Embed Size (px)
Citation preview
FundingOTKA 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
D5dD3d D2h
Na2C60 and A4C60 (A=K, Rb, Cs) are nonmagnetic Mott – Jahn – Teller insulators [1].
In C60n- coupling of the t1u electrons with Hg vibrations leads to pn 8Hg Jahn—Teller systems. [2]
The Ih symmetry of C60 can be distorted by this coupling to [2]:
EMO
t1u e1u + a2u eu + a2u b1u + b2u + b3u
The shape of the C604- is prolate, the shape of C60
2- is oblate. [3]On the warped APES [4] either the D3d distortions are minima and the D5d maxima, or vice versa.The D2h distortions are always saddle points. [5, 6]
In isolated C60n- the Jahn—Teller effect is dynamic, pseudorotation takes place [4]:
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 C60
4- in orthorhombic Cs4C60 was found to be D2h by neutron diffraction. [7]
The reduced symmetry leads to the following splittings of the HOMO:
[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 C60 and Other Icosahedral Complexes, Princeton University Press, Princeton, 1997.[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.
Splitting of the IR active T1u vibrational modes:
T1u E1u + A2u Eu + A2u B1u + B2u + B3u
Infrared spectra of A4C60 and Na2C60 at various temperatures
600 800 1000 1200 1400
0.25
0.30
0.35
0.40
0.45
600 800 1000 1200 1400
0.25
0.30
0.35
0.40
0.45Na
2C
60
487 K
Tra
nsm
issi
on
Wavenumber (cm-1)
600 800 1000 1200 1400
600 800 1000 1200 1400
Rb4C
60 360 K
K4C
60 375 K
Cs4C
60 448 K
Tra
nm
issi
on
(a
rb. u
nits
)
Wavenumber (cm-1)
600 800 1000 1200 1400
0.3
0.4
0.5
0.6
600 800 1000 1200 1400
0.3
0.4
0.5
0.6
Rb4C
60 120 K
K4C
60 120 K
Tra
nsm
issi
on
Wavenumber (cm-1)
600 800 1000 1200 1400
0.3
0.4
0.5
0.6
0.7
600 800 1000 1200 1400
0.3
0.4
0.5
0.6
0.7Cs
4C
60
136 K
Tra
nsm
issi
on
Wavenumber (cm-1)
Cubic crystal field averaged out by rotation [11]:
Weak tetragonal (D4h) crystal field [9, 10] with reorientation [8]:
Strong tetragonal (D4h) crystal field [8]with reorientation [8]:
Strong orthorhombic (D2h) crystal field [7]without reorientation:
[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.
Threefold splitting of T1u C604-: D2h Threefold splitting of T1u C60
4-: D2h Twofold splitting of T1u C604-: D3d or D5d Twofold splitting of T1u C60
2-: D3d or D5d
Discussion
orthorhombic Cs4C60: The distortion found in [11]:
Low temperature tetragonal K4C60, Rb4C60: D2h distortion dominated by crystal fieldthe 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
c
a
The effect of strong crystal field:
Static D2h distortion dominated by the crystal field.
The effect of heating:
The distortions on the graphs correspond to distortions along the axes shown on the molecule.
B B
C
CD
D
D
D
A
Heating
Ep
ot
Ep
ot
Ep
ot
Ep
ot
B B B BB B B BC C
C CC C
C C
D DD D
D DD DAA
A
Cs4C60: The phase transition between 293 and 623 K [11] can lead to both static and dynamic distortion.K4C60, Rb4C60: 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:
If ”distortion A” is not the one present at low temperature, then on heating the first step is to move from the low temperature D2h distortion to “distortion A“.
The dark blue atoms are pushed closer to the center of the molecule.
In the shown case the isolated molecule has D5d minima. The scheme is analogous for D3d minima. At low temperature the lowest minimum is that of "distortion A". The farther the axis of the distortion from the crystallographic c axis, the higher the energy of the distortion. At low temperatures only the lowest energy levels are occupied, which is the reason why the D2h distortion appears. On heating the D2h minimum arising from the crystal field weakens. At the same time the differences between the D5d distortions gradually disappear. This, together with the occupation of higher lying energy levels, leads to the appearance of D3d/D5d distortions besides the D2h 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 Na2C60. As the distortion of the molecules can be detected with IR spectroscopy: pseudorotation>vibration
