Superhyperfine interactions and covalency contribution to axial zero field splitting for |MnF6|4− complexes in fluorides

I. Phys. Chem. So/ids Vol. 42, No. 9. pp. 7X9-798, 1981 Printed in Great Britain.

~ZZ-3697/Sil~~l~,~/O Pergamoo Press Ltd.

SUPFR~YPERF~NE INTERACTIONS AND COVALENCY CONTRIBUTION TO AXIAL ZERO FIELD SPLITTING FOR jMnF,l”- COMPLEXES IN FLUORIDES J. EMERY, Laboratoire

de spectroscopic

A. LEBLE

and J. C. FAYET

du solideE.R.A.682.Faculte

des sciences 72017 Le Mans Cedex, France

(Received11March 1980,acceptedf 1 February 198t) Abstract-An approximate L.C.A.O.-M.O. calculation based upon the one-electron ionic hamiltonian initially derived by Sugano and Shulman, gives satisfactory agreement with measurements of superhyperfine interactions at the ligand shell and outer shell nuclei, for Mn” in AMF? crystals, when one takes into account an external crvstal potential acting on the IMnF$ complex. The results obtained for cubic symmetry are extrapolated to an independent bond model in order to discuss the covalency contribution to axial zero field splitting.

I. INTRODUCTION

The superhyper~ne interactions for (3d)” ions, without ground state orbital degeneracy (n = 3,5,8), in octahedral sites of fluorides are commonly interpreted within a simple L.C.A.O.-M.O. framework in which the electron spin is located in an antibonding M.O. Experimental results are converted into terms of transferred spin densities f_,f,,,fn. Within this framework, Sugano and Shulman (S-S) have earlier proposed an approximate S.C.F. [I] treatment for the antibonding M.O. Their ealelllation scheme accounts satisfactorily for the measured superhyperfine interaction in KNiF, and KznF3;VZ’[I-31. In this scheme, one assumes that occupied antibonding and bonding M.O’s of the same symmetry are orthogonal. Such M.O.‘s can be obtained by diagonalizing a single hamiltonian on an orthogonalised atomic orbit& (A.O.) basis. The hamiltonian which has been used is given in detail below, and extended from divalent Ni”(e,)‘[l] and V*‘(f,,)“[2,3] to divalent Mn”(tz,)i (es)* ions in this work. Indeed, for this ‘S state ion the different measurements used to estimate spin transfers (neutronsf41. NMR[S], ENDOR[6], P.A.C.171) give rise to large doubts on the actual transferred densities. These doubts prevent any definite conclusion being made about the covalency contribution to the quadrupolar zero field splitting of spin levels in distorted octahedral[&lO] sites. We attempt to cast some light on this problem through a simple and approximate theorical model. The results of our calculations are compared to experimental results [l I] for AMnK and AMR: Mn*’ isostructural crystals in which the Mn”-Fbond length changes smoothly from 2 A to 2.3 A neglecting the lattice relaxation in the doped crystals. f. EXPERIMENTAL AND THEORXAL ~AMEWORKS The antibonding M.0.s which are singly occupied have the following form[l2]:

The bonding orbitals *,“(tz,, e,,, es.s)= Ni’f~i + yip;) assumed to be orthogonal, i.e.: hi = .S + n, both for up and down spin. Then, the spin densities transferred on the ligand are expressed by are

Estimates of these with the help of different measurements are indicated in Table 1. The results for &,f,,-f,,, through the superhyperfine (s.h.f.f interaction with the ligand, measured by 19FNMR in KMnF,, RbMnK or by EPR AMR:Mn’* crystals are listed in Table 2. Briefly, neutron scattering by an antiferromagnet (MnF*) gives the total spin transfer cfr +f,? + ?f,,) through the intensities of diffraction peaks from the magnetic structure[4]. NMR on 19F nuclei in AMnFr crystals or EPR on doped crystals permits the measurement of the s.h.f. tensor from which one deduces fq and fR -fn, by taking into account the point dipole and overlap contribution[ 131. In RbMnR : Cd’+, and Cs Cd F3 : Mn” the hyperfine field at nearest neighbor (&Cd nuclei arises through overlap of polarised 2p(r F- orbitals with the 5s Cd’+ orbital. This hyperfine field can be measured by ENDOR in Cs Cd R:Mn’“, [6] or by P.A.C. in RbMnF~: “3Cd[7], and serves to give an estimate of fn by calibration with respect to the [Ni-F Cd] systems[l4], or by direct calculationjl4f. In addition s.h.f interactions with next nearest neighbor (nnn)‘“F nuclei have been also measured by ENDOR[IS]. They may be used as a control for spin transfers on ligand nuclei through an overlap model. We will describe the difficulties of estimating the actual bond lengths for lMnF6/-4 in doped crystals. We shall assume that they are not too far from the corresponding M*+- F- distance in the host lattice. On the other hand, the conflicting estimates in Table I, i.e. jr = 1% or j- =4%, evidences the difficulties of interpreting quite different effects through a single simplified 789

J. EMERY et al.

790

Table 1. Comparison of experimental transferred spin densities measuredby differentmethods

Rfk

licst

Technics

Ih Ft

References

fLM

neutron dif.

13 I

N.M.R.

I4

N.M.R.

141

P.A.C. (Cd)

I6

E.P.R.

/IO/

fs = 0.44 I

151

fo = 4,3% et fS + fo + 2 f * 12.7 % l!

fs + fo + 2 f, = 3.3 %

= 2.1 K Mn F3

2.12

I

f, = 0.52 %

fo - f, - 0.18 %

f, = 0.52 %

fc - f, = 0.3

%

Rb Mn F3

2.23

I

fo = 3.8% et fs + f, + 2 f, = 11.5%

fo - f, = 0.5 %

CS Cd F3 E.N.D.0.R

(Cd)

4

Table 2. Experimental results for Mn” ion in AMF? compounds

Host

H-F Length in ;1

fb - fn %

WC7

1.993

- 1.35

K&F3

2.026

KMnF3

I121

0.14

0.6

1141

2.1

0.018

0.52

I

RbnnF3

2.12

0.35

0.52

141

KCdF3 550K

2.145

0.26

0.52

1211

TlCdF3

2.197

0.42

0.51

1211

RbCdF3

2.2.

0.35

0.51

I211

RbCaF3

2.228

0.69

0.48

I211

CsChF3

2.23

0.44

0.5

1101

CsCaF3

2.262

0.42

0.45

1211

V”,“‘“(rJ + 2

+ Vcry3t-

Ref.

0.68

theorical.model. Nevertheless, one can note consistency for all estimations based upon hyperfine interactions. Details about the derivation of the S-S’s hamiltonian can be found in the initial paper for e, orbitaIs[l] or in Ref.[2,3] for fZKorbitals. Its expression for [MnF$within the ionic approximation (Xi= Si = y, = 0) is:

hiA = -++

fs %

((~i~(2)lld2))

M2)ll47i(2))

in atomic units, where: Vcoretr ) = _ 7. t 16.23e --3-Qr’ M I r1

I

41

is due to metal inner electrons (Is up 3p) and nuclei[ 161: VT(r)) is due to the athFm inner electrons (Is) and nuclei; Jo runs over all occupied e, and tag metal orbitals; k runs over all 2s 2pF- orbitals; VCrys,represents the potential due to the crystalline surroundings and was reduced initially to a flat potential. tf(2)l/.ff2))=

f*(r,) $+

f(rzf doz

and Pzl is the permutation operator of electrons 1 and 2. The M.O. model used here, built from singly occupied antibonding orbitals and from orthogonal doubly occupied bonding orbitals, has been previously used to discuss the spin hamiltonian parameter D for IMnF614complexes[8-IO]. Actually, we are able to calculate an antibonding M.O.

Superhyperiine interactions and convalency

of any symmetry (e, or f2J and its corresponding orthogonal M. 0. by diagonalizing this hamiltonian on an orthogonal (o,x basis. In this way the orthogonality constraint is verified (hi = yi + S). Of course, what is questionnable in this procedure is its reliability, since a rigourous treatment would involve a Hartree-FockRoothaan[ 171calculation, for a two half closed she11(e* and frlR)problem. An Hartree-Fock-Roothaan (H-F-R) hamiltonian is characterized by a closed shell HartreeFock hamiltonian completed by coupling operators. We may notice that the hamiltonian which is used in this work has a similar structure in which the coupling operator would be-(cpi\]pi) within an ionic approximation. We assume that this hamiItonian is accurate enough for our purpose. Our confidence in it is supposed by its ability to account for super-hyperfine interactions in simpler divalent (t2$[2, 31 and (e,)*[l] ions. It is clear that the calculation also suffers from the use of a cluster approximation in place of band theory. The ionic approximation and some numerical simplifications are also involved in the model. We have used this hamiltonian on an atomic orbitals (A.O.) basis constitued by 3d Ri~hardson’s orbitals for Mn”[18] and by an analytic fitf 1] of the numerical Froese’s resultsI for F-. Coulombic, hybrid, and exchange integrals up to three center integrals, have been calculated with programs previously established[20, 161. Our results have to be viewed as a basis on which to discuss the trends of bond length and crysta1 coordination effects on the super-hyperfine interaction and covalency contribution to the zero field splitting for a /MnFh14-cluster. The covalency contribution to the quadrupolar spin hamiltonian D(3S,z - S(S + 1)) for trigonaf or tetragonal symmetry can be expressed by[lO]: D(cov) =; 2 [d,(3 cos 8,” - I)] Y

791

where g runs over the ligands 0, is the angle of Mn-Faxis with the trigonal or tetragonal axis; and d, = a &‘(SLM2- YLM~) +b

with AL&f= SLM+YLM dLM=Aexp

(

--g

,L=O,l >

b = -

Do

All energiesin cm-l fz

in atomic units

M=O,?l.

The primed summation goes over (L, M) = (O,O), (1,O) and (1,l). The above formula comes from a recent calculation of mechanisms initially proposed by Sharma et al. [8]. Numerical values for a, b, c, A and Ro have been extracted from Ref.[lO], and are listed in Tables 3(a) and (b). The parameters &,,, the overlap integrals &.M, and the covalency parameters AL,+,hold for independent Mn2”Fbonds, and are related in cubic symmetry to the molecular parameters by Aou=+jAs,&o=

$A”_A,_=,=~L

with similar relations for the y’s and S’s 3.RESULTSOFCALCULATION-HYPERFINEINTERACTIONS ANDTRANSFE~EDSPIN

DENSITIESINCtiBlC SITES

The results with V,,, = 0 are listed in Table 4a. The calculated values are too large with respect to any experimental values. They are listed on line A in Tables 4(a), (b) and 5(a), W, W. 3.2. lnjuence of the externnl potentiat We may develop the effective potential arising from the crystalline su~oundings, either around the Mn*’ ion or around each ligand. By choosing V=O at the Mn nuclei, and for V,,, the same form as for a point charge

Table 3(a). Spin orbit constants, energy vatues,fddintegralsfor a IMnF$- cluster

~

c &.MALM

LM

792

J. EMERY Table

3(b).

A

for dl M = A exp(-RIRo)

A and RO coefficients

d00 6.3381

dLn = A

exp (-

d10

dll

-2.3153

0 .a082

The above assumptions are sufficient to calculate (4 V.~P) and (xlV,,,]x) matrix elements when one neglects, in conformity with our model, the overlap between ligand orbitals, further terms giving vanishing matrix elements. For the cross-term (cp]V,,,]x) we should in principle take into account high order terms in the expression for V,,,. We assumed that:

R/Ro)

0 in A

‘Ro

(cplV&)= f SkPlVe&)+ (xlVext~x)l.

potential, one finds:

(origin at the Mn*+ ion). VcXt= v,tz

et al.

a

[B,“~Y,‘(R,)tB,‘~Y,qn,)]

(origin at the F,- ion, with the z, axis pointing towards

the metal).

Table

4(a).

Dependence

d)

ys

‘Ia

YT

on R(R

1.9

= metal-ligand

2.00552

The external potential has recently been treated in a similar way by Richardson et a/.[211 for Cr”. However this term has a limited effect on the final result, inasmuch as the approximation is not too bad, and our purpose is to estimate the main features of the influence of the external potential potential by using a simple expression for it. As a starting point we have calculated the external crystal field parameter B4’ within a point charge approximation. We have used previous calculations for the perovskite lattice[22,23], by subtracting for every site the contribution of the point charge in the complex. The

distance)

of the covalency

2.1

2.2

parameters

(y$, y<,, yn)

2.3

A

0.5075

10-l

0.4274

10-l

0.3689

10-l

0.3171

10-l

0.2733

10-l

B

0.4848

10-l

0.4088

10-l

0.3533

10-l

0.3041

10-l

0.2625

10-l

C

0.4853

10-l

0.4090

10-l

0.3534

10-l

0.3042

10-l

0.2625

10-l

D

0.4705

10-l

0.3939

10-l

0.3388

10-l

0.2908

10-l

0.2505

10-l

E

0.4699

10-l

0.3936

10-l

0.3387

10-l

0.2907

10-l

0.2504

10-l

A

0.2681

0.2670

0.2721

0.2863

0.3103

B

0.2558

0.2532

0.2563

0.2675

0.2868

C

0.2311

0.2287

0.2313

0.2406

0.2568.

0

0.2191

0.2186

0.2227

0.2334

0.2508

E

0.2380

0.2373

0.2418

0.2540

0.2739

A

0.3523

0.3516

0.5556

0.3676

0.4020

B

0.3399

0.3375

0.3394

0.3462

0.3780

C

0.3530

0.3508

0.3533

0.3633

0.3950

D

0.3530

0.3506

0.3533

0.3633

0.3950

E

0.3428

0.3404

0.3424

0.3514

0.3816 I

Superhyperfine

interactions and covalency

193

Table 4(b). Dependenceon R of the transfer parameters(A,,A,,L,) In Tables4 and 5 we take into account

as: line A : VO= Bi”= Bz’= 0;

B : VO= -0.0733,B,’ = BP = 0; C: VO= -0.0733,B,*= OBZ’= -3.663; D: Vo= -0.0733,B,@=-1.37 Bt”= -3.663: E: Vo= -0.0733,B,‘= -1.37 B?*=-0.8 R(i)

?i

b

an

1.9

2.00552

A

0.2321

0.1866

0.1523

0.121471

0.9548

10-l

E

0.2307

0.1856

0.1517

0.1213

0.9773

10-l

c

0.2315

0.1865

0.1526

0.1223

0.9697

10-l

D

0.2228

0.1784

0.1450

0.1151

0.8995

10-l

E

0.2219

0.1775

0.1440

0.1140

0.8860

10-l

A

0.4471

0.4294

0.4197

0.4184

0.4272

B

0.4357

0.4165

0.4048

0.4005

0.4049

c

0.4130

0.3937

0.3813

0.3751

0.3762

D

0.4030

0.3850

0.3737

0.3686

0.3707

E

0.4204

0.4025

0.3917

0.3881

0.3927

A

0.4926

0.4680

0.4536

0.4488

0.4683

B

0.4810

0.4547

0.4382

0.4301

0.4451

c

0.4932

0.4673

0.4514

0.4447

0.4615

D

0.4932

0.4673

0.4514

0.4447

0.4615

E

0.4836

0.4574

0.4410

0.4333

0.4486

approximation is probably valid for (q/V,,&) since the external ions are far away from the central Mn*’ ion. No important contribution of this term has been found, and it will be neglected. The point charge crystal field components at the F- ion are: V0= -0.0733, B,* = -1.37, BzO= -3.663. u.a. The corresponding calculations are listed in lines B, C and D in Tables 4(a) and (b), and S(a), (b) and (c). The dependance of yi on the overlap integral Si is represented in Figs l(atl(c). The “external Madelung potential” at the F- site, results in a decrease of the calculated values for spin transfers towards values which are in better agreement with (fs + f_ t 2fn), measured through hyperfine interactions (Table I), while f- -fir is too high in comparison with experiment (case B). The point charge electric field gradient contributes to reverse the sign of f= -f,, in contradiction with experiment (case C). The electric field at WCS Vol. 41. N&-F

2.1

2.2

2.3

the ligand contributes to admix 2s orbitals into 2pa orbitals, and mainly tends to lower fs and fm (case D). Since the point charge crystal field is a rough estimation of the effective crystal field acting on the ligand, we have fitted the parameter BZoto account for fv - f,, when R is close to 2.1 A (KMnF3 and RbMnF~). In that way our calculations account satisfactorily for all measurements of super-hyperfine interactions (Tables I, 2 and line E in Tables 4 and 5). The calculated value for _L,is too high for small distances f 1.05% instead of 0.6% at 2 .&I,in the correct range for R = 2.2 A (0.43% instead of OSO%),and is too low for higher distances. This discrepancy is not astonishing since the contact term is proportional to Ix(O)r and is very sensitive to the exact value of the wave function at the F- nuclei. As suggested by S-S, we have extended the A.O. basis by orthogonalizjng the calculated e, M.O. to the Is F- orbitals and we have recalculated As. The experimental values lie between the values calculated from the initial M.O. and from the corrected M.O. (Fig. Id).

194

J.

EMERY

In comparison with EPR or NMR data, the calculated values of fC -f,, exhibit also an increase with increasing distances from 2 A to 2.2 A. The uncertainties in the experimental values (0.1% or 0.2%) prevent a precise comparison. The total transferred spin densities are too high by 2% at 2.2A with respect to the values deduced from ENDOR and EPR. Of course, it would be possible to fit the parameters of the external field for better agreement with experiment. As a complementary comparison with experiment, we may quote the measurements of isotropic hyperfine in-

et al.

teractions at nnn F- nuclei[lS] in KM,R. Indeed in this ionic crystal, these interactions can arise from overlap of polarized 2p,, 2p,, 2s atomic orbitals centered at a nn Fnuclei with atomic orbitals centered at nnn F- nuclei. The isotropic interaction is giveo approximately by: tr a* =& A&L

+L)(sjz*>*

-2(2f,f,)“*(s~s)(sl~*~1 here S represents the effective spin, the value for Mn2+

Fig. I(a). Dependenceof y, on overlap integral S,. For A, B, C, D. E, see above.

Fig. l(b). Dependence of y,, on overlap

L__

23

I 2.2

integral S,,.For A. B, C, D, E, see above.

Ii 2 I

I

015 1 I

s,

19 R,

A

”

Fig. I(c). Dependence of yT on overlap integral S,. For A, 8, C. D. E. see above.

Superhyperfke

I 19

I 22

I 21

I 20

R,

interactions

I 2.3

A

Fig. l(d). Isotropic superhypc~oe jnteraction A, with nnn Fnuclei. (1) Experiment. (2) Calculated 3d(Mr?“), 2s (F-) basis (3) Calculated for 3d(Mn”), Zs(F-), IS (F-) basis.

Table S(a). Dependence on R

f*

f (r

f n

of the

R(f)

1.9

z.clos52

A

1.8

8

and covalency

795

being 5/2, and AI. is the isotropic superhyperfine constant. [Z*) is the 2p orbital centered on the nn F- and pointed towards the nnn F- nuclei. Is) and IS) represent the 2s orbitals respectively centered on the nn F- and mm F- nuclei. A more refined formula can be found in Ref[lS]. The experimental value is tr a* = 0.67 MHz. The calculation with our results gives tr a* =0.7MH.z. This good agreement supports our model and cannot be obtained by using the results of neutron scattering, which lead to tr a* = 0.22 MHz[lS]. To summarize, our calculations show the following points: (a) The transfer coefficients hi = Si + yi are not proportional to St, particularly for A, and A,, (Figs. I(a)l(c). This result would question the proposals of Novak and Veltrusky[9], Folen[24], Narayana[25] to estimate the covalency and overlap contribution to axial field splitting in distorted sites. (b) the even component of the field acting on the ligands has an important role, the potential at the ligand nuclei acting on the total spin transfer and the field gradient acting on fn-fo. This is a normal effect, since the mixing between 3d and 2p orbitals is driven roughly by their relative energy. In LiF: Mn”, (f,, - f,J is higher

transferred

spin densities (f$,f,,? fn)

2.1

2.2

2.3

1.16

0.77

0.49

0.30

1.77

1.15

0.77

0.49

0.31

c

1.79

1.16

0.78

0.5

0.31

5

1.65

1.06

0.7

0.44

0.27

E

1.64

1.05

0.69

0.43

0.26

A

6.66

6.15

5.87

5.83

6.08

B

6.33

5.70

5.46

5.35

5.46

C

5.69

5.17

4.05

4.69

4:72

ll

5.41

4.94

4.66

4.53

4.58

E

5.89

5.4

5.12

5.02

5.14

A

6.07

5.45

5.14

5.04

5.48

B

6.76

5.17

4.8

4.62

4.95

C

6.08

5.46

5.09

4.94

5.33

0

6.08

5.46

5.09

4.94

5.33

E

5.85

5.23

4.66

4.69

5.03

796

J. EMERY ef al. Table 1.9

Table

5(c).

5(b).

Dependence

2.00552

on

R of

j,, - j.

2.1

2.2

2.3

A

0.60

0.67

0.73

0.80

0.6

B

0.55

0.61

0.66

0.72

0.51

C

-0.39

-0.29

-0.25

-0.25

-0.6

D

-0.67

-0.52

-0.44

-0.41

-0.7

E

0.04

0.17

0.25

0.33

Dependence

on R of the total transferred

spin density

(j, + j,, + 2j,)

0.11

(see above Tables 4, for lines A. B,

C, D, E) &

1.9

2.00552

2.1

2.2

2.3

A

19.83

18.26

16.94

16.40

17.35

B

19.67

17.27

15.83

15.09

15.67

C

19.63

17.24

15.81

15.07

15.68

D

19.23

16.92

15.55

14.86

15.5

E

19.22

16.91

15.53

14 .a4

15.47

by a factor of 5 than in RbMnFj[l3]. Actually the external field gradient has the opposite sign in the rock salt lattice. From the same reason it cannot be safe to compare spin transfers in MnFZ and KMnF, (Table I). (c) Our model is not appropriate to account for diffraction intensities from the magnetic structure of MnF,. Nevertheless, it appears that neutron measurements on antiferromagnets (MnF2, CrF3, FeFX)[4,281 generally give values for fs, f<,,j,, which are lower than those obtained other techniques by (NMR, EPR, P.A.C., ENDOR). 4.

COVALENCYCONTRIBUTIONTO AXIALZEROFlELDSPLITTlNG

FOR DISTORDEDOCTAHEDRALSITES.

By following S.D.0.[27,8] we shall separate the mechanisms which give rise to the zero field splitting, into a crystal field contribution and into covalency and overlap contributions. Within the L.C.A.O. gntibonding M.O. scheme, the first involves electronic spin located in 3d A.O.‘s. The second ones involves the spin transfers, i.e. the Ai’s, yi’s, S’s to first and second order as outlined in $11, and are considered in the present paper. Until recently these contributions have been estimated by

assuming that the total transferred spin density was given by neutron scattering experiments[8,9] and driven by overlap[9,24,25]. The recent experimental evidence that the spin transfers are probably larger than the early estimates, and our calculation scheme indicates that overlap does not play a predominant role. Starting from the cubic octahedral sites in perovskites, we can in principle, generate any crystal site by changing the angular coordinates, the bond length and the external field acting on the IMn F6(4- cluster. All internal contributions, due to the geometry of the complex, could be calculated by adapting the above procedure to lower symmetry. The cost would be computer time consumption. For the sake of simplicity, we shall assume that the above calculations, relevant for a cubic complex, may reveal the trends of the dependance on bona length of the spin transfers at individual ligands in an independent bond approximation. The key function d(R,) which defines the covalency contribution has been calculated by using our results in the case of a flat external potentiel acting on the complex, and for various external fields acting on the ligands (Fig. 2). Below, we survey the consequences of our model upon the spin hamiltonian parameter D for several dis-

Superhyperline

interactions

and covalency

197

from a flat potential to a potential which differs by -0.073 U.A. at the F- site makes the value of d, decrease by about 50 10-4cm-‘. Such effects, which depend on the host, cannot be negligible in comparison with the effects which arise from the internal distortions of the complex. In K2znF4 and in KzMgF4, the octahedra in the host are contracted along the tetragonal axis, while the isotropic interaction, i.e. f$, is lower for the axial fluorines than for the equatorial fluorines[24,25]. Quite different external potentials at the two different ligand sites could contribute to this phenomenon (Table Sa) and would result in a covalency contribution to D difficult to estimate through overlap considerations[24,25]. For a trigonal distortion with Dx,, symmetry, the covalent contribution due to angular distortion may be expressed by:

I

I

I

19

20

21 R,

I 22

I

I 23

A

Fig. 2. d(R,) spin hamiltonian coefficient in the individual metalligand bond scheme. For A, B, C, D, E, see above. H and 10:calculated d(R) values (from Novak and Veltrusky). H:y, proportional to S+ = k,Si. IO: ionic model A, = SC.

torted.IMnF614mcomplexes. For a tetragonal complex the contribution of covalency to the parameter D would be: D,,, = 2[d,// - d,,] = 2 $

[R// - &I

for small distortions. From the curves in Fig. 2, one may deduce a positive contribution for an octahedron elongated along the tetragonal axis for R > 2.15 A. Such a positive contribution has been invoked to account for the experimental value of D in the tetragonal phase of RbCaFj[lO, 111.The slope of the curve does not depend on the external field acting on the ligands. Our calculations give DC,, = OM(c/a - 1) in the case of a displacive phase change. This contribution has to be added to the point charge crystal field contribution O.O8(c/a- 1) [I I] to give a calculated value DEa~C = 0.14(c/a - I) in comparison with the experimental one 0.12(c/a - I)[1 I]. Conversely, the contribution of covalency would be negative for an octahedron contracted along the tetragonal axis. This effect would be reversed for low distances, i.e. for KMgFj or KZnFs hosts, since the curves in Fig. 2 exhibit a minimum near 2.15 A. We suggest to verify the above proposals about the influence of bond lengths, an investigation of the effect of uniaxial stress along the cubic axis in the AMF, : Mn” series. The covalent contribution to D in stressed crystals would considerably change on going from KMgF, to CsCdF+ On the other hand, the covalent contribution to D can be affected by the external potential acting on the ligands. From the curves in Fig. 2, one sees that going

i.e = -18.10-“cm-’ for an angular distortion by I” from the ternary axis. Such a contribution would not be negligible in AMK:Mn” crystals stressed along the ternary axis. CONCLUSION

The recent estimate of transferred spin densities in AMF,: Mn** by EPR, NMR, ENDOR, and P.A.C conflict with the initial one obtained by neutron scattering. Within the L.C.A.O.-M.O. framework, an approximate S.C.F. calculation, similar to the one earlier used by Sugano-Shulman for Ni*+, gives results in satisfactory agreement with all measurements based upon superhyperfine interactions, when one takes into account an external potential due to the host lattice and when one assumes a weak relaxation of the host around the Mn2+ impurities. The results of the calculations, which show that overlap does not play a dominant role, are used as a basis on which to estimate the covalent contribution to axial zero field splittings. In comparison with previous work, our proposals result in a change of sign of the contribution from short distances to long distances and show the role of the external potential due to the host lattice acting on the ligands.

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