# Hall resistivity in unconventional spin density wave in (TMTSF)Pf below K

###### Abstract

It is well documented that SDW in (TMTSF)PF undergoes another phase transition at K, though the nature of the new low temperature phase is controversial. We have shown recently that the new phase is well described in terms of unconventional SDW (USDW) which modifies the quasiparticle spectrum dramatically. In this paper we show that the same model describes consistently the Hall resistivity observed in (TMTSF)PF.

###### keywords:

transport measurements, magnetotransport, organic superconductors, , ,

## Introduction

Since the discovery of superconductivity in (TMTSF)PF in 1979 [1], the Bechgaard salts or the highly anisotropic organic superconductors (TMTSF)X (where TMTSF is tetramethyltetraselenfulvalene and X is anion PF, AsF, ClO …) are one of the most well studied systems [2]. The quasi-one-dimensionality (1D) is a consequence of the crystal structure, where the TMTSF molecules are stacked in columns in the direction (along which the highest conductivity occurs), and the resulting anisotropy in conductivity is commonly taken to be . The rich phase diagram of (TMTSF)X salts exhibits various low temperature phases under pressure and/or in magnetic field, among which the spin density wave (SDW), field induced SDW (FISDW) with quantum Hall effect and spin triplet superconductivity are very intriguing [3].

(TMTSF)PF is metallic down to K, where the transition into the semiconducting SDW takes place. It is known that SDW in (TMTSF)PF undergoes another transition at (at 3.5–4K at ambient pressure) [4, 5, 6]. The indication of the subphase was first seen by NMR [4], where diverges and the spin susceptibility changes at . The transition at is preserved through the entire phase diagram. Furthermore a calorimetric transition at 3.5K with a large hysteretic phenomenons in the temperature range 2.5–4K (caused by the sample history) has been observed and interpreted as an indication of a glass transition [6]. On the other hand, the low frequency dielectric relaxation of SDW in (TMTSF)PF did not show the existence of the glass transition [7]. Since then the SDW state was widely investigated, but the nature of the subphase remained controversial. Recently we have studied the axis magnetoresistance (MR) of (TMTSF)PF at ambient pressure and with magnetic field rotated within the plane. The MR has different behaviour for K and K [8]. For K MR is described in terms of the quasiparticle in a magnetic field, where the imperfect nesting term [9, 10] plays the crucial role. However, in order to describe MR below 4K we have introduced a rather artificial scattering term.

More recently, unconventional density waves (UCDW or USDW) have been proposed as a possible ground state in electronic systems in organic conductors and heavy fermions [11]. Unlike the conventional DW, the UDW is defined as the DW where the order parameter depends on the quasi-particle momentum . In particular, UCDW appears to describe the striking angular dependent magnetoresistance (ADMR) found in the low temperature phase of (ET)KHg(SCN) [12, 13]. On the other hand, we have shown that the remarkable features of ADMR in (TMTSF)PF below K (the decrease in the quasiparticle energy gap for and the sudden change in the angular dependence of the energy gap in the presence of magnetic field as the temperature crosses ) can be described within the model SDW plus USDW using the USDW order parameter , where with [14, 15].

In this paper we shall present the Hall resistivity data in (TMTSF)PF for K and K and discuss them within the model of SDW+USDW.

## Hall resistivity

The Hall resistivity in two crystals of (TMTSF)PF with dimension mm and mm was measured with 6 contact method as shown in inset of Fig.1. The results shown and discussed here were obtained on one of them, and similar qualitative behaviour was observed on another sample, too. The measurements were performed between 2.0K and 6.3K, with magnetic field up to 9T. The direction of the monocrystal is the highest conductivity direction, the intermediate conductivity is perpendicular to in the plane and the lowest conductivity direction is perpendicular to the (and ) plane.

The current flow was along the axis, the magnetic field along direction and the Hall voltage was detected along the axis.

The general and dependencies are consistent with earlier data by Uji et al. [16], although their main objective is the study of the rapid quantum oscillation. As is readily seen from Fig.1 and 2, the negative Hall resistivity is much smaller for K than for K. According to [17], the Hall resistivity in the quasi one dimensional system is given by

(1) |

where is the conductivity tensor.

If we neglect the quantum Hall effect, which contributes a new term in [18], we obtain

(2) |

where is the quasiparticle density and is the quasiparticle energy gap in the presence of magnetic field .

On the other hand, it is well known that has no activation form where is parallel to the axis [2, 15]. A possible explanation is that the conductivity parallel to the axis has another channel of which quasiparticle has no energy gap. A similar approach has been used in the quantitative analysis of in the FISDW state in (TMTSF)PF under high pressure [19]. Therefore, the fitting of our Hall data is done with

(3) |

where and are temperature dependent constants, and

(4) |

We took these expressions from [15], with and . Here, we limit ourselves to the case . The results of the fitting procedure are shown on both figures as the dotted lines (the values of and are given in Table 1). We have an excellent agreement with the experimental data. We note that is almost independent of temperature, while decreases as temperature decreases. The values of ’s used in the present fitting ( and ) are somewhat smaller than the ones used earlier [15], but they are of the same order of magnitude. Also, the exponent is somewhat strange (naturally, we expect ), but the similar exponent has been found in fitting the diagonal component of the magnetoresistance tensor [15].

(K) | (cm/T) | (T) |
---|---|---|

6.3 | ||

5.6 | ||

4.2 | ||

3.5 | ||

3.0 | ||

2.5 | ||

2.0 |

The agreement between the model and experimental data implies that the appearance of USDW below , over the preexisting SDW, with a new quasiparticle energy gap appears to describe the Hall resistivity consistently. In particular, the rapid increase of the Hall resistivity below testifies the rapid change in the quasiparticle energy gap across . In order to further test the present model the Hall resistivity data with the magnetic field away from the axis are highly desirable.

## Conclusion

We have completed the study of the resistivity tensor in (TMTSF)PF below . For we have shown that an approach with USDW+SDW below gives an excellent fit of the Hall resistivity data. This further supports our proposal that USDW appearing on top of existing SDW in (TMTSF)PF below gives a consistent description of the resistivity tensor.

## Acknowledgments

This experimental work was performed on samples prepared by K. Bechgaard. We acknowledge the participation of N. Francetić in the experiment and useful discussions with B. Dóra, A. Virosztek and S. Tomić.

This paper is dedicated to memory of Michael J. Rice. His interest and support of our work and our friendship over many years have been important to us.

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