# Hall effect study of field induced quantum oscillations in (TMTSF)2PF6 at 10.5 kbar

Denis Jerome, Brigitte Piveteau, L. Brossard, Alec Moradpour, M. Ribault

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Denis Jerome, Brigitte Piveteau, L. Brossard, Alec Moradpour, M. Ribault. Hall effect study of field induced quantum oscillations in (TMTSF)2PF6 at 10.5 kbar. Physica B, 1986. hal-05007777

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Distributed under a Creative Commons Attribution 4.0 International License
HALL EFFECT STUDY OF FIELD INDUCED QUANTUM OSCILLATIONS IN (TMTSF)₂PF₆ AT 10.5 KBAR

L. BROSSARD, B. PIVETEAU, D. JEROME, A. MORADPOUR and M. RIBAULT

Laboratoire de Physique des Solides-Associé au CNRS- Université de Paris-Sud-91405 ORSAY (France)

Above a temperature dependent threshold field $H_{th}$, a transverse magnetic field $H$ parallel to $c^*$ axis induces giant oscillations in the Hall voltage $V_H$ of (TMTSF)₂PF₆ under an hydrostatic pressure of 10.5 Kbar. Hysteresis are observed only when the Hall voltage goes from condensed holes ($V_H < 0$) to condensed electrons ($V_H > 0$): this is the signature of first order transitions between various SDW sub-phases, as for (TMTSF)₂C₂O₄ in the relaxed state. But each SDW sub-phase is itself subdivided by a weakly first order transition driving the transverse nesting vector of the Fermi surface from an electron pocket to an hole one, as for (TMTSF)₂C₂O₄ in the hyper-relaxed state. At a given $H$, the amplitude of $V_H$ increases and then saturates with decreasing temperature. Although this suggests a semi-metallic behaviour, the compound is never compensated due to the alternate condensation of electrons and holes with $H$. These features are compared with the Hall voltage results in (TMTSF)₂C₂O₄.

From ambient pressure up to 9 Kbar, the ground state of (TMTSF)₂PF₆ is a Spin Density Wave (S.D.W.) state with a wavevector close to (2k_F, π/2b, 0) at 1.7 K¹, but is superconducting for hydrostatic pressure in excess of 9 Kbar². At ambient pressure, a magnetic field $\parallel c^*$ and greater than 18 T, induces between 10 and 4 K oscillations of the magnetoresistance of Shubnikov de Haas type (S.de H.) whose frequency indicates a longitudinal nesting vector (2k_F, 0, 0)³. On the contrary, in the high pressure regime and at T>1 K, high magnetic field $\parallel c^*$ induces above a threshold field step-like structure of the Hall voltage and temperature independent wiggles of S.de H. type in the transverse magnetoresistance. Moreover, no field hysteresis effects were observed such as might suggest first order transitions⁴. These results were interpreted⁴ in a rigid (i.e. no field dependent) 2D Fermi surface with compensated, small electron and hole closed orbits. More recently, it has been claimed⁵ that the discrepancies between PF₆ and C₂O₄ salts could come from the low temperature (24 K) C₂O₄ anion ordering⁶, which should imply the presence of very soft vibrational modes; such modes could interact with the electronic states to alter the field induced transitions from second order (PF₆ case) to first order (C₂O₄ case).

In order to elucidate these open questions, we have performed magnetoresistance and Hall effect measurements on (TMTSF)₂PF₆ at 10.5 Kbar, at $T \le 1.2$ K under magnetic field $\parallel c^*$ up to 7.5 T; more detailed experimental results can be found elsewhere⁷. The aim of this note is to try to clear up mainly these problematic discrepancies.

<figure><img src="image_3.png" /><figcaption>FIGURE 1</figcaption></figure>

Temperature evolution of the giant Hall oscillations of (TMTSF)₂PF₆ under a pressure of 10.5 Kbar. The magnetic field $H$ is $\parallel c^*$.
First of all, Fig. 1) shows the very clear temperature dependence of the giant oscillations in the Hall voltage, which are growing in place with decreasing temperature; They appear above a threshold field $H_{th}$ increasing with temperature. A plot⁷ of the negative extrema of the Hall voltage or of the positive one, leads to a fairly periodicity with 1/H with a frequency of ~ 22 T quite close to the frequency of 28 T measured in $CLO_4(R)$ salt⁸: in both cases these frequencies promote transverse nesting vectors⁹. Far above $H_{th}$, i/ the oscillations show a sluggish saturating behaviour as T decreases for a given field and ii/ at a given temperature, their amplitude increase quasi-linearly with $(H-H_{th})$ up to 7 T, in a quasi-symmetrical manner around $V_H = 0$. The only differences with the $CLO_4$ salt in the "hyper-relaxed" state (with a 0.3 K/h cooling rate)⁸ are: i/ the Hall voltage plateaus cannot truly be identified and ii/ electrons and holes successive condensations play equally important roles.

<figure><img src="image_4.png" /><figcaption>FIGURE 2
Magnetic hysteresis of the giant Hall oscillations at T = .39 K of $(TMTSF)_2PF_6$ under a pressure of 10.5 Kbar. The magnetic field is // c*.</figcaption></figure>

Fig. 2 shows, at .39 K, a clear hysteresis effect with the magnetic field : as in the case of the "relaxed" $CLO_4$ salt¹⁰, this is the signature of a cascade of first order transitions between successive S.D.W. sub-states. But, the hysteresis is observed only when the Hall voltage is driven from a hole character ($V_H < 0$) to an electron one ($V_H > 0$) with increasing field, and vice versa when the field is decreasing.

At this stage, a new point thus appears : with increasing field, no hysteresis is observed when the Hall voltage goes from an electron character to a hole one. How such a transition can be of either second order or weakly first order will be discussed now; a careful examination of the cross section of the calculated Fermi surfaces¹¹ of the TMTSF salts shows many features :

i/ the optimal nesting vector of the F.S. is not in fact a single one, since it is not exactly commensurable with $2k_F$; indeed, two close inflexion points located on the same sheet of the 1D F.S. can lead to the best possible nestings of this surface. Associated with these two points, transverse nesting can promote either a hole or either an electron small pocket. This can explain that it is possible to observe a succession of Hall plateaus either > 0 or either < 0, according as the nesting corresponds to electron or hole small pocket respectively. If the electronic gas is not locked into one type of pocket, it seems possible to generalise the quantified nesting model⁹ to an alternation of Hall plateaus > 0, then < 0 and so on¹².

ii/ under pressure, the transverse transfer integral $t_b^1$ as also the warping of the F.S. increase; this induces a closeness of the two inflexion points on the same sheet of the F.S. and increases the probability of driving the nesting from a hole to an electron pocket and conversely. If these two points are enough close from one another, the lack of residual disorder in the case of $PF_6$ salt, could allow the nesting vector to slide from one point to another, thus from an electron pocket to a hole one in the present experimental case. This could be achieved quasi-continuously inside a given S.D.W. sub-phase.

Secondly, in the case of the "relaxed" $CLO_4(R)$ salt, the anion ordering creates also 2 close inflexion points at $k_a = 2k_F \pm \delta$, where $\delta$ is proportional to the anion ordering gaps which appear at $k_b = \pm \pi/2b$. But the anion ordering takes place into domains whose dimensions increase with decreasing cooling rate. The phase difference between the order parameters related
to contiguous domains is perceived as a residual disorder by the carriers during their cyclotron revolution; it is believed that this residual disorder lock the nesting vector upon the electron pocket just above $H_{th}$ for an unknown reason (probably due to very subtle details of the F.S.). Now, either for more and more slow cooling rates or either for greater magnetic fields, the dimensions of the ordered domains increase or the spatial extension of the quantified orbits decreases respectively. In both cases, the residual disorder rate seen by the carriers is decreasing; the system goes towards an unlocked situation and thus the nesting vector slides quasi-continuously to a hole pocket inside a given S.D.W. sub-phase.

Thus we suggest that the transport dynamics in $PF_6$ salt and in the "hyper-relaxed" state of $C_2O_4$ salt are relevant of a detailed Fermi surface structure. It seems reasonable to predict that a sufficiently slow cooling rate of $(TMTS)_2C_2O_4$ would lead to observe - with a correlated narrowness of the Hall plateaus - the oscillating structure of the $PF_6$ salt.

### ACKNOWLEDGEMENTS

It's a pleasure to thank L. Ducasse for sending us the calculated cross-sections of the Fermi surface of $PF_6$ and $C_2O_4$ salts at various temperatures and/or pressures. We want to thank also J.Cooper, M. Héritier, P. Lederer and G. Montambaux for stimulating discussions.

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