Funding OTKA T 049338

Fulleride ions in various crystal fields studied by infrared spectroscopy

G. Klupp, K. Kamarás Research Institute for Solid State Physics and Optics, P. O. Box 49, H-1525 Budapest, Hungary,

email: [email protected]

Introduction to Jahn —Teller effect in fullerides

Na 2 C 60 and A 4 C 60 (A=K, Rb, Cs) are nonmagnetic Mott – Jahn – Teller insulators [1].

In C 60 n coupling of the t 1u electrons with H g vibrations leads to p n  8H g Jahn—Teller systems. [2] The I h symmetry of C 60 can be distorted by this coupling to [2]: D 5d D 3d D 2h The shape of the C 60 4 is prolate, the shape of C 60 2 On the warped APES [4] either the D 3d is oblate. [3] distortions are minima and the D 5d The D 2h distortions are always saddle points. [5, 6] maxima, or vice versa.

In isolated C 60 n the Jahn—Teller effect is dynamic, pseudorotation takes place [4]: The reduced symmetry leads to the following splittings of the HOMO: E MO t 1u e 1u + a 2u Splitting of the IR active T 1u vibrational modes: T 1u E 1u + A 2u e u + a 2u E u + A 2u b 1u + b 2u + b 3u B 1u + B 2u + B 3u In crystals the crystal field of the cations can disturb the pseudorotation and static Jahn—Teller effect can appear [4]. The crystal field can even dominate the distortion.

The C 60 4 in orthorhombic Cs 4 C 60 was found to be D 2h by neutron diffraction. [7] [1] M. Fabrizio and E. Tosatti, Phys. Rev. B

55

:13465, 1997.

[2] C. C. Chancey and M. C. M. O’Brien, The Jahn-Teller effect in C 60 Princeton, 1997.

and Other Icosahedral Complexes, Princeton University Press, [3] A. Auerbach, N. Manini and E. Tosatti, Phys. Rev. B

49

:12998, 1994.

[4] S. Tomita, J. U. Andersen, E. Bonderup, P. Hvelplund, B. Liu, S. Brondsted Nielsen, U. V. Pedersen, J.Rangama, K. Hansen and O. Echt, Phys. Rev. Lett . 67 :1886, 2005.

[5] A. Ceulemans, J. Chem. Phys.

87

:5374, 1987.

[6] M. C. M. O’Brien, Phys. Rev. B

53

:3775, 1996.

[7] P. Dahlke and M. J. Rosseinsky, Chem. Mater . 14 :1285, 2002.

Infrared spectra of A

4

C

60

and Na

2

C

60

at various temperatures

0.5

0.4

0.3

0.7

Strong orthorhombic (D 2h ) crystal field [7] without reorientation: 600 800 1000 1200 1400 Cs 4 C 60 136 K 0.7

0.6

0.6

0.5

0.4

0.3

600 800 1000 Wavenumber (cm -1 ) 1200 Threefold splitting of T 1u  C 60 4 : D 2h 1400 0.6

0.5

0.4

Strong tetragonal (D 4h ) crystal field [8] with reorientation [8]: 600 800 1000 Rb 4 C 60 120 K 1200 1400 0.3

600 K 4 C 60 120 K 800 1000 Wavenumber (cm -1 ) 1200 Threefold splitting of T 1u  C 60 4 : D 2h 1400 0.3

0.6

0.5

0.4

Weak tetragonal (D 4h ) crystal field [9, 10] with reorientation [8]: 600 800 1000 Cs 4 C 60 448 K Rb 4 C 60 360 K 1200 1400 600 K 4 C 60 375 K 800 1000 Wavenumber (cm -1 ) 1200 Twofold splitting of T 1u  C 60 4 : D 3d or D 5d 1400 0.45

0.40

Cubic crystal field averaged out by rotation [11]: 600 800 1000 1200 1400 Na 2 C 60 487 K 0.45

0.40

0.35

0.30

0.35

0.30

0.25

600 800 1000 Wavenumber (cm -1 ) 1200 1400 Twofold splitting of T 1u  C 60 2 : D 3d or D 5d 0.25

[8] G. Klupp, K. Kamarás, N. M. Nemes, C. M. Brown and J. Leao, Phys. Rev. B

73

:085415, 2006.

[9] R. M. Fleming, M. J.Rosseinsky, A. P. Ramirez, D. W. Murphy, J. C. Tully, R. C. Haddon, T. Siegrist, R. Tycko, S. H. Glarum, P. Marsh, G. Dabbagh, S. M. Zahurak, A. V. Makhija and C. Hampton, Nature

352

:701, 1991.

[10] C. A. Kuntscher, G. M. Bendele and P. W. Stephens, Phys. Rev. B

55

:R3366, 1997.

[11] T. Yildirim, J. E. Fischer, P. W. Stephens and A. R. McGhie, Progress in Fullerene Research, p. 235, 1994.

The effect of strong crystal field:

orthorhombic Cs

4

C

60

:

The distortion found in [11]:

c

The dark blue atoms are pushed closer to the center of the molecule.

a

Static D 2h distortion dominated by the crystal field.

Low temperature tetragonal K

4

C

60

, Rb

4

C

60

:

D 2h distortion  dominated by

crystal field

the crystal field is the largest where the K-C distances are the smallest, ie. in the

c

direction  a possible distortion can be “distortion

A

“:

c a

Discussion The effect of heating:

Cs

4

C

60

:

The phase transition between 293 and 623 K [11] can lead to both static and dynamic distortion.

K

4

C

60

, Rb

4

C

60

:

gradual decrease of

crystal field

due to thermal expansion and the gradual

occupation of higher energy levels

.

If “distortion A“ is present at low temperature, then:

The distortions on the graphs correspond to distortions along the axes shown on the molecule.

Heating

D C B A B D D C D

B

A

B C C D D



B

A

B C C D D



B

A

B C C D D



B B C C D D

 In the shown case the isolated molecule has D 5d minima. The scheme is analogous for D 3d farther the axis of the distortion from the crystallographic

c

minima. At low temperature the lowest minimum is that of "distortion A". The axis, the higher the energy of the distortion. At low temperatures only the lowest energy levels are occupied, which is the reason why the D 2h distortion appears. On heating the D 2h minimum arising from the crystal field weakens. At the same time the differences between the D 5d distortions gradually disappear. This, together with the occupation of higher lying energy levels, leads to the appearance of D 3d /D 5d distortions besides the D 2h distortion. This way on heating the molecule first starts to pseudorotate between "distortion A" and the two "distortion B"-s, meaning a static-to-dynamic transition. The confinement of the pseudorotation then gradually decreases as the temperature rises, to the state where, in the case of an averaged out crystal field, it is free. This is the case of the high temperature Na 2 C 60 . As the distortion of the molecules can be detected with IR spectroscopy: t pseudorotation > t vibration

If ”distortion A” is not the one present at low temperature, then

on heating the first step is to move from the low temperature D 2h distortion to “distortion

A

“.