Optical absorption and magnetic circular dichroism of MnBr2

Physica 128B (1985) 133-143 North-Holland, Amsterdam

OPTICAL ABSORPTION AND MAGNETIC CIRCULAR DICHROISM OF MnBr2 H.J.W.M. H O E K S T R A , H.F. F O L K E R S M A and C. H A A S Laboratory of Inorganic Chemistry, Materials Science Center of the University, Nijenborgh 16, 9747 A G Groningen, The Netherlands Received 10 September 1984

Absorption and Magnetic Circular Dichroism spectra of MnBr2 in the spectral region 17 000-31 000 cm -1 at temperatures between 2.3 and 250 K and for magnetic fields up to 5 T are reported. The observed bands are attributed to d-d transitions on the Mn 2÷ ions. An assignment of the observed spectra is given with the aid of a parametric calculation of the energy levers. Exchange interactions between neighbouring Mn 2÷ ions play a dominant role in the absorption process. The breaking of the parity and spin selection rules leads to four possible mechanisms for electric dipole d-d transitions: (A) vibronic/spin--orbit single-ion, (B) vibronic/exchange, (C) exchange/spin-orbit, and (D) fully exchange induced transitions. It could be shown from an analysis of the dependence of the spectra on temperature and magnetic field that all four mechanisms occur in MnBr2.

1. Introduction

2. Experimental part

The present work on MnBr 2 was stimulated by recent spectroscopic investigations of MnI 2 [1]. Both MnI 2 and MnBr 2 crystallize in the Cd(OH)2 structure, with Mn 2÷ ions occupying octahedral sites which are slightly trigonally distorted. MnBr 2 is antiferromagnetic with a N6el temperature of Try= 2.16K [2,3]. The magnetic structure below TN has been investigated with neutron diffraction [3]. The optical spectra of high-spin 3d 5 ions on sites with an inversion center are of special interest as the electric dipole d - d transitions are both parity and spin forbidden. In undiluted compounds exchange interactions between neighbouring Mn 2÷ ions may induce an important contribution to the d--d transitions (see ref. [1] and references given there). The d - d transitions may also be made allowed by vibronic and spinorbit interactions. An insight in the importance of the various mechanisms may be obtained by studying the magnetic field and temperature dependence of the absorption and magnetic circular dichroism (MCD) spectra.

Single crystals of MnBr 2 were grown with the Bridgman technique. For the measurements we used a crystal with a thickness of 75/xm. Absorption and MCD spectra observed in the spectral region 17000-31000 cm -~ are given in figs. 1-6. All spectra have been measured on crystal plates perpendicular to the crystallographic c axis, the direction of the incident light and the applied magnetic field were parallel to the c axis. As units we used absorbance (= optical density) A for the absorption and AA (= A _ - A + ) for the MCD signal. A short description of the equipment has been given in ref. [1]. The spectra are in good agreement with those of refs. [2, 4], but give more information on fine structure and magnetic field dependence. For vibronically induced d - d transitions one expects a temperature dependence of the dipole strength. Measurements show that the dipole strength of t h e 6Alg(6S)--'>~Flg(4P) transition depends on temperature in accordance with the coth(htou/2kT ) law (fig. 7). For the theoretical curve we have taken hi%= 143cm -1 for the

0378-4363/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

134

H.J. W.M. Hoekstra et al. / Optical absorption and MCD of MnBr2 I

*Eg

I

0.3

T=2.3 K

0.2

0.5

II

+e +alg+e

I

I I

I

T=2.3 K

~ = 0 1

t'Alg

0 ~'

I

L

, 5T

I

+alg +2alg +3alg

J

1.0 '~__~__~.3T ~

÷2alg

o

T

~ -1.0 19000 0-/cm-1

18000

Fig. 1. Absorption A and MCD AA of the 4Tl~(4G)transition of MnBr2.

+a2u

2.3 K

0.~,

'7 ~ 0.3

3

o

4

-1.0 -2.0 23000

0.2

I

I

I

I

I

I

I

I

23500 o-/cm-1 Fig. 3. Absorption and MCD of the 4A]g,4Eg(4G) transition.

0.1 0 2.0 ~1.0 ~"

~0

5T

~

3T

-

-1.0 I

21000

,

I

22000 o-/cm-~

Fig. 2. Absorption and MCD of the 4T2g(4G)transition.

phonon frequency (see ref. [5] and table I). This frequency is also found in the spectra. The dipole strength of the bands arising from the free ion 4D state (*r2~+ 4Eg) depends only slightly on temperature (fig. 7); the dipole strength of the other d - d transitions of MnBr 2 are temperature independent within the experimental error ( - 3 % ) . The dipole strength of all the observed bands depends strongly on the magnetic field strength (figs. 8 and 9). At a temperature of 2 , 3 K the dipole strength decreases 30-50% if the magnetic field is raised to 5 T . The magnitude of the

H.J. W.M. Hoekstra et al. / Optical absorption and MCD of MnBr2 etalg ÷e..2alg i÷2aIQ ::+3a,g

'EgI *el*a q ÷eialg 1+2am

~TzgU'S/vE'÷e ÷aIg I

2.0

U~z

II

tl

alg

it

2a~g I

E"

I

135

1.5

3a,g I

alg

2alg

I

I

1.0

pkT= 2.3 K

,.<,

0.5

1,0

0.03

0.1

0

-0.1

0

©

T

2B000

27500

/ I

~_..__3 T

- 0.02

o-/cm -~

Fig. 5. Absorption and MCD of the 4Eg(4D) transition. 3T I

26500

,

~

erlcm-I

,

,

I

27000

Fig. 4. Absorption and MCD of the *T28(4D) transition.

magnetic field dependence of the dipole strength differs from band to band (fig. 9). These effects indicate that the spin-forbiddenness is partly overcome by exchange interactions, as one expects a magnetic field dependence of the dipole strength only for exchange-induced transitions [1]. For single-ion transitions the zeroth m o m e n t M 0 of the M C D is proportional to the magnetization. The curves in fig. 10 represent the theoretical behaviour of M 0 for this mechanism. The experimental dependence on the magnetic

field strength of M 0 deviates from this behaviour (fig. 10). M 0 of some of the transitions shows a decrease if the magnetic field is raised from 3 to 5 T at T = 2.3 K. These effects are ascribed to the presence of exchange-induced transitions which have a non-vanishing zeroth m o m e n t of the M C D in the presence of spin-orbit interaction.

3. Assignment of the spectra The Mn 2+ ions of M n B r 2 are surrounded by a trigonally distorted octahedron of bromine ions. However, the trigonal distortion is quite small and we expect that the energy levels can be calculated with an octahedral crystal field model. W e have carried out a parametric calculation, analogous to that described in ref. [1], to cal-

136

H.J.W.M. Hoekstra et al. / Optical absorption and MCD of MnBr2 I

Table I Phonon frequencies (in cm-1) of the optical modes at the point F [5]

1

T=2,3 K H=IT 0.2

ats es a2,(LO) a2u(TO) eu(LO) eu(TO)

3 0.1

51"

151 9o 263 (calculated) 234 225 (calculated) 143

0.3

5T: 0 o

-0.s

- 1.0

i

I

J

,

I

J

30000

i

J

t

|

,

t

,

,

30500 o-icm-1

31000

Fig. 6. Absorption and MCD of the ~T1s(4P)transition. culate the e n e r g y levels of the d 5 configuration. F o r this calculation we used the R a c a h p a r a m e t e r s B and C for the electrostatic interaction, the p a r a m e t e r 10 D q for the cubic crystal field splitting and the p a r a m e t e r s sr and if' for spin-orbit interaction. 3

i

i

!

i

x =4Tlg(~'P) =~'Eg+~Tzg(~O)

2x

x

Fine structure has been observed for the transitions to the 4Als , 4Eg(4G), 4Eg(4D) and 4T2s(4D) states (figs. 3-5). The observed fine structure is attributed to phonons of alg, e u (TO and LO) symmetry in point F and phonons of e symmetry in point K of the first Brillouin zone. The assignment of phonon progressions or phonon side bands to phonons of alg or e u symmetry is obscured by the fact that the frequencies of these phonons are almost the same (ref. [5], table I). T h e presence of an e, p h o n o n is due to the parity-forbidden d - d transitions, m a d e possible by simultaneous emission of the u n g e r a d e e u p h o n o n ; o n e expects only a single p e a k (n = 1) at low t e m p e r a t u r e , c o r r e s p o n d i n g to emission of one e u p h o n o n . T h e interaction with a~g p h o n o n s , on the o t h e r hand, is caused by the differences b e t w e e n the nuclear equilibrium coordinates of g r o u n d and excited states, and will lead to p h o n o n progressions with peaks n = 0, 1, 2, 3 . . . . ( F r a n c k - C o n d o n effect). i

o

i

i

[

T=/+K

o c~

0.5

c~

0

I

I

I

100

I

200 T(K)

Fig. 7. Experimental temperature dependence (A and x) of the dipole strength of some transitions of MnBr2; the solid line is the theoretical dependence for the vibronic transition coth(htou/2kT) with hta. = 143 cm-1.

I I

I

3 I

I

2 H (Testa)

Fig. 8. Magnetic field dependence at 4 K of the dipole

strength Do of the 4A1s, 4Eg(4G) transition; the theoretical curve is calculated with the pair approximation.

137

H.J.W.M. Hoekstra et al. I Optical absorption and MCD of MnBr2 1.0

T=2.3 K x

"

~ ~

=~'T~o(I"P)

o/~P)

o ='Eg'('D)

*='T2gl~O) I--

'* 0.5

o cI -a-

/~" x

0.5

I

I

I

I

I

I

1

2

3

~

5

6

:~Eg(~O) . =4T2g(~O)

o

x

015 H/(T-O) (Tes[a/K)

H (TesIa) T=2.3 K x =~'Alg~Eg(~G) o =~T2g(~51

1.0

a =~'T1g(~G) J ,~ 0.5

0.5

o

o

x =~Tzg{ G)

~

. . . . &

~

0

I

I

1

2

I

I

3 /, H (Tesla)

i

I

~

6

0

4Alq,~ Eg(~Gl(pos. part) a =~Alg,~Eq(~G)(neg part)

I

I

0.5

1

HI(T-O) (Tesla/K)

Fig. 9. Magnetic field dependence at 2.3 K of the dipole strength of the transitions of MnBr2; the solid line represents the theoretical curve calculated with the pair approximation.

Fig. 10. Relative values of the zeroth moment of the MCD as a function of HI(T- O) observed at T = 2.3 K; the solid line is the magnetization.

W e a k phonon side bands corresponding to a phonon frequency of about 100 cm -1 have been observed for all absorption bands which consist of sharp peaks (figs. 3-5). This frequency corresponds approximately to a phonon of eg symmetry (table I). An explanation might be a lowering of the crystal symmetry for the excited states. However, this explanation is unlikely as these excited states belong mainly to the elec3 2~ and from symmetry tronic configuration t2ge considerations it follows that the diagonal matrix elements of any low-symmetry potential vanishes for this configuration [7]. A more reasonable explanation is that the energy separation of about 100 cm -1 is caused by a vibronic coupling with phonons at the boundary of the first Brillouin zone. Calculated dispersion curves [5] show the presence of four branches with a phonon frequency of about 100cm -~ near the points M

and K of the first Brillouin zone. For the parametric calculation of the energy levels we have first calculated the values for B, C and 10 D q by comparing calculated energy levels with the centers of gravity of broad bands or with the strongest peak of a 4F~ multiplet if a phonon progression of atg symmetry has been observed. O u r best results for the parameters B, C, 10 D q are close to the values obtained in ref. [4]. The parameters for spin-orbit interaction ~" and sr' are obtained from the spin-orbit splitting of the 4T2~(4D) state. Three zero-phonon lines have been observed (fig. 4). This corresponds to a splitting into four spin-orbit components with two of these (E'g and U'g 5/2) (almost) degenerate, as expected for a first order spin-orbit splitting. For the fitting of the spin-orbit parameters we have used that, due to the covalency of the

138

H.J.W.M. Hoekstra et al. / Optical absorption and MCD of MnBr2

d-electrons, sr' is expected to be smaller and ~" larger than the free ion value ~'d ( - 3 5 0 cm -1) [7]. Deviations from the free ion value will be considerable as the spin-orbit coupling constant of 4p-electrons of the ligand Br-ion is large, ~'Lp 2460cm -1. The results of the parametric calculation together with the observed position of the absorption peaks are given in table II. The agreement between the calculated and observed energy levels is quite good. The parameters for electrostatic interaction B and C are reduced with respect to the free ion values B 0 = 960 cm -~, Co = 3325cm -1 [8]. This reduction is due to covalency [7]. If spin--orbit coupling is neglected, the 4Alg and 4Eg(4G) states are calculated to be degenerate; covalency will cause a lifting of the degeneracy. Following the arguments of ref. [1] we attribute the peak at the low energy side to the zero-phonon 4Eg(4G) transition. The assignment of the other peaks of t h e 4Eg, 4Alg(4G) band is given in fig. 3 and table II. The assignment of the peaks observed in the 4Eg(4D) and 4T2g(4D) bands is given in figs. 4 and 5.

4. Discussion of the transition mechanism

The d-d transitions in MnBr z are either magnetic dipole or electric dipole transitions. The oscillator strength of an allowed magnetic dipole transition is about 10 -6 [7]. If spin-orbit interaction is neglected, the total spin S is a good quantum number, and all magnetic dipole transitions between t h e 6mlg ground state of Mn 2+ and the excited states (with S = 3/2 and S = 1/2) are spin forbidden. Spin-orbit interaction can overcome this selection rule, because it mixes states of different spins S. If the coefficient of mixing between sextet (S = 5/2) and quartet (S = 3/2) states is a, then the oscillator strength of a spin-forbidden magnetic dipole transition (AS = 1) will be of the order of fm--~ 10-6Ot2" Mixing of sextet and quartet states is also possible by exchange interactions between pairs of ions; in that case the coefficient a refers to the mixing caused by this mechanism. The oscillator strength of the observed absorption bands in

Table I1 Assignment and comparison between calculated and observed (0 T, 2.3 K) energy levels of MnBr2; (t) means maximum of the absorption band. Of the 'WIg(4D) and 4Es(4D) transitions only the zero-phonon lines are given; for the other peaks, see figs. 4 and 5. The parameters used in the calculations are 1 0 D q = 6 7 9 0 c m -1, B = 6 7 1 c m -l, C = 3 2 7 0 c m -t, sr = 580cm -l and sr ' = - 2 0 c m -1. Calculated Spin-orbit energy (cm-1) component 18364 18384 18596 18740 21346 21356 21485 21566 23056

U' 5/2 E" U' 3/2 E' E' U' 5/2 U' 3/2 E" E', E", U'

23049

U'

24940 25637 26229 26236 26273 26307 27744 27747 27750 29542 29966 30620 30719 31208 31315 31452 31485 31829

E" U' U' 5/2 E' U' 3/2 E" E" U' E' U' E' E" U' E' U' 3/2 U' 5/2 E" U'

State

Observed energy (cm -l)

4TI(4G)

18300 (t)

4T2(4G)

21500 (t)

aE(4G) 4E + e 4A1(4G) 4E + alg 4E + eu(LO) 4A1 + alg 4E + 2a18 4A1 + 2alg 4Al + 3alg 2T~(2I)

23085 23180 23220 23252 23300 23360 23400 23492 23630

26306 *r2(4D) 26345 26375 4E(4D)

27560 (t)

2T1(2I) 2T~(2I)

4Ti(4P)

30000 (t)

2E(21)

MnBr 2 is of the order of 10-S [4] and therefore cannot be due to magnetic dipole transitions (except for a few weak lines). We conclude that the observed bands must be due mainly to electric dipole transitions. Electric dipole transitions between d-states in MnBr 2 are both spin and parity forbidden.

H.J. W.M. Hoekstra et al. / Optical absorption and MCD of MnBr2

Several types of electric dipole transitions for such doubly forbidden d - d transitions of high spin Mn 2+ complexes have been discussed in the literature [1, 9-11]. The spin selection rule A S = 0 can be overcome by spin-orbit interaction, the parity selection rule by a coupling with ungerade vibrations. Both spin and parity selection rules can be overcome also by exchange interactions between the Mn 2÷ ions. This leads to four different mechanisms for electric dipole transitions (table III). We have evidence from the experimental data that all four mechanisms A - D contribute to the absorption in MnBr 2. In the first place there is the classical single-ion mechanism A, where the spin selection rule is overcome by spin--orbit interaction and the parity selection rule by coupling with ungerade vibrations. The oscillator strength f at low temperature is of the order of fe = 10-3~ 2 for reasonable values of the vibronic coupling strength [7, 12], so that these transitions are much stronger than the magnetic dipole transitions, and of the same order of strength as the observed bands. The other mechanisms (B, C, D) involve an exchange interaction between a pair of Mn 2+ ions. In mechanism B the spin restriction is lifted by the exchange interaction, the parity restriction by the vibronic interactions. In mechanism C the spin selection rule is overcome by spin--orbit interaction, the parity selection rule by exchange interactions. In mechanism D the exchange interactions are responsible for lifting both spin and

parity selection rules. The various mechanisms can be distinguished by the temperature and field dependence of the oscillator strength and the magnitude of the MCD signal. For vibronic mechanisms A and B we expect an increase of the oscillator strength with increasing temperature proportional to c o t h ( h t o u / 2 k T ), where tou is the frequency of the ungerade vibration involved [13]. For transitions of type B and D the MCD signal is expected to be weak, and the transition probability changes by applying a magnetic field [1]. For absorption bands consisting of sufficiently well-resolved peaks one can observe the contributions of a non-vibronic mechanism separately, because the latter mechanism involves the creation (or annihilation at higher temperatures) of an ungerade phonon. The dipole strength of vibronic transitions depends on temperature. From the experimental results shown in fig. 7 it follows that the transitions to the 4Tlg(4P) state are almost purely vibronic and the transitions to t h e 4 E g + 4TEg(4D) states are for a small part ( - 1 0 % ) caused by vibronic interactions. The dipole strength of the other investigated d-d transitions of MnBr 2 does not show any appreciable temperature dependence within the experimental error ( - 3 % ) , so that we may conclude that for these transitions the parity selection rule is overcome mainly by exchange interactions. The dipole strength of exchange-induced transitions of types B and D, in the pair approximation, is given by [1]

Table III Mechanisms of electric dipole d-d transitions in MnBr2 (s.o. is spin-orbit, ex is exchange and vibr is vibronically induced)

Selection rule

Spin (AS ---0) Parity (g ~ u) Temperature dependence of .g Magnetic field dependence of ,f MCD

139

Single-ion

Pair of ions

A

B

C

D

s.o. vibr

ex vibr

s.o. ex

ex ex

coth{fitou/2k T)

coth(htou/2k T)

-

-

+

+ small

+

+ small

H.J.W.M. Hoekstra et al. I Optical absorption and MCD of MnBr2

140

Do: const. E as, W],

(1)

S'

'L0

where S' is the resultant spin of the pair of ions a and b, a s, is the occupation probability of the ground state leyels an_d W_s, is a 6 - j symbol 1 2 1 3 1 1 ( W s, = 0, -~,2 ~X/~, - ~ / ~ , ~X/~, 0 for S ' = 0, 1, 2, 3, 4, 5, respectively [11]). From eq. (1) and the energies of the ground state: i

Es,Ms. =

-J{S'(S' +

1)-

+ 2tZBMs,H ,

S,(S a+

1)-

Sb(Sb +

1)}

i

i

i

HIT (Tosla/KI

(2)

where J is the exchange constant for the interaction between the two ions a and b, it follows that the dipole strength of exchange-induced transitions B and D depends on the magnetic field strength H. For transitions A and C such a pronounced dependence is not expected. From the experimental results given in figs. 8 and 9 we deduce that all the observed bands are at least partly due to exchange-induced transitions of types B and D. The MCD of the transitions to states arising from the 4G flee-ion term is relatively weak, indicating a small contribution from single-ion transitions A and transitions of type C. Moreover, the behaviour of the zeroth moment of the MCD of the 4Alg , 4Eg(4G) band as a function of the magnetic field strength deviates strongly from what is expected for a transition of type A or C (see the discussion below and figs. 10 and 11). Thus the 4Alg , 4Eg(4G) transition is mainly due to exchange-induced transitions of types B and D, and we find a value of J = - 0 . 2 cm -~ for the exchange constant by fitting the calculated behaviour of the dipole strength D Oas a function of H to the observations at T = 4 K (fig. 8). The value J = - 0 . 2 cm -~ is of the correct order of magnitude. From magnetic susceptibility measurements one obtains (with 0 = - 4 . 7 K [14] and kO=2zJS(S+l)/3; z=6, S=~) J= -0.09 cm -1. The theoretical curve fits quite well with the experiments at T = 4 K (fig. 8). At lower temperatures (fig. 9) this is not the case; this must be due to the limited validity of the pair approximation in the region near T N. The behaviour of the zeroth moment M 0 of the MCD as a function of the magnetic field strength

Fig. 11. Relative values of the zeroth moment of the M C D of the positive part of the 4Ate, 4Ez(4G) transition; the curve represents the theoretically expected behaviour calculated from eq. (6) in the pair approximation with J = -0.2 ¢m -t for the e x c h a n g e c o n s t a n t in t h e g r o u n d state.

for single-ion transitions A to an excited 4F multiplet is, in first approximation, proportional to the magnetization [1] and is given by Mo = const. Bs/2{5IzBH/k ( T - 0)},

(3)

where Bs/2 is the Brillouin function and /z B the Bohr magneton. The same behaviour is expected for transitions of type C. Here and in the rest of this paper we have taken into account (MCD) C-terms only and we have neglected (MCD) B-terms which are much weaker at low temperature [15]. The zeroth moment M 0 of the MCD belonging to exchange-induced transitions B and D vanishes in first approximation. Spinorbit interaction produces small contributions to M0 which are in the pair approximation given by (see [1]) M 0 = const. ~', as, Bs,(2tznS'H/kT)W2s,~(S').

(4)

S'

The coefficients are ~ ( S ' ) = - 3 / 2 0 , 1/30, 7/40, 3/10 for S = 1, 2, 3, 4, respectively. The theoretical curves obtained from eq. (3) are given in fig. 10. the curve calculated from eq. (4) with J = - 0 . 2 cm -1 is given in fig. 11. The experimental data given in fig. 10 deviate strongly from the behaviour expected for a single-ion mechanism (eq. (3)). Thus the experiments on the field dependence of M 0 show that there are indeed

H.J.W.M. Hoekstra et al. / Optical absorption and MCD of MnBr2

appreciable contributions from exchange-induced transitions of types B and D to M 0. In order to obtain numerical values for the MCD-absorption ratio we have calculated the ratio of the MCD parameters (for definition see [1]) C O and D o (for H = 0) at small values of ~taH/k(T- O) with the equation

f AA(H, T)e -1 de I

1

f AA(O T, T)e de

Co ~BH D Ok ( T - 0)'

141

Table IV Values for Co~Do (0 T) of the transitions of MnBr2 Final state

Co/Do(O T)

AL

*rtz(4G) *F2g(4G) 4Atz, 4Eg(4G)

-0.01 -0.004 +0.001 -0.02 -0.08 +0.08

4 4 4

~r~z(4D) 4EB(4D) ~l'lg(4P)

2

2 1

(5)

where e is the photon energy and 0 the N6el temperature. In eq, (5) we have used T - 0 instead of T in order to correct for antiferromagnetic interactions, using that M 0 is proportional to the magnetization for single-ion transitions and neglecting small contributions from exchanged-induced transitions to M 0. The values obtained for Co/Do(OT) obtained in this way are given in table IV. There is clearly a connection between the values Co/Do and the change of the orbital quantum number AL (see also refs. [1] and [16]). Next we discuss in more detail the transition mechanisms for the various bands. The transitions to the states arising from the free-ion 4G term are characterized by relatively weak MCD signals (table IV) and a strong dependence of the dipole strength on the magnetic field strength which indicates that the transitions are almost completely exchange-induced transitions B and D. The absence of any temperature dependence of the dipole strength at higher temperatures ( T = 10-200K) shows that the transitions are mainly caused by the non-vibronic exchangeinduced mechanism D. The weak MCD signals are due to exchange-induced transitions and to single-ion transitions (see figs. 10 and 11 and the discussion above). The MCD of transitions of types B and D is expected to decrease if the magnetic field is raised from 3 to 5 T at T = 2.3 K (fig. 11), the MCD of single-ion transitions increases if the magnetic field is raised. Both phenomena are observed in the MCD spectrum of t h e 4Alg , 4E~(4G) band (fig. 3). The MCD peaks in fig. 3 assigned to the phonon-assisted

4Es(+eu(TO)) and 4Alg(+a2,(TO)) increase with increasing magnetic field strength and can therefore be attributed mainly to the vibronic singleion mechanism A. MCD parameters for this mechanism have been calculated [1, 17]. It is reasonable to assume that also in MnBr 2 the dominant vibronic interaction is caused by vibrations of the tl, symmetry as these vibrations modulate the metal-ligand distance. The MCD of a vibronic single-ion transition A to the 4Alg state is expected to be positive and due to coupling with the t~, 7 = 0 vibrational modes (in the complex trigonal component system); coupling with the tl, 7 = _1 vibrational modes will give no MCD signal for this mechanism [17]. This is in agreement with the observations (fig. 3); for the trigonal site symmetry of the Mn 2÷ ions in MnBr 2, the t~, y = 0 corresponds to a2, symmetry, and therefore only vibronic interaction with vibrations of a2, symmetry yields a nonvanishing positive MCD signal for the vibronic single-ion mechanism A. The MCD signals attributed to transitions to the excited states 4mlg+ e u + nalg (see fig. 3; n = 0, 1) are therefore assigned to vibronic exchange-induced transitions B; this is confirmed by the fact that these signals decrease if the magnetic field is raised from 3 to 5 T at T = 2.3 K (see fig. 3). The excited 4A~(4G) state is isoconfigurational 3 2 if spin-orbit coupwith the ground state (t2~eg) ling and configuration interaction is neglected. Therefore, according to the Franck-Condon principle, one does not expect a strong vibronic progression for transitions of this type. This is indeed as is observed for the vibronic single-ion transition A to t h e 4Alg s t a t e (4Alg + a2u; see fig. 3). On the other hand, the exchange-induced

142

H.J.W.M. Hoekstra et al. I Optical absorption and MCD of MnBr2

transitions B and D to the s t a t e s 4Atg+ na~ with n = 0 , 1 , 2 , 3 and4Atg+e u+malgwith m = 0 , 1 show a phonon progression (fig. 3). Apparently the Franck-Condon principle does not hold for exchange-induced transitions. This must be due to the fact that the exchange interaction between a pair of ions depends strongly on the overlap of the wave functions, and therefore also on the distance between the ions. This effect leads to a vibronic coupling and to vibronic progressions with a~ phonons even for isoconfigurational transitions. A theory of the influence of vibronic interactions on exchange-induced transitions has not been published so far. The transitions to the states arising from the free ion 4D term with symmetry *F2~ a n d 4Eg are for the main part non-vibronic (fig. 7) and exchange-induced (fig. 9) (mechanism D). The MCD signal of the zero-phonon lines of both bands increases with increasing magnetic field strength indicating also an important contribution from non-vibronic mechanism C. The absorption spectra of both bands show clearly a phonon progression belonging to the breathing mode atg. This progression is also observed in the MCD spectra but at higher energy extra peaks are observed, which are ascribed to the presence of phonon-assisted single-ion and exchange-induced transitions. The transitions to the 4T~g(4P) state are almost purely vibronic (fig. 7). The dipole strength decreases if the magnetic field strength is raised, but this decrease is less than that for the 4A~g, 4Eg(4G) band, indicating that the spin-forbiddenness is partly overcome by spin-orbit coupling and partly by exchange interactions. Therefore the transitions to t h e 4Tlg(4P) state can be ascribed for the main part to vibronic exchangeinduced (B) and vibronic single-ion transitions (A). The line shape of some of the absorption bands changes if the temperature is lowered below TN (T N= 2.16K). In particular, the line shape of the zero-phonon band of the transition to the 4Eg(4G) state at 23085 c m -1 changes strongly with the magnetic field and temperature, especially below TN (fig. 12). This band is due to an exchange-induced transition on a pair of Mn 2+

i

. . . .

i

,

,

,

2.0 - l . ~ z e r ° - p h ° n ° n

6Alg.__~~Eg

AT=3.2K IJ _TI 1.s., 1.o •

AT:

1.8 KI

/

..,.&

^~AT= 1.8

05

d "'v T = 1,8 K

2300() '

' "3oA,v ' ' O'(C m-l)

Fig. 12. Absorption spectrum of

the

4Alg,

4E~(4G) transition.

ions. The broadening is due to exciton dispersion, i.e. the hopping of excitons from one Mn 2+ ion to another. The hopping integral depends strongly on the correlation between the directions of the spins of the two ions involved. As a consequence the line shape depends in a sensitive way on the type of magnetic order. These effects have been described in detail in another publication [6]. From the spectra a value of t = 10 cm -t for the transfer integral for hopping of a 4Eg(4G) exciton between two Mn 2+ ions with parallel spins in MnBr 2 could be deduced.

5. Conclusions

The d-d transitions of Mn 2÷ in MnBr2, although doubly forbidden for electric dipole radiation, are fairly intense. A study of the dependence of absorption and MCD on temperature and magnetic field strength showed that several mechanisms contribute to the d--d transitions of MnBr 2. The spin-forbiddenness is overcome by exchange or by spin-orbit interactions; the parity forbiddenness is overcome by

H.J.W.M. Hoekstra et al. / Optical absorption and MCD of MnBr2

vibronic or by exchange interactions. This leads to four different mechanisms which all have been observed for the d-d transitions of MnBr 2. The spectra show splittings due to spin--orbit interaction, vibronic progressions with phonons of the breathing mode and phonon side bands due to the creation of ungerade phonons. The position of the absorption bands and the spinorbit splittings could be reproduced rather well by a parametric calculation involving parameters for the crystal field splitting, electron repulsion and spin-orbit interaction. References [1] H.J.W.M. Hoekstra, P.R. Boudewijn, H. Groenier and C. Haas, Physica B121 (1983) 62. [2] Y. Farge, M. Rggis and B.S.H. Royce, J. Physique 37 (1976) 637. [3] E. Wollan, W. Koehler and M. Wilkinson, Phys. Rev. 110 (1958) 638.

143

[4] R. Pappalardo, J. Chem. Phys. 31 (1959) 613. [5] G. Benedek and A. Frey, Phys. Rev. B21 (1980) 2482. [6] H.J.W.M. Hoekstra, H.F. Folkersma and C. Haas, Solid State Commun. 51 (1984) 657. [7] S. Sugano, Y. Tanabe and H. Kamimura, Multiplets of Transition-Metal Ions in Crystals (Academic Press, New York and London, 1970). [8] J.S. Gritiith, The Theory of Transition-Metal Ions (Cambridge University Press, 1971). [9] D.D. Sell, R.L. Green and R.M. White, Phys. Rev. 158 (1966) 489. [10] L. Dubicki and Y. Tanabe, J. Phys. Soc. Japan 21 (1966) 692. [11] J. Ferguson, H.J. Guggenheim and Y. Tanabe, J. Phys. Soc. Japan 21 0966) 692. [12] Y. Sakisaka, J. Phys. Soc. Japan 38 (1975) 505. [13] C.J. Ballhausen, Introduction to Ligand Field Theory (McGraw-Hill, New York, 1962). [14] J.W. Stout, W.B. Hadley and C.L. Brandt, U.S. Dept. Com., Office Tech. Serv., P.B. Report 143 (1958) 420. [15] P.J. Stephens, Adv. Chem. Phys. 35 (1976) 197. [16] H.J.W.M. Hoekstra and C. Haas, Physica B, to be published. [17] H.J.W.M. Hoekstra, Thesis, Groningen (1984).