Electronic structure of the copper(II) ion doped in cubic KZnF3Lucjan Dubicki, Mark J. Riley, and Elmars R. Krausz Citation: The Journal of Chemical Physics 101, 1930 (1994); doi: 10.1063/1.467703 View online: http://dx.doi.org/10.1063/1.467703 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/101/3?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Optical studies of the uniaxial stress-induced orbital alignment of the Cr2+ centers in KZnF3 single crystal J. Chem. Phys. 144, 234310 (2016); 10.1063/1.4953798 Effects of a quantum‐mechanical lattice on the electronic structure and d–d spectrum of the (MnF6)4−cluster in Mn2+ :KZnF3 J. Chem. Phys. 90, 6409 (1989); 10.1063/1.456307 Combinations of the TOE constants of the fluoroperovskites CsCdF3 and KZnF3 measured as a function oftemperature J. Acoust. Soc. Am. 70, S89 (1981); 10.1121/1.2019103 ENDOR Study of the Unpaired Spin Density in KZnF3:Mn2+ J. Appl. Phys. 41, 1116 (1970); 10.1063/1.1658840 EPR Determination of the Nearest‐Neighbor Exchange Constant for Mn2+ Pairs in KZnF3 J. Appl. Phys. 40, 1137 (1969); 10.1063/1.1657566

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Electronic structure of the copper(lI) ion doped in cubic KZnF3 Lucjan Dubicki, Mark J. Riley, and Elmars R. Krausz Research School of Chemistry, Australian National University, Canberra, ACT, 0200, Australia

(Received 28 February 1994; accepted 6 April 1994)

The absorption and magnetic circular dichroism spectra of 1 %-3% copper(II) doped into the cubic perovskite host KZnF3 are measured over the temperature range 1.8-300 K. Sharp magnetic dipole allowed transitions 2Eg(rs)--+2T2gCr7.rS) are observed together with accompanying vibrational fine structure. The spectra are interpreted on the basis of a tetragonally elongated Cu~- ground state geometry which arises from strong lahn-Teller coupling. This results in a statistical distribution of three equivalent elongations which can undergo reorientation on the electron paramagnetic resonance time scale. The lahn-Teller coupling within the 2T2g multiplet is partially quenched by spin-orbit coupling and the lowest Kramers doublet r7 has an octahedral geometry, while the higher lying r s state has a small tetragonal distortion. This system presents an excellent opportunity to study the spectroscopy of the copper(II) ion in a cubic environment.

I. INTRODUCTION

It is well known that in six coordinate copper(II) sys­tems, the ground state electronic structure is strongly coupled to the geometry of the complex. 1 The geometry obtained from crystallography can be used to draw conclusions about the ground electronic state. Conversely, the study of the elec­tronic structure by electron paramagnetic resonance (EPR) or optical spectroscopy can be used to draw conclusions about the molecular geometry. These latter methods, as well as being complimentary to crystallographic studies, have the advantage of acting on a much faster time scale. The spec­troscopic measurements probe the local environment of the metal ion, whereas the crystallographic study is of the bulk solid and can be complicated by twinning, antiferrodistortive ordering or random disorder.

The geometry of a complex is driven by the ground state electronic structure, but in the crystal, one has to also con­sider packing and cooperative interactions. The spectro­scopic study of K2CuF4 clearly reflects the antiferrodistortive ordering of tetragonally elongated octahedra,2 although early crystallographic (and optical) studies were interpreted in terins of compressed octahedra. The effects of cooperative interactions can be minimized by doping the Cu(II) ion into a host lattice, but the complex is then only amenable to spec­troscopic studies and the electronic properties must then be used to infer the geometry. Optical spectroscopy has the ad­vantage of offering information about the geometry of the excited electronic states.

We have recently reported the EPR3,4 and optical5- 7

spectroscopies of a series of Cu~- complexes in doped crystals. In these cases, the Cu(II) complex adopted a tet­ragonally compressed geometry, which was a result of a te­tragonal compression imposed by the host lattice. We now extend our studies to the case of the Cu(II) ion doped into the cubic perovskite lattice of KZnF3. Sharp magnetic dipole origins were found in both the absorption and magnetic cir­cular dichroism (MCD) spectra. These can be interpreted in terms of simple expressions for the g values and magnetic dipole transition strengths obtained from ligand field theory. The present study indicates that the Cu~- complex adopts a

tetragonally elongated geometry in the ground electronic state. The lowest component of the excited 2T2g multiplet is essentially octahedral, while the higher component has a small tetragonal elongation.

II. EXPERIMENT

Large single crystals (5X5X 10 mm3) of KZnF3 doped with nominal 1 % to 3% Cu(II) ions were prepared by Guggenheim by using the Bridgeman technique. KZnF3 has the classic perovskite structure,s where the zinc ion is coor­dinated to six equivalent F- ions which form a net of comer sharing octahedra. The Zn-F bond length is 202.9 pm, while the mean Zn-F bond lengths of five reported compounds4

containing the ~- complex range from 203 to 204 pm. It has been shown from EPR studies9 that cooperative interac­tions between the copper centers are absent at these low Cu(II) concentrations. The experimental details for the mea­surement of MCD, absorption, and fluorescence spectra have been discussed elsewhere.3,7

III. RESULTS

The absorption and fluorescence spectra of Cu(II)lKZnF3 are shown in Fig. 1. The lowest energy sharp line in absorp­tion is resonant with the highest energy line in emission and is therefore a zero phonon origin. Hence the fluorescence is from the metal centered excited state, one of the few ex­amples known for a Cu(U) ion.7 The fluorescence lifetime was found7 to be 1.8±0.1 JLs.

Figure 2 shows the MCD together with the absorption spectrum. The sharp magnetic dipole origins and the accom­panying vibrational fine structure are better resolved in the MCD spectrum. The relevant experimental data and the spectral assignments are collected in Table I. These assign­ments are justified in the following sections: The magnetic dipole origins, although relatively sharp for a Cu(II) com­plex, still have half-widths of the order of 10 cm -I. This is due mainly to inhomogeneous broadening caused by crystal imperfections. Additional broadening occurs in the presence

1930 J. Chern. Phys. 101 (3), 1 August 1994 0021-9606194/101 (3)/1930/9/$6.00 © 1994 American Institute of Physics

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Dubicki, Riley, and Krausz: Spectroscopy of Cu(lI) doped in KZnF3 1931

.----r----,-----,--..----.----.---.--~ 0.2 TABLE 1. Spectroscopic data for KZn(Cu)F3 ·

t i!;-

j

/\ 0.1 -l

J L-_...L.._-L_---lL--_.L..._-L_---L __ L---.J 0.0

12000 Wavenumber [em"]

~

FIG. I. The absorption and fluorescence spectra of Cu(II)IKZnF3 at 4.2 K.

of a magnetic field because of the anisotropy of the g values and the fact that the spectra are a superposition of axial and transverse species (see Sec. IV F).

Figures 3 and 4 show the temperature dependence of the MCD spectra. The two magnetic dipole origins display a different temperature dependence which leads to unambigu­ous assignments. Figure 5 shows a more detailed view of the vibrational fine structure built on each origin.

IV. DISCUSSION

A. EPR spectrum

In cubic hosts, six coordinate Cu(II) ions always adopt a geometry of lower symmetry due to the Jahn-Teller effect.' The lower geometry adopted is overwhelmingly a tetrago­nally elongation, with there being only one apparent example lO of a tetragonally compressed geometry for Cu(II) ions in a cubic host. At a cubic site, the ground electronic

0.15

0.10

I 0.05 <

C! 0.0 0

~ ~ ..

0 9

6000 8000 10000 12000

Wavenumber [em"] _

FIG. 2. The absorption (8 = 0 T) and MCD (8 = 5 T) spectra of Cu(II)IKZnF3 at 1.8 K. The light and applied magnetic field are directed along the (001) direction. No signals were resolved to lower energy down to 2000 cm- I .

Origin Assignment (cm- I)

r B(Eg) ..... r 7(T2g )'It 3 6829 --> r B(T2g )'It 1> 'It 2 8129

Mr. M =-2.2

r7 r7(T2g) ..... rB(Eg) 6829

AAIA

-1.1 +1.6

Ar. A =1.4

r7

Franck-Condon maxima (cm- I)"

7600 9500

6150

Half-width (cm-I)b

2000 4000

"The uncertainty in the energies is ± 100 cm- I for the broad bands and ±2 cm -I for the sharp lines.

bHalf-width=full width at half-height.

state of six-coordinate Cu(II) is nominally r 8 e E g ,t~e3). Here the symmetry labels of Bethell and Mulliken'2 are used to describe the spin-orbit and orbital electronic states, re­spectively. This state is subject to a large Jahn-Teller cou­pling to the e g vibration, the displacements of which are shown in Fig. 6(a). Formally, a r 8 state can also couple with a t2g vibration, but this coupling will be negligible compared to the e g coupling because of the E g orbital nature of the ground r 8 state. This is not so obvious for the excited r8 '2 ( T2g ) electronic state (see Sec. IV C).

The X band EPR spectrum of CU(II)/KZnF3 is isotropic down to -20 K, below which the spectrum becomes aniso­tropic with g values characteristic of a tetragonally elongated geometry.9,13 The g values at 4.2 K measured9 on single crys­tals are gil = 2.569 and g 1. = 2. 141. The isotropic spectrum above 20 K arises from reorientation between the equivalent minima with an elongated geometry on a faster time scale compared to that of the EPR. Table II collects the experimen­tal EPR data for both tetragonally elongated and compressed

8000 Wavenumber [em"]

9000

FIG. 3. The temperature dependence of the (001) MCD spectrum of Cu(II)IKZnF3 with an applied magnetic field of 5 T. Note that the spectrum at 40 K has been multiplied by a factor of 5.

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1932 Dubicki, Riley, and Krausz: Spectroscopy of Cu{lI) doped in KZnF3

B=5T

IM = 0.005

\~ ~ ----......_--=2:;;:0::.:K'--_1

6800 6850 6900 8100 8150

Wavenumber [em"] _ 8200

FIG. 4. The temperature dependence of the (001) MCD spectrum of the magnetic dipole origins with an applied magnetic field of 5 T.

Cu~- species together with the metal fluoride bond lengths. The host lattice principally determines the sign, not the mag­nitude, of the ground state distortion.

The g values for an elongated complex with a 'IJI xL y2

ground state are given to third order by2

gll=ge+8kllvll-(ge+kll)vi - 4kol VIIVol,

- + 2k' 2 2 12k 2 gol -ge olVol - gevll-igeVol + IIVol (1)

whereg e =2.0023, VII = kUAo1Exy, Vol = k~AOIExZ'yz' and Exy and ExZ,YZ are the vertical Franck-Condon energies for the transitions 2EgCZB\)--+2T2i2B2) and 2T2i2E), respec­tively. The prime on k' indicates that the orbital reduction parameter connects e g and t 2g orbitals, while k is the orbital

1.8K ~~U ~U~ B =5 Tesla

A

~~ V~,

.§'i~.~_/\I/ 7000 7500 8000 8500 9000

Wavenumber [em"] _ 0

FIG. 5. The (001) MCD spectrum at 1.8 K and 5 T showing the vibrational fine structure based on each origin.

b)

FIG. 6. (a) The ligand displacements for the Qu and Q. components of the lahn-Teller active eg vibration of a ML6 complex. (b) A combination of the t2g vibrations of a ML6 complex which leads to a trigonal geometry.

reduction factor acting within the t 2g orbitals. We use the common approximation A;=k;AO' where AO (=830 em-I) is the free ion spin-orbit coupling for the Cu(II) ion. 14

In the above expressions, the g values are insensitive to the orbital reduction parameter k compared to k'. A much more accurate estimate of k can be obtained from the energy separation of the magnetic dipole origins of the 2 T 28 mUltip­let. This is described in the following section where the cubic parameter k is estimated to be -0.95.

If we use k=0.95, k' =0.84, and the experimental tran­sition energies then Eq. (1) gives an excellent fit to gil' but the calculated value of gol -2.09 is significantly smaller than the observed value of 2.14. Similar results are obtained from a diagonalization of the full d9 ligand field matrix, indicating that Eq. (1) is an accurate approximation to the static model. The inclusion of tetragonal anisotropy in k' does not resolve this problem as an exact fit requires kll - 0.84 and the unreasonably high value of k~ - 0.98.

TABLE II. The EPR parameters, metal fluoride bond lengths, and Franck-Condon transition energies of copper(II) in several fluoride hosts.

Host R (pm) g~a gJ. Exy (cm-')b E xz•yZ (cm- I ) Reference

KZnF3 203{x6) 2.569 2.141 7600 9500 10 K2CuF4 222(x2)

193(x2) 2.47 2.08 9420 12140 2,14 194{X2)

K2ZnF4 202(X2) 2.003 2.387 10700 -8750 3,4 203(x4)

Ba2ZnF6 196(X2) 1.992 2.367 -13 000 9500 5,6 205(x4)

"All g values were measured at 4.2 K except for K2CuF4 (77 K). bEXY and Exz•yZ are the Franck-Condon energies for the electronic transi­tions to the 2T2geB2) and 2T2geE) states, respectively. The ground state is 2EeB I ) for tetragonally elongated and 2EeA I ) for tetragonally com­pressed copper(II) ions.

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Dubicki, Riley, and Krausz: Spectroscopy of Cu(lI) doped in KZnF3 1933

Since the EPR becomes isotropic9 above 20 K, the bar­riers between the tetragonal minima are small. The potential energy surfaces near the minima should then be fairly shal­low and zero point motion of the Q E vibration may mix some 'I' z2 into 'I' xL y2, thereby raising g1. and lowering gil' A small vibronic mixing will significantly alter the calculated value of k ~ . A detailed vibronic analysis is beyond the sub­ject of this paper. We neglect the tetragonal anisotropy in k' and interpret the g values for Cu(II)/KZnF3 by using a k' of 0.85.

However, it should be noted that Eq. (1) works very well for K2CuF4 , where there is a larger static tetragonal distor­tion. In this case, both g values can be fitted accurately with k' =0.84. A similar situation occurs in compressed Cu~­chromophores. For the strongly compressed Cu(II)lBa2ZnF6,6 the analog of Eq. o? gives a good fit to both g values with k' =0.86. However, for Cu(II)IK2ZnF4 ,

where the host compression is smaller, the static model can­not explain the observed gll=2.003. A small vibronic mix­ing of 'l' xLy2 into 'l' Z2 has been invoked3 to account for this larger than expected value.

B. SpIn-orbit splitting of the 2 T2g multiplet

In the absence of vibronic coupling, the 2Eg-+2T2g tran­sition of Cu~- in octahedral symmetry is split by spin-orbit coupling into r~-+r7' r~ transitions. The energy interval be­tween these transitions is given by

~Ea= E(r~) - E(r 7) = H[(~o+ A/2)2+6A '2]112_ ~o

+5A/2}. (2)

The parameter ~o represents the cubic ligand field splitting of the e g and t 2g orbitals in the absence of Jahn-Teller cou­pling. This is given by ~o = 3e u - 4e 1T in terms of the angu­lar overlap (ADM) parameters, I where 3 e u and 4e 1T repre­sent the anti bonding energies of the metal e g and t 2g orbitals, respectively. A is the spin-orbit coupling constant for t2g spin orbitals, while A' is the spin-orbit coupling between eg

and t 2g orbitals. There is no tetragonal anisotropy in the A values as Eq. (2) applies to the complex at octahedral sym­metry. Unlike the g values in Eq. (1), ~Ea is more sensitive to k than to k' . Figure 7 shows the calculated splitting ~Ea for various values of k as a function of ~o. Here k' is fixed at the value (0.85) determined in Sec. IV A. The horizontal dotted line is at the observed magnetic dipole energy separa­tion, which is seen to be much larger than 3/2 A, which is equal to ~Ea if spin-orbit coupling between the ground (r~) and excited (r~) states is ignored.

Another experimental quantity of interest is the energy difference between the excited r 7 state and the ground r~ state in the octahedral limit

- 5AI2}. (3)

Since we are dealing with the ligand field parameters at the undistorted octahedral geometry of the 2T2g state, the value of I1Eb can be obtained from the luminescence spectra

1500

1400

'"5 k= 1.0 "' .... 1300

~ 1200

1100

10000'-'--'--'---'-50 ..... 0-0 -'--'--'--'-10-'0-00-'--'--'--'-1-1

5000

FIG. 7. The spin-orbit splitting tJ.Ea of the r7 and r~ states of Tzg parent­age as a function of the octahedral ligand field tJ.o using Eq. (2), h' =706 em-I, and h=kX830 em-I. The observed splitting for Cu(II)lKZnF3 and the expected 312 A splitting for a 2T2g state noninteracting with the 2Eg

state, are indicated by horizontal dotted and dashed lines, respectively.

rather than the absorption spectra. The observed lumines­cence maximum at 6150 cm- I will overestimate this energy difference as this maximum corresponds to the Franck­Condon overlap with the lower branch of the Jahn-Teller potential energy surface. I1Eb is estimated to lie in the range 5250-5600 cm- I and we use ~Eb_5400 cm- I in our cal­culations.

Inserting ~Ea= 1300 cm- I, ~Eb=5400 em-I, and A'=706 em-I into Eqs. (2) and (3), we obtain ~o=6100 cm -\ and k = 0.95. The above value of ~Ea is likely to be an underestimate as the r~ state is subject to a weak r 8 ® e g

Jahn-Teller coupling (Sec. IV C), but the correction is ex­pected to be small.

The cubic anisotropy k' < k reflects differential cova­lency in the metal-ligand bonds. The covalencies of the t 2g orbitals is expected to be small as they participate only in 7T

bonding which is considerably weaker than the a- bonding of the e g orbitals. Similar conclusions were reached in the op­tical study of Cu(II)lBa2ZnF6.6

In summary, the analysis of the g values, the transition energies of the magnetic dipole origins, and the lumines­cence spectrum provide the following parameters: ~0=6l00 cm- I , k=0.95, k' =0.85, A=790 cm- t , and A'=705 cm- I. If the tetragonal anisotropy in k (and hence Xo) is neglected, then these parameters should apply unchanged to the equi­librium geometries of rL r 7 , and r~. The tetragonal ligand field parameters of these states will, of course, be different.

c. Excited state distortions

The states of the 2T2g multiplet are subject to the com­peting effects of spin-orbit and Jahn-Teller coupling. The Jahn-Teller coupling can occur with both the e g and t 2g vibrations as shown in Fig. 6. It is well established from the EPR evidence that at low temperature, the ground state of the complex has a tetragonally elongated geometry. We tum now

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1934 Dubicki, Riley, and Krausz: Spectroscopy of Cu(lI) doped in KZnF3

to the question of the excited state geometry at the electronic origins, which is determined by the minima of the potential energy surfaces.

Neglecting spin-orbit coupling, the T 2/i9(e g + t 2g ) Jahn-Teller coupling can result in either three equivalent minima at a tetragonal geometry or four equivalent minima at a trigonal geometry. With spin-orbit coupling, 2T2g splits into f 7 and f 8 states. In order to interpret the electronic fine structure, we examine the simplest model where the spin­orbit splitting of the f 7 and f 8 states partially quenches the T 2/i9(e g + t2g) Jahn-Teller coupling. This gives an vibroni­cally inactive f7 state and an isolated f8®(e g+t2g) Jahn­Teller problem.

The first-order Jahn-Teller coupling constants (A I) can be defined from the one electron matrix elements given by Baccil5 in terms of AOM ligand field parameters

A I (T2®t2)=-( g/:;, /17)=- 2~1T. (4)

Here the coupling constants refer to states rather than orbitals and we follow the normal phase conventions given, e.g., by Ham. 16 If we assume that the antibonding energy of the 3d orbitals varies as the inverse fifth power of the bond length,17 then

10 e 1T A I (T2®e)= --;;3 Ii . (5)

The coupling constants of the f 8®(e g + t 2g ) problem can be related to that of the T 2g ® (e g + t 2g) problem by

A I (f 8®e)= 1I2A I (T2®e), (6)

A I (f 8®t2)= 1Ij3A I (T2®t2)' (7)

We achieve this by transforming the electronic basis of the T 2g state into a cubic basis with either tetragonal (for f 8 ® e) or trigonal quantization (for f 8®t2).11 The minimum of the potential energy surface is determined only by the magnitude of these coupling constants and is given by the ratio of the Jahn-Teller stabilization energies l8

_ Ai(f 8 ®e) /Ai(f8 ®t2 )

17- 2K 2K' e t2

(8)

where Ke and Kt2 are the force constants of the e g and t 2g vibrations, respectively, in units of cm -I pm -2. Tetragonal minima (distortion along e g) exist for 17> 1 and trigonal minima (distortion along t 2g) for 17<1. By taking into ac­count the reduced masses for e g and t 2g vibrations, this con­dition is found to be dependent only on the frequency

17=25( :::r. (9)

Hence the t 2g vibrational frequency must be one-fifth the frequency of the e g vibration for there to be trigonal minima. This is most unlikely, and in what follows, we assume that the equilibrium geometry of the f 8 excited state has minima

along tetragonal rather than trigonal directions. Interestingly, the same conditions as given by Eq. (9) apply in determining which type of minima exist in the T 2g ® (e g + t 2g) problem. Furthermore, from Eqs. (5) and (6), it can be inferred that the displacement along the e g vibrational coordinate (Q e) is positive, as in the ground state, and the elongation is given by

o 5 e 1T -3 -2 1 Qe(f8)=~-R-(1.722XIO Xhve ) -, (10)

,,3 Cu-F J.L

where e 1T and h ve are given in cm -I, R and Q~(f 8) are given in picometers, and J.L is given in atomic mass units. There is no displacement along the other component of the e g vibrational coordinate (Q E)' A tetragonal elongation in the f 8 excited state is confirmed from the MCD data shown in the following section.

D. Intensities

The magnetic dipole strengths can be calculated from perturbation formula by using the symmetry adapted D 4h

wave functions constructed from the coupling coefficients of Koster et at. II These are given in the Appendix. The three states that arise from the T 2g multiplet are labeled qr I' qr 2'

and qr 3' which are in descending energy order for a tetrago­nally elongated complex. At low temperatures, the EPR in­dicates that the tetragonally elongated geometry occurs ran­domly along the three equivalent cubic directions. The experimentally determined magnetic dipole absorption A and magnetic circular dichroism aA will then be due to 1/3 axial and 2/3 transverse D 4h Cu~- centers

A=t(Aax+2Atr), aA=t(aA ax +2aA tr). (11)

The A and aA values are proportional to the magnetic dipole strengths M and aM, respectively, where

M.B=~«m_)~+(m+)~) aM.B=(m_)~-(m+)~ (12)

[in the first half of Eq. (12) the factor of 2 has been inadvert­ently omitted in Eq. (8) of Ref. 2] and

(m:t)ax=('I'~1 += fz(mx±imY)I'I'~),

(m:t)tr=('I';1 += fz<my±imz)I'I'~). 'I' g and 'I' e denote the ground and excited states, respec­tively, ma=kala+8sSa is the magnetic dipole operator, and the wave functions are quantized along z for axial chro­mophores (Bllz) and quantized along x for transverse chro­mophores (Bllx).

Figure 8 shows the calculation of M and aM for a range of parameters appropriate to the present problem. The dotted and full lines represent the results using perturbation formu­las (given in the Appendix) and exact diagonalization, re­spectively. As can be seen, the perturbation formulas are valid for the range of parameters under investigation. The calculations in Fig. 8 were made with the parameters k=0.95, k'=0.85, ao=6100 cm- I , and ae =5500 cm- I ,

so that there is always a qr xL y2 ground state, while the tetragonal field of the 2T2g state at is allowed to vary. The tetragonal parameters ae and at are the one electron tetrag-

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Dubicki, Riley, and Krausz: Spectroscopy of Cu(lI} doped in KZnFa 1935

1.0

0.5 '" '" 'P~'

~ 0.0 ---

<l -0.5

-1.0

-1.5 -4 -2 o 2 4

1.5

1.0

~

0.5

'PI 0.0

-4 -2 0 2 4

2 '. '. 'P2 ' •••

~ -- a ~ 'P3

-1 'PI

-2 -4 -2 a

~/')... 2 4

FIG. 8. The calculated absorption and MCD magnetic dipole strengths av­eraged over one axial and two transverse chromophores displayed as a func­tion of the tetragonal field il, for the 2T2g multiplet. This can also be viewed as a function of the tetragonal coordinate Q 8' The dotted and full lines are from perturbation expressions in Table III and Eq. (A2), and exact diago­nalization. respectively. The parameters k=O.95, k'=O.85, r=O.l, ~r=5500 em-I, and .io=6100 cm- I have been used. The values of il, for the equilibrium geometry of qr 3(il,-O) and qr 2(il,- >..) are indicated by vertical lines.

onal splittings of the e g and tZg orbitals, respectively, !::.(,=E(x2 _ y 2)-E(Z2) and !::.t=E(xy)-E(xz,yz).

The ratio !::.MIM in Fig. 8 is equal to !::.AIA and is decisive for assigning the transitions in the present case. While A and !::.A of the origins depend on the vibrational overlap between the ground and excited states, the quantity !::.AIA is independent of these factors. The lowest energy origin has !::.AIA = -1.1 and the higher energy origin has !::.AIA = + 1.6, which from inspection of Fig_ 8(c) must be assigned to the transitions 'I' xL y2-t 'I' 3 and 'I' xL y2-t 'I' z, respectively. Furthermore, the 'I' 3(f 7) state must have a near zero tetragonal field, where !::.AIA reaches the minimum value of - 1.0_ The '1'2 component of the f 8 excited state has a positive tetragonal field of !::.,1'A~ 1.0_ The values of !::.,I'A which fit the !::.AI A of the qrz and '1'3 origiI).S are indicated by the vertical lines in Fig_ 8_

E. Vibrational reduction parameters

The calculated values of M zi M 3 = 0.58 and !::.M21!::.M3= -0.93 can be taken directly from Fig. 8. These differ from the observed values 1.4 and -2.2, respec-

tively, given in Table L In both cases, they differ by the same factor of -2_5 which will be equal to the ratio of the vibra­tional reduction factors Rzi R3 • These vibrational reduction factors are equal to the square of the vibrational overlap be­tween the lowest vibrational levels in the ground and excited states_ We now make the assumption that these reduction factors are due to a different relative displacement along the e g vibrational coordinate (Q 0) alone. This assumption then implies that the displacement along the a 1 g coordinate is identical for both 'I' z and '1'3 states.

Since a good estimate of the ground state geometry can be made and the geometry of the '1'3 excited state is close to Oh' the RzIR 3 value can be used to estimate the '1'2 excited state geometry. The ground state Jahn-Teller distortion of CuF;l- in pure compounds is typically in the range 35-40 pm. 14 These values should be larger than what one might expect for an isolated CuF;l- complex as the pure com­pounds will have cooperative interactions. However, if Q~= 35 pm is taken for the 'I' xL y2 ground state and Q~= 0 for the '1'3 state, the ratio of the vibrational reduction factors requires Q~= 1.6 pm for the equilibrium geometry of the '1'2 excited state. This value is calculated from the Franck­Condon overlap factors and using 300 cm -1 as the frequency of the effective e g vibration and 19 amu for the reduced mass. Thus a small difference in the geometry of the '1'2 and '1'3 excited states results in a significant difference in their vibrational reduction factors R 21 R 3 =. 2.5.

It is interesting to compare this crude estimate for Q~ with that predicted by Eq. (10) in Sec. IV C. If we use e

7T= 1000 cm- I and RCu_ F =203 pm, then Eq. (10) gives

Q~= 2.8 pm. It must be remembered that Eq. (10) is also a crude approximation as it assumes r 8 Q9 e coupling in isola­tion. Both these values are likely to be smaller than the real value for Q~ as the experimentally determined value of !::.AI A= + 1.6 for qrz gives !::.t-'A which implies a larger distor­tion than the above estimates_

A third sharp origin belonging to the transition to the '1'1 state does not appear in the spectrum. Besides having the weakest calculated magnetic dipole strength, it would be ex­pected to be further reduced as the minimum Q 0 is even further displaced from the ground state. However, this minima along Q 0 will actually be a saddle point in the Q 0- Q E coordinate space, separating two minima with "'1'2

type" electronic properties. In fact, like the 'I' z2 wave func­tion of the r 8 ground state, there is no well-defined minimum corresponding to a '1'1 electronic state in the f 8 excited state. The accompanying vibronic structure may have mixed '1'1 and '1'2 electronic character, but a definite assignment to a '1'1 state is not possible.

Collecting the results of this section, one can draw a schematic potential energy surface for the Cu(II)lKZnF3 sys­tem with respect to the Q 0 vibrational coordinate. This is shown in Fig. 9. The sharp origins are shown as the vertical arrows terminating in the horizontal lines. The vibrational structure of the spectrum shown in Fig. 5 is due to overlap of the lowest vibronic level of the ground state with higher vibronic levels of the Jahn-Teller active e g vibration in the excited states as well as transitions due to a displacement with respect to the totally symmetric stretch coordinate. The

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1936 Dubicki, Riley, and Krausz: Spectroscopy of Cu(II) doped in KZnF3

-4 o 4 Qe (dimensionless)

FIG. 9. The schematic potential energy surfaces of the Cu~- complex in KZnF3 as a function of Q 8 as determined from spectroscopic measurements. The vertical arrows indicate the Franck-Condon maxima in the absorption and emission spectra, while the horizontal dotted lines indicate the observed magnetic dipole origins. The r j notation refers to the system at 0 h symme­try (Qo=O), while the 'l'i notation is more appropriate to the tetragonal field at large values of Q 8 •

'I' x2 _ y2 -+ 'I' z2 transition was not observed and is expected to be extremely broad in the region -5500 cm- I as indicated in Fig. 9. We could not distinguish this transition from the background using our samples. We are certain that it lies substantially below the r7 origin at 6829 cm- I as (i) even with a large static distortion in a pure compound such as K2CuF4 , the transition is below the T2g state; and (ii) the complex would not be expected to luminesce from the r 7('1' 3) state if the state there were an electronic state below close in energy.

F. Llnewidths

The magnetic dipole linewidths are of the order 10 cm- I . This unfortunately obscures the splitting of the sharp origins in an applied magnetic field which are calculated to be of the order -5 cm -I at 5 T. The splittings arise because there are tetragonally elongated Cu~- octahedra oriented both axially and transversely with respect to the incident light. The magnetic dipole amplitudes are given in the Ap­pendix [Eq. (A2) and Table IV]. The M and AM parameters averaged over the axial and transverse species are given in Table III. The expressions for the g values derived from the wave functions (AI) have been given elsewhere (Table IV in Ref. 2).

It is now a simple matter to simulate the MCD spectra of the sharp origins and a schematic version is given in Figs. 10 and II, where the half-widths of the Gaussian line shapes are assumed to be 5 cm -I. Figure 10 shows that the negative AM observed for the '1'3 origin is due mainly to the trans­verse species. Furthermore, the Zeeman splitting between the

TABLE m. The magnetic dipole absorption and MCD parameters averaged over one axial and two transverse chromophores.a

Transitionb M 11M I1MIM

'I' xLy2--+

1-<2ai) 1-< -2ai) '1'1 -1

'1'2 1-<2a~+b~) 1-<2a~ + 4a2b2) 2a~+4a2b2 2a~+bi

'1'3 1-<2aj+bj) t(2aj + 4a3b3) 2a~+4a3b3 2a~+b~

'The parameters a j and b i are given by Eq. (A2) in the Appendix. ~is table applies to the saturation limit where 'I' xL y2 - is 100% popu­lated.

negative and positive signals is very small (-0.5 cm -I). Consequently, as the temperature is raised, the MCD of '1'3 remains a single band with rapidly decreasing intensity (Figs. 3 and 4).

Figure 11 shows that the transverse species also domi­nates the MCD of the '1'2 origin. In this case, gxC'I' 2) has a positive sign and the splitting between the positive and nega­tive absorptions is [gxC'I' 2) + gxCx2- y2)]JLBBx-6.4 cm- I. Hence as the temperature increases, the transitions from 'I'~Ly2± are resolved.

~

Axial (B II z)

f'i'3-

I I I I I I

'i'3+

'i' ,...y'+

'i'x·.y'_

Transverse (B II x)

1.0 +---'---...... -.....".-:--:!= ... ~-...... --...... --+ '" , '" , ~ O.S

~ '" '" '" " '"

.E 0.0 .... ..::::=-OO:::::::~-------=:-w;;;::~ ... t! ~ -0.5

-1.0 +----..---r--~=--.---._-_+

-6 -2 o 2 4 6

Wavenumber [em' I]

FIG. 10. The calculated Zeeman splitting and circularly polarized magnetic dipole strengths for the 'I' xLy2-+'I' 3 transition. The Gaussian line shape has a half-width of 5 em-I, and g,('I' 3)=gx('I' 3)- -1.93. Expressions for the g values of '1'3 and '1'2 are given in Ref. 2. The 11M magnitudes are multi­plied by 1/3 and 213 for axial and transverse species, respectively, as in Eq. (11).

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Dubicki, Riley, and Krausz: Spectroscopy of Cu(II) doped in KZnF3 1937

Axial (B II z) Transverse (B II x)

1.0 +---"---'----''----'---...... --+ Transverse

-1.0 +----r---.----.r--....... --.__--+ -6 -4 -2 o 2 4 6

Wavenumber [cm·I ]

FIG. II. The same as for Fig. 10, except for the 'I' xL y2-> 'I' 2 transition. The g values are g,(qr2)--1.9 and gx(qr2)=0.6.

V. CONCLUSIONS

The absorption, MCD, and fluorescence spectra of cop­per(II) doped into cubic KZnF3 crystals provides information on the equilibrium geometry of the ground and excited elec­tronic states. The f 8 ground state undergoes a large Jahn­Teller distortion which results in three minima at a geometry of a tetragonally elongated octahedron. The temperature de­pendence of the MCD shows that on the time scale of elec­tronic transitions, the octahedra remain localized. The statis­tical distribution of 113 axial and 2/3 transverse oriented species with respect to the (00l) direction provides a simple explanation for the absorption and MCD spectra.

The equilibrium geometry of the 2T2g(f 7) state is octa­hedral. Luminescence to the ground state will overlap into all three ground state minima and random crystal strain which make each minimum slightly inequivalent will then localize the complex at a strongly elongated geometry. The equilib­rium geometry of the higher 2T2g(f 8) state has a small te­tragonal elongation.

The detailed understanding of the optical processes in Cu(II)/KZnF3 gained in the present study allows one to speculate on various optical devices. For example, selec­tively exciting the origin of the 'I' XLy2(f 8)--+2T2g(f 7) tran­sition with a narrow band laser preferentially excites trans­verse species. (As shown in Fig. 10, excitation into the lower energy edge of this origin in a magnetic field can exclusively excite the transverse species.) The relaxed geometry of the f 7 state is octahedral and the complex will have equal prob­ability of the 'I' XLy2(f 8)+-2T2g(f 7) decay ending in one of three equivalent tetragonal elongations. Therefore, in one absorption/decay cycle, there is 113 probability of the trans­verse species converting to an axial species. Continuous ex-

TABLE IV. The magnetic dipole amplitudes for the transitions

'I' xLy2-> 'I' 1.2.3'

'III '1'2 '1'3

('I' g:t Imxlqri:;:)a al a2 a3 ('I' g:tlmylqr I:;:) ±ia l +ia2 +ia3 ('I' g:tlm,lqrj:t) ±b2 ±b3 ('I' g:t Im:;:axlqrj:;:) ±v'1a l

('I' g:t Im:taxlqr i:;:) :;::v'1a2 :;::v'1a3

('II;:!: I m :!:trlqri:;:) 1 1

1 .fi (a2 + b2) 1 .fi (a3 + b3)

qr;:tlm:;:trlqri:;:} 1 1

-I .fi (a2- b 2) -I-(a -b3) .fi3

a All functions are quantized along the molecular z axis except where indi­cated.

citation in this manner will bleach the sample with the end result being a portion of the crystal having Cu~- species oriented axial to the incident laser.

Such an experiment could be used to study the tempera­ture dependent relaxation rate of the oriented sample. Alter­natively, three orthogonally aligned lasers could be used to switch between the three possible orientations. The EPR, ab­sorption, and magnetic circularly polarized spectra form a coherent picture of the behavior of copper(II) ions in a cubic environment, which is understood from a simple ligand field viewpoint.

ACKNOWLEDGMENTS

The authors wish to thank Professor H. Bill (University of Geneva) for communicating his results on the single crys­tal EPR of Cu(II) doped KZnF3'

APPENDIX: SECOND ORDER MAGNETIC DIPOLE AMPLITUOES FOR 2 Eg(1If xLy2)--+2T29(1If 1,2,3)

TRANSITIONS

The wave functions derived2 from the D 4 coupling co­efficients of Koster et al. 11 are convenient for a perturbation treatment of the magnetic dipole strengths. They are given here in complex tetragonal form

'I' I::!:(f 6)= ::til += 1I2X:;:),

'l'2::!:(f7)=+=i(cos el::t1l2Xo)+sin el+=1I2X::!:», (Al)

'l'3::!:(f7)=+=i(-sin el::t1l2Xo)+cos el+=1I2X::!:»,

where Is Msf M) are the nine-electron functions

1 1+= 1I2X::!:) = +=12 (I += 1/2yz)::til += lI2xz»,

l::t 1I2Xo) = l::t 1I2xy),

and

l-l12yz) = IYZ(xZ)2(xy )2(Z2)2(x2_ y2)21,

and tan(2e)=v'1A/(A/2-At ).

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1938 Dubicki, Riley, and Krausz: Spectroscopy of Cu(lI) doped in KZnF3

The matrix elements of the magnetic dipole operator are given in Table IV. All functions are quantized along the mo­lecular z axis except where indicated. For Bllx, the wave functions which diagonalize the Zeeman Hamiltonian are 'It~ = ( 1I\I'1)('l' :!: ± 'It =t,)

If the tetragonal anisotropy in the orbital parameters is neglected, then the parameters for the magnetic dipole am­plitudes (Table IV) are

1 al = -12 [k' - r(k-l)],

1 a2= -12 {k' s- r[2c.)2+s-k(s+cI .)2)]},

1 a3= -12 {k' c- r[c- 2s Ii-k(c-sf Ii)]}, (A2)

bl=O, b2=-2ck'+rs(2+k)fli,

b3 = 2sk' + rc(2 + k)f.)2,

where s=sin 8, c=cos 8, and r is an average mixing coeffi­cient between t2g and e g orbitals r= A' f[E(t2g) - E(e g)]av. More complex expressions which do not assume this average are given in Table VII of Ref. 2. In the octahedral limit, where s = ..[1i3 and c = ~2f3, b3= -2a3 and v1 al +a2

= b 2 . The latter relationship is consistent with the fact that the magnetic dipole allowed r 8--+ r 8 transition requires two independent parameters.

I D. Reinen and C. Friebel, Struct. Bonding 37, I (1979). 2M. J. Riley, L. Dubicki, G. Moran, E. R. Krausz, and 1. Yamada, Inorg. Chern. 29, 1614 (1990).

3 M. 1. Riley, M. A. Hitchman, and D. Reinen, Chern. Phys. 102, II (1986). 4M. J. Riley, L. Dubicki, G. Moran, E. R. Krausz, and I. Yamada, Chern.

Phys. 145, 363 (1990). sG. Steffen, D. Reinen, H. Straterneier, M. J. Riley, M. A. Hitchman, K. Recker, H. Mathies, and J. R. Niklas, Inorg. Chern. 29, 2123 (1990).

6D. Reinen, G. Steffen, M. A. Hitchman, H. Straterneier, L. Dubicki, E. R. Krausz, M. J. Riley, H. Mathies, K. Recker, and F. Wallrafen, Chern. Phys. 155, 117 (1991).

7L. Dubicki, E. Krausz, M. Riley, and I. Yamada, Chern. Phys. Lett. 157, 315 (1989).

8E. Herdtweck and D. Babel, Z. Krist. 153, 189 (1980). 9H. Bill (private communication).

IOL. A. Boatner, R. W. Reynolds, Y. Chen, and M. M. Abraham, Phys. Rev. B 16,86 (1977).

II G. F. Koster, J. O. Dimmock, R. G. Wheeler, and H. Statz, Properties of the Thirty-Two Point Groups (MIT, Cambridge, MA, 1963).

12 P. W. Atkins, M. S. Child, and C. S. G. Phillips, Tables for Group Theory (Oxford University, Oxford, 1970).

I3C. Friebel and D. Reinen, Z. Anorg. AUg. Chern. 407, 193 (1974). 14D. Reinen and S. Krause, Inorg. Chern. 20, 2750 (1981). ISM. Bacci, Chern. Phys. 40, 237 (1979). 16F. S. Ham, in Electron Paramagnetic Resonance, edited by S. Gerschwind

(Plenum, New York, 1972), pp. 1-119. 17M. A. Hitchman, Inorg. Chern. 21, 821 (1982). 181. B. Bersuker and V. I. Polinger, Vibronic Interactions in Molecules and

Crystals (Springer, Berlin, 1989), pp. 67-9.

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