Journal of ~ w Temperature Physics, Vol. 142, Nos. 3/4, February 2006 (© 2006) DOI: 10.1007/s !.0909-006-9006-1

Anisotropic SDW Dynamics in (TMTSF)2PF6

Martin Dressel , Kons tant in Petukhov~ and Marc Schettter

1. Physikalisches Institut, Universitgt Stuttgart, Pfaffenwaldr~ing 57, D-70550 Stuttgart, Germany

The anisotropic transport properties of the spin-density-wave model-com- pound (TMTSF)2PF6 have been studied by dc and microwave methods. Ac- cording to mean-field theory, the activation energy in the SD W state below TSDW = 12 K is approximately 20 to 25 K in all directions when mea- sured by dc methods. Microwave experiments along the a, b t and c* axes reveal that the collective transport, which is considered to be the fingerprint of the spin-density-wave condensate, is present in the a and b ~ directions, but not along the least conducting c* axis. In contrast to common quasi one-dimensional models, the density wave also slides in the perpendicular b I direction. Can this behavior be explained by the nesting properties of the quasi one-dimensional conductor?

PACS numbers: 72.I5.Nj, 75.30.Fv, 7~.70.Kn.

1. I N T R O D U C T I O N

At TSDW = 12 K, the one-dimensional organic conductor (TMTSF)2PF6 undergoes a metal-insulator transition to a SDW ground state. From NMR experiments ~ the nesting vector has been determined to be Q = [0.5a*, (0.24+ 0.03)b*, (-0.06 ± 0.20)c*], i.e. incommensurate and tilted due to the inter- chain coupling (Fig. 1). The instability of the Fermi surface causes the complete opening of an energy gap as seen from the activated de transport p(T) cx exp{A/T}, with A ~ 20 K to 27 K independent from the direction probed. 2 In addition to the single-particle excitations, collective transport is expected to occur along the chains. 3 This was confirmed by the non-linear conductivity above some characteristic threshold field E r and by the ob- servation of the pinned-mode resonance in the microwave range. 4,'5 Is this collective transport linked to the nesting vector or to the chain direction?

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134 M. Dressel, K. Petukhov, and M. Scheffler

2. R E S U L T S

The dc t ransport of (TMTSF)2PF6 single crystals was measured along the a, b', and c* axes by a standard four-probe method. In addition, the microwave resistivity at 24 and 33.5 GHz was determined using cavity per- turbat ion technique; for further details see Ref. [2,6 8]. The main microwave results are present in Fig. 2 as an Arrhenius plot. Up to six samples of dif- ferent batches have been studied for each orientation; the sample-to-sample spread is within the uncertainty to determine the slope. Similar results are obtained at 24 GHz, but both frequencies are too close to allow for any conclusions on the frequency dependence. Most surprisingly, the activation energy along the a and b' axes is much smaller compared to the dc behav- ior, while for the c* orientation the results at microwave frequencies perfectly agrees with the dc profile. Right below TSDW the activation energies obtained for the three directions are (5.9 ± 0.4) K, (6.0 ± 0.3) K, and (20.7 ± 0.4) K.

3. D I S C U S S I O N

The significantly reduced values of the activation energy for the a and b' directions compared to dc data infer a strong frequency dependent response which is associated with the collective mode contribution to the electrical transport. This implies that the pinned mode resonance is present in the b' direction in a very similar manner compared to the a axis. Our conclusions are supported by previous studies 9 on the non-linear t ransport in the field- induced spin-density-wave phases which indicate that the phason mode is responsible for the break down of the quantum-Halt-effect regime.

In general it is assumed that the density wave can slide only along the chain direction our findings, however, give clear evidence for a collective contribution to the conductivity in the perpendicular direction. No indica- tions of a collective response is observed along the c*-direction. Hence the sliding density wave has to be considered a two-dimensional phenomenon with severe implications on the theoretical description.

~ Q=(2k F T:/b,O) % Fig. 1. Schematic Fermi sur-

face nesting of a quasi one- dimensional system with inter- chain coupling in the b-direction.

102

Anisotropic SDW Dynamics in (TMTSF)2PF 6

T (K) 20,0 10.0 6.7 5.0

I I I

135

E O

v *o 101

10 -1

E O

O_..

10 -2

E

v

o.. 10 .4

o ° ° ° ° D O

' I ' I I I I

e i

i I I I i I I

o _~ [] DD O O

D D

, I , I i I t

0.05 0.10 0,15 0.20

/ ' ~ C * =

o (22.8 + 1.4) K [] (19.3 + 0.4) K • (20.1 + 0.3) K

Ab,= • (5.8 + 0.2) K • (6.5 + 0,4) K o (6.8 + 0.6) K • (6.1 + 0.2) K ,* (5,2_+ 0.2) K [] (5.6+ 0.2) K

A a =

• (6.0 + 0.2) K o (5.9 + 0.4) K • (6.0 + 0.4) K [] (4.9 + 0.8) K

l IT (K -1)

Fig. 2. Temperature dependent microwave resistivity of (TMTSF)2PF6 along the a, b / and c* directions measured at 33.5 GHz. The individual curves for different samples vary slightly, however, the overall behavior is the same. For the c* axis the activation energy is approximately the same as measured by dc. In the a and b / directions, however, the slope is significantly lower: A ~ 6 K in both cases.

136 M. Dressel, K. Petukhov, and M. Scheffler

The nesting vector Q of a density wave indicates the direction (in k- space) for which the electron gas becomes instable with respect to pertur- bation. The superstructure due to the spin (or charge) density modulation eventually causes the energy gap at the Fermi energy to open. A sliding of the entire density wave results in non-linear t ransport and the pinned-mode resonance. This collective t ransport is not directly linked to the Fermi sur- face topology. The warping of the Fermi surface by interchain interaction tilts the nesting vector out of the chain axis. It implies some hopping be- tween the chains, but not necessarily coherent transport. From temperature dependent dc and optical experiments, 5 however, we know that at low tem- peratures (TMTSF)2PF6 develops a metallic, Drude-like conductivity in the b' direction. Does this imply that the collective SDW transport is possible also perpendicular to the chains? Further experiments are required to cast light on this issue.

4. C O N C L U S I O N

The enhanced conductivity found by microwave experiments on (TM- TSF)2PF6 evidences a collective t ransport not only along the chains, but also in the perpendicular b' direction. Thus the sliding SDW condensate is not confined to the chains, but it is a two-dimensional phenomenon. This conclusion, in fact, should hold for most of the spin and charge density wave materials when some finite interchain coupling is present.

A C K N O W L E D G M E N T S

We thank G. Untereiner for the crystal growth and sample preparation. The work was supported by the Deutsche Forschungsgemeinschaft (DFG).

R E F E R E N C E S

1. T. Takahashi et al., J. Phys. Soc. Jpn. 55, 1364 (1986). 2. K. Petukhov and M. Dressel, Phys. Rev. B 71, 073101 (2005). 3. G. Griiner, Dens i t y Waves in Solids (Addison-Wesley, Reading, 1994). 4. S.Tomid et at., Phys. Rev. Left.62, 462 (1989). 5. S. Donovan et al., Phys. Rev. B 49, 3363 (1994). 6. M. Dressel et al., Phys. Rev. B 71, 075104 (2005). 7. P. Zomoza et al., Eur. Phys. J. B 46, 223 (2005). 8. M. Scheffler and M. Dressel, to be published. 9. L. Balicas, Phys. Rev. Lett. 80, 1960 (1998).