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The ENDOR supertransferred hyperfine interactions in linear metal-anion-cation bonds
JOURNAL
OF MAGNETIC
RESONANCE
66,
148-l 50 (1986)
NOTES The ENDOR SupertransferredHypefine Interactions in Linear Metal-Anion-Cation Bonds S. GALINDD*,~ Instituto National de Investigaciones Nucleares, Agricultura No. 21. Cal. Escanddn, C.P. 11800, Mexico, D.F. Mexico AND
C.D. ADAMS Clarendon Laboratory, Parks Road, Oxford University, Oxford OX1 3PQ, United Kingdom Received April 3, 1985
The electron-nuclear double-resonance (ENDOR) spectra of 3d” ions in diamagnetic host crystals whose nuclei have nonzero spin are a current subject of study. These spectra are very often characterized by the presence of superhyperhne structure which arises from transferred hyperIme interactions with the nearest-neighbor ligands and supertransferred hyperfme interactions with the next-nearest-neighbor ligands. A number of papers have dealt with the problem of estimating the so-called supertransferred hyperhne parameters from superhypertine structure measurements. One reason for this interest is the fact that these parameters are helpful in the understanding of degrees of covalency in ionic crystals (I). Besides this fact, the models used to interpret these parameters are related to mechanisms of superexchange in magnetically ordered compounds (2). Among the most extensively used models to interpret the next-nearestneighbor anisotropic A,, A,, and isotropic A, supertransferred hyperfine parameters is the one proposed by Taylor et al. (3). This model has also been used in connection with perturbed-angular-correlation (PAC) measurements (4). However, a reexamination of the formulae for the supertransferred hyperfine parameters given in the work of Taylor et al. (3) reveals the omission of some terms and multiplicative factors. Since these results have been quoted and referred to in the literature during recent years (5), it seems appropriate to give, in this note, the corrected formulae. The approach of Taylor et al. considers a configuration interaction independent bonding model (6). In this scheme, one-electron functions are taken to be atomic * Member of Sistema National de Invest&adores. t This work was performed at the Clarendon Laboratory during tbe tenure of a British Council Fellowship. # Present address: Unilever Research, Port Sunlight Laboratory, Quarry Road East, Babington, Wirral, Meyerside L63 3JW, United Kingdom. 0022-2364186 $3.00 Copyrisht (Q 1986 by Academic F’rcs, Inc. AU righta of reproduaion in sny form resemd.
148
149
NOTES
orbitals of the ions taking part in the bond. Covalency is taken into account by adding configurations in which one electron has been “transferred” from one ion to another. Each configuration is described by a Slater determinant of one-electron orbitals; thus, the wavefunction of the system is in general a sum of the determinants. The relevant orbitals considered in Taylor’s analysis are shown in Fig. 1. The derivation of the hyperhne parameters is extensively described in Ref. (3). Here, we quote only our results. For the isotropic interaction,
where
and
METAL
ANION
CATION /---.\
/ I i\ \\
0 +
-- --’
\
\ ; II
28,2S
34x, FIG. I. Orbitals considered in the analysis of the interactions. (a) A,, (b) A,, (c)A,, in metal-anion-cation b,onds. Unoccupied orbitals shown with broken lines.
150
NOTES
The overlap integrals are S8zs= (Cation 2slAnion 2s),
S, = (Metal 3dzz1Anion 2s),
S,z, = (Cation 2slAnion 2p,),
S,, = (Metal 3dzz1Anion 2p,),
and @,dand ~2~3~ are admixture coefficients. For the anisotropic interaction, A, = A,2s
[ss2p&d
+
&2&&d
+
scd)12
-
A*
+
[2%@a3pSo2pSad
2ac3pSc2pS~d
+
+
~~~3&&&%2pl
2aadaa3p&2p&d
+
s2,daz3J3p
where = $&P,P( r-3)2py
4,
and The overlap integrals are S,,2P= (Cation 2p,lAnion 2p,)
and
S,,, = (Cation 2p,lAnion 2s)
and a,3p describes the admixture of the Anion 2p, - Metal 3pn transfer configuration. The second relation for the anisotropic interaction is
where and and ur3P are admixture coefficients, and Snd = (Metal 3dJAnion
2p,>,
Sr2P = (Cation 2p,lAnion 2~~).
A comparison of the present results with those of Ref. (3), reveals the omission of direct contributions from 3s, 3p, and 3p, electrons as well as a factor of 2 in the following tetI’kIS: 2&,3&,&& 2&,3,$&,S~d and 2~,$,S&&. It should alSO be noticed that the present formulae in contrast to those given in Ref. (3) are symmetric, as they should be, with respect to a change in “dummy indexes.” REFERENCES 1. J. OWEN AND J. H. M. THORNLEY, Rep. Prog. Phys. 29,675 (1966). 2. P. W. ANDERSON, in “Solid State Physics” (F. Scits and D. Turnbull, Eds.), Vol. 14, p. 99, Academic Press, New York, 1963. 3. D. R. TAYLOR, J. OWEN, AND B. M. WANKLYN, J. Phys. C 6,2592 (1973). 4. H. H. RINNEBERG AND D. A. SHIRLEY, Phys. Rev. B 13,2138 (1976). 5. D. R. TAYLOR, D. Phil. Thesis. University of Oxford, 1967; J. OWEN AND D. R. TAYLOR, .I. App. Whys. 39,791 (1968); H. H. RINNEBERG AND D. A. SHIRLEY, Phys. Rev. Left. 3&l 147 (1973); M. E. ZIAE, D. Phil. Thesis. University of Oxford, 1977; M. E. ZIAE AND J. J. OWEN, J. Phys. C9, L529 (1976); M. E. ZIAE AND J. J. OWEN, .I. Phys. C Sol. State Phys. C 16, 5039 (1983). 6. J. HUBBARD, D. E. RIMMER, AND F. R. A. HOPGOOD, Proc. Phys. Sot. 88, 13 (1966).
OF MAGNETIC
RESONANCE
66,
148-l 50 (1986)
NOTES The ENDOR SupertransferredHypefine Interactions in Linear Metal-Anion-Cation Bonds S. GALINDD*,~ Instituto National de Investigaciones Nucleares, Agricultura No. 21. Cal. Escanddn, C.P. 11800, Mexico, D.F. Mexico AND
C.D. ADAMS Clarendon Laboratory, Parks Road, Oxford University, Oxford OX1 3PQ, United Kingdom Received April 3, 1985
The electron-nuclear double-resonance (ENDOR) spectra of 3d” ions in diamagnetic host crystals whose nuclei have nonzero spin are a current subject of study. These spectra are very often characterized by the presence of superhyperhne structure which arises from transferred hyperIme interactions with the nearest-neighbor ligands and supertransferred hyperfme interactions with the next-nearest-neighbor ligands. A number of papers have dealt with the problem of estimating the so-called supertransferred hyperhne parameters from superhypertine structure measurements. One reason for this interest is the fact that these parameters are helpful in the understanding of degrees of covalency in ionic crystals (I). Besides this fact, the models used to interpret these parameters are related to mechanisms of superexchange in magnetically ordered compounds (2). Among the most extensively used models to interpret the next-nearestneighbor anisotropic A,, A,, and isotropic A, supertransferred hyperfine parameters is the one proposed by Taylor et al. (3). This model has also been used in connection with perturbed-angular-correlation (PAC) measurements (4). However, a reexamination of the formulae for the supertransferred hyperfine parameters given in the work of Taylor et al. (3) reveals the omission of some terms and multiplicative factors. Since these results have been quoted and referred to in the literature during recent years (5), it seems appropriate to give, in this note, the corrected formulae. The approach of Taylor et al. considers a configuration interaction independent bonding model (6). In this scheme, one-electron functions are taken to be atomic * Member of Sistema National de Invest&adores. t This work was performed at the Clarendon Laboratory during tbe tenure of a British Council Fellowship. # Present address: Unilever Research, Port Sunlight Laboratory, Quarry Road East, Babington, Wirral, Meyerside L63 3JW, United Kingdom. 0022-2364186 $3.00 Copyrisht (Q 1986 by Academic F’rcs, Inc. AU righta of reproduaion in sny form resemd.
148
149
NOTES
orbitals of the ions taking part in the bond. Covalency is taken into account by adding configurations in which one electron has been “transferred” from one ion to another. Each configuration is described by a Slater determinant of one-electron orbitals; thus, the wavefunction of the system is in general a sum of the determinants. The relevant orbitals considered in Taylor’s analysis are shown in Fig. 1. The derivation of the hyperhne parameters is extensively described in Ref. (3). Here, we quote only our results. For the isotropic interaction,
where
and
METAL
ANION
CATION /---.\
/ I i\ \\
0 +
-- --’
\
\ ; II
28,2S
34x, FIG. I. Orbitals considered in the analysis of the interactions. (a) A,, (b) A,, (c)A,, in metal-anion-cation b,onds. Unoccupied orbitals shown with broken lines.
150
NOTES
The overlap integrals are S8zs= (Cation 2slAnion 2s),
S, = (Metal 3dzz1Anion 2s),
S,z, = (Cation 2slAnion 2p,),
S,, = (Metal 3dzz1Anion 2p,),
and @,dand ~2~3~ are admixture coefficients. For the anisotropic interaction, A, = A,2s
[ss2p&d
+
&2&&d
+
scd)12
-
A*
+
[2%@a3pSo2pSad
2ac3pSc2pS~d
+
+
~~~3&&&%2pl
2aadaa3p&2p&d
+
s2,daz3J3p
where = $&P,P( r-3)2py
4,
and The overlap integrals are S,,2P= (Cation 2p,lAnion 2p,)
and
S,,, = (Cation 2p,lAnion 2s)
and a,3p describes the admixture of the Anion 2p, - Metal 3pn transfer configuration. The second relation for the anisotropic interaction is
where and and ur3P are admixture coefficients, and Snd = (Metal 3dJAnion
2p,>,
Sr2P = (Cation 2p,lAnion 2~~).
A comparison of the present results with those of Ref. (3), reveals the omission of direct contributions from 3s, 3p, and 3p, electrons as well as a factor of 2 in the following tetI’kIS: 2&,3&,&& 2&,3,$&,S~d and 2~,$,S&&. It should alSO be noticed that the present formulae in contrast to those given in Ref. (3) are symmetric, as they should be, with respect to a change in “dummy indexes.” REFERENCES 1. J. OWEN AND J. H. M. THORNLEY, Rep. Prog. Phys. 29,675 (1966). 2. P. W. ANDERSON, in “Solid State Physics” (F. Scits and D. Turnbull, Eds.), Vol. 14, p. 99, Academic Press, New York, 1963. 3. D. R. TAYLOR, J. OWEN, AND B. M. WANKLYN, J. Phys. C 6,2592 (1973). 4. H. H. RINNEBERG AND D. A. SHIRLEY, Phys. Rev. B 13,2138 (1976). 5. D. R. TAYLOR, D. Phil. Thesis. University of Oxford, 1967; J. OWEN AND D. R. TAYLOR, .I. App. Whys. 39,791 (1968); H. H. RINNEBERG AND D. A. SHIRLEY, Phys. Rev. Left. 3&l 147 (1973); M. E. ZIAE, D. Phil. Thesis. University of Oxford, 1977; M. E. ZIAE AND J. J. OWEN, J. Phys. C9, L529 (1976); M. E. ZIAE AND J. J. OWEN, .I. Phys. C Sol. State Phys. C 16, 5039 (1983). 6. J. HUBBARD, D. E. RIMMER, AND F. R. A. HOPGOOD, Proc. Phys. Sot. 88, 13 (1966).