o m the experimental results, and t o discuss this information with respect t o the electronic structure o f the c o m p l e x. This problem is also valid for the a b o v e discussion, which gives only a qualitative interpretation o f the investigated transition metal o x y g e n b o n d s in forsterite. For a more detailed discussion o f this p r o b lem, additional experiments like, e. g., E N D O R measurements are necessary. [1] H. Niebuhr, Elektronenspin-Resonanz von dreiwertigem Eisen in Forsterit. Habilitationsschrift, FB Geowissenschaften, Marburg [2] J.-M. Gaite, Etude de Proprietes Locales dans les Cristaux de Basse Symetrie & l'aide de la Resonance Paramagnetique Electronique d'ions ä l'etat S. Dissertation, Orleans [3] H. Rager, Phys. Chem. Minerals 1, 371 (1977). [4] J. R. Smyth and R. M. Hazen, Amer. Mineral. 58, 588 (1973). [5] A. Abragam and B. Bleaney, Electron Paramagnetic Resonance of Transition Metal Ions, Clarendon Press, Oxford [6] A. J. Freeman and R. E. Watson, Hyperfine Interactions in Magnetic Materials, in: Magnetism Vol. IIa, Chapter 4. Editors: T. G. Rado and H. Suhl, Academic Press, New York E. Simanek and K. A. Müller, J. Phys. Chem. Solids 31, 1027 (1970). J. S. van Wieringen, Disc. Faraday Soc. 119, 118 (1955). R. M. Golding and W. C. Tennant, Mol. Physics 25, 1163 (1973). L. Pauling, Die Natur der chemischen Bindung, Cornell University Press, Ithaca, N.Y M. B. Hannay and C. F. Smyth, J. Amer. Chem. Soc. 68, 171 (1946). W. Gordy and W. J. O. Thomas, J. Chem. Phys. 24, 439 (1956). J. C. M. Henning, Physics Letters 24 A, 40 (1967). F o r comparison, the corresponding magnetic hyperfine parameters A obtained for the ions 5 7 F e 3 and 5 5 Mn 2 in forsterite are also listed in Table 3. T h e hyperfine interaction and c o v a l e n c y o f M n 2 ions in different hosts were already discussed in detail b y Simänek and Müller [7], and v a n Wieringen [8]. A c c o r d i n g t o that, the hyperfine constant decreases with increasing c o v a l e n c y. A t M 2 in forsterite the 5 5 M n 2 - H F constant is isotropic and yields c m - 1 [2], Comparing this value with published data [7, 8] the covalent contributions t o the M n - 0 b o n d in forsterite turns o u t t o be roughly [7] [8] [9] [10] [11] [12] [13] Download Date :33 PM