Domain walls at the endpoint of the organic superconductor (TMTSF)2PF6 under pressure Ning Kang, Pascale Auban-Senzier, Denis Jérome, Claude Pasquier, Belal Salameh, Serguei Brazovskii

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Ning Kang, Pascale Auban-Senzier, Denis Jérome, Claude Pasquier, Belal Salameh, et al.. Domain walls at the spin density wave endpoint of the organic superconductor (TMTSF)2PF6 under pressure. 2009. ￿hal-00457963￿

HAL Id: hal-00457963 https://hal.archives-ouvertes.fr/hal-00457963 Preprint submitted on 19 Feb 2010

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N. Kang,1 P. Auban-Senzier,1 D. J´erome,1 C.R. Pasquier,1 B. Salameh,1, 2 and S. Brazovskii3 1Laboratoire de Physique des Solides, UMR 8502-CNRS, Univ.Paris-Sud, Orsay, F-91405, France 2Department of Applied Physics, Tafila Technical University, Tafila, Jordan 3LPTMS-CNRS, UMR 8626, Univ.Paris-Sud Bat 100, Orsay, F-91405, France

We report a comprehensive investigation of the organic superconductor (TMTSF)2PF6 in the vicinity of the endpoint of the spin density wave - phase transition where phase coexistence occurs. At low temperature, the transition of metallic domains towards is used to reveal the various textures. In particular, we demonstrate experimentally the existence of 1D and 2D metallic domains with a cross-over from a filamentary superconductivity mostly along the ′ c⋆-axis to a 2D superconductivity in the b c-plane perpendicular to the most conducting direction. The formation of these domain walls may be related to the proposal of a soliton phase in the vicinity of the critical pressure of the (TMTSF)2PF6 phase diagram.

PACS numbers: 73.61.-r, 73.23.-b, 73.50.-h

Understanding the evolution from a magnetically or- ature in the pressure regime where Tc remains constant dered metallic (possibly insulating) ground state to a was suggested by transport data along the most conduct- paramagnetic and metallic (M) (potentially supercon- ing axis and also supported by a drastic enhancement ducting) ground state is a long standing problem in con- of the upper critical field6–8. Furthermore, Vuletic et densed matter physics. Such a situation is encountered in al.4 pointed out the existence of a particular pressure, very diverse systems such as heavy fermion compounds, Pc0, related to a sudden vanishing of SC coherence. Si- cuprates, and the recently discovered pnictide supercon- multaneous measurements of NMR and transport at a ductors. In all these systems the parameter controlling given pressure have corroborated the claims for macro- the phase stability can be a dopant concentration, pres- scopic coexistence coming from transport data and have sure or magnetic field. Pressure was also at the origin of also provided an analysis of the volume fraction as a the discovery of superconductivity (SC) in the quasi one function of temperature9,10. However, the comprehen- dimensional charge transfer salt, (TMTSF)2PF6 , where sive pressure mapping of this coexistence regime SDW- an insulating itinerant antiferromagnetic phase known as M(SC) in the P T phase diagram is still missing as well a spin density wave (SDW) ground state is stabilized at as how the minority− phase M self-organizes within the low temperature through a second order phase transi- majority SDW phase. On theoretical grounds, various tion. As the magnetic order can be driven to zero tem- approaches have been developed: Ginzburg-Landau like perature by pressure with the stabilization of SC above models have succeeded to obtain a phase coexistence be- P 9 kbar, one would be entitled to believe that the tween SC and SDW states11 and a modulation of the SC c ≈ (TMTSF)2PF6 phase diagram provides a good exper- and SDW order parameters along both a and b axes has imental playground for the study of a SDW quantum been suggested12. A microscopic approach has also been critical point. The study of the border region between developed13,14 based on the soliton theory which leads SDW and SC becomes therefore an important issue for to a modulation of the SC and SDW order parameters organic superconductivity since no consensus exists yet along the a-axis. regarding the pairing mechanism and there has been a In this paper, we explore the emergence of the minority proposal for a microscopic coexistence of magnetic and phase, metallic (or SC at low temperature) from the pure superconducting order in a narrow pressure domain im- SDW state and how it evolves towards the homogeneous plying non nested region on the Fermi surface in the metal (or SC) state under pressure. We use superconduc- 1 2,3 vicinity of the boundary Pc . Early studies have rec- tivity as a tool to decorate the texture by comparing the ognized that the transition from the SDW to the metallic temperature dependence of resistivity experiments per- state is of first order in this pressure regime which has formed along the a, b′ and c⋆ axes. This texture is in been in turn extensively revisited by various techniques favor of the soliton model. in the last decade. Resistivity measurements were per- Resistivity measurements were performed in high- 4 formed by Vuletic et al. making small pressure incre- quality (TMTSF)2PF6 single crystals from the batch 5 4 ments up to Pc and subsequently by Kornilovet al. at a used in an earlier study . Gold plated electrical con- fixed pressure but monitoring the distance to Pc via an tacts were evaporated on the sample surfaces to mea- ′ ⋆ applied magnetic field. Both studies concluded to the sure ρa, ρb and ρc along a, b and c axes respectively coexistence of the two phases SDW/M or SDW/SC al- on different samples. The resistance measurements were though in spatially separated regions. The possibility of performed using a standard low frequency lock-in detec- metallic slabs becoming superconducting at low temper- tion. The applied current was chosen in order to remain 2

much weaker one between Pc1 and Pc0 (phase B) and fi- nally, Tc remains pressure independent above Pc0 (phase C). Phase A, Pc2 = 6.6

1K, only ρc exhibits a partial SC transition. In contrast, ρa(T ) exhibits the same insulating behavior as in the low pressure purely SDW state over the whole measured T range. ρb(T ) follows ρa(T ) except near Pc1 where it exhibits a saturation at low temperatures. The onset Tc (P ), in Fig.1, is defined by the onset of supercon- ductivity namely, the maximum of ρc(T ) at a given pres- sure, see Fig.2a. The sensitivity of SC to magnetic field is shown in Fig. 2(b) and (c) by the evolution of ρc(T ) FIG. 1. (Color online) Phase diagram of (TMTSF)2PF6 as de- with the applied magnetic field at P = 7.3 and P = 7.8 termined from resistivity measurements along the three axes kbar. The upward curvature of the upper critical field (circles: ρa; squares: ρb; triangles: ρc ). The filled (open) down to the lowest temperatures is in agreement with symbols correspond to the transition towards SC (SDW) re- 6–8 spectively. The contrast of colors between Pc2 and Pc illus- previous reports in (TM)2X salts . In this phase A, trates the increase in SC volume fraction from Pc2 up to Pc a higher pressure increases Tc and reduces the broadness corresponding to the three different regimes explained in the of the transition. Such a behavior is typical of phase text. Based on the knowledge of TSDW and Tc , the pres- separation as long as SC domains are smaller than the sure of 5.5 kbar in ref9 would correspond to 8.8 kbar with the penetration depth. Our data are also compatible with present pressure scale. the formation of filaments elongated mainly along the c⋆- axis which may cross the whole thickness of the sample approaching Pc1. Indeed, our observations looks quali- below the SC critical current along the considered axis tatively similar to the results for SC wires17 where the for each pressure and to minimize heating effects. The inherent presence of phase slips give rise to finite resis- measurements were carried out in a dilution refrigerator tance below Tc. (T 50mK) with a magnetic field always applied along Phase B, Pc1 =7.8

FIG. 2. (Color online) Phase A: (a) Temperature depen- dence of ρa, ρb and ρc at P = 7.8 kbar. (b) Temperature FIG. 4. (Color online) Phase B, P=8.3kbar: (a) Temper- dependence of ρc at P = 7.8 kbar for magnetic fields ranging ature dependence of ρa, ρb and ρc. The line through the data from 0 to 0.8T by step of 0.1T . The insert shows the deduced points of ρb corresponds to the fit of ρb by the BKT model. (b) upper critical field line. (c) Temperature dependence of ρc at Temperature dependence of ρb for different magnetic fields. P = 7.3 kbar for different magnetic fields.

ρa mimics the evolution of ρb in phase B. In particular, a ’double transition’ in ρa(T ) is observed nearly up to Pc. Phase D: superconductivity appears to be homoge- neous above Pc = 9.4 kbar. The starting frame of any in- terpretation is the electronic zone in the reciprocal lattice with the electronic spectrum E(~k) satisfying the nesting condition E(~k + Q~ ) E(~k) (with the accuracy of ∆ since at low T the state≈ − is insulating). The commonly used model limits the major spec- trum also to only nearest neighbors overlaps: E(~k) = 2t cos k 2t 0 cos k leading to the common-sense − a a − b b nesting wave number Q~0 = 2π(1/2, 1/2, 1/2). (The FIG. 3. (Color online) Phase B, P=8.0kbar: temperature wave numbers, ki, are taken in units of inverse lat- dependence of ρa, ρb and ρc at zero magnetic field. tice parameters.) But the SDW was always recognized to be incommensurate, and moreover its wave number has been well determined, in a and b directions, as low T2D 0.45K, by a model considering a 2D SC Q~ = 2π(1/2, q , q ) - with q = 1/4 0.05, not ∼ SDW b c b above its Berezinskii-Kosterlitz-Thouless (BKT) transi- 1/2! These direct X-ray results18 agree with± simula- 19,20 tion temperature, TBKT 0.15K, where the resistance tions from the NMR studies giving qb as 0.2 or 0.3. ∼ 1/2 21 2D TBKT That was elucidated by band structure calculations as reads, R (T ) = R0 exp G ,where BKT −  i T −TBKT  an ill-expected interference of oblique inter-stack over- 2D Gi TBKT /√tbtc is the 2D Ginzburg parameter and laps, tb1 between the nearest molecular stacks in b direc- ∼ 16 R0, a fitting parameter . tion, but among molecules which are next nearest neigh- Phase C, P 0 = 8.6

Φ0 = arctan(tb1/tb0), one sees that the interference sight counterintuitive, that the SC develops first in the does not± destroy the nesting but shifts its vector, in b direction of worst conduction. direction, from π to qb = π 2Φ0. For room temperature In conclusion, we have reported the first comprehensive crystal parameters the effect− is small as expected, but, investigation of the coexistence region in the pressure- 21 at low T , it becomes as large as to shift qb from 1/2 to temperature phase diagram of (TMTSF)2PF6 near the the vicinity of 1/4. critical pressure Pc , in which the SC phase is inhomoge- The metalization and progressive destruction of the neous and spatially modulated. This regime is character- SDW state is determined by the antinesting energy ized by conducting (SC) slabs perpendicular to the most ′ ′ Eanti(~k) = (E (~k)+ E (~k + Q~ ))/2. It is given by the conducting axis which originate from the coalescence of ⋆ smaller contributions E′(~k) = 2t cos k 2t′ cos2k metallic domains elongated mainly along the c -axis at − c c − b b considering them at the new nesting vector Q~ as it is low pressure as evidenced from the onset of superconduc- tivity first along c⋆ while the system remains insulating determined by the dominant term. The conventional ′ b along the perpendicular directions. At increasing pres- candidate for unnesting, 2t cos2k , gives E (~k) = ′ b b anti sure, metallic (SC) coherence sets in along the b direction t′ (cos2k + cos(2k +4πq− )). For the commonly sup- b b b b as well. An improvement of the model, coherent to both −posed q = 1/2, the two terms are identical giving b new and old overlooked observations, is proposed to un- b ~ ′ Eanti(k) = 2tb cos2kb. But now, for qb = 1/4, the two derstand the counterintuitive experimental picture. Our − b ~ terms have opposite signs, so Eanti(k) just vanishes. Al- study might be extended in the SDW/M regime above 22 though qb may not be exactly 1/4, the incommensurabil- Tc as already suggested , even if the texture is more diffi- b ~ ity of the SDW induces a noticeable decrease of Eanti(k). cult to extract in this regime. The existence of a textured Also, the effect of oblique overlaps slightly decrease with SC phase at the border of the SDW/metal transition in 21 pressure , hence the compensation of unnesting in b di- (TMTSF)2PF6 could help to shed new light on the nature rection reduces and this direction starts to play a big- of coexistence of two ordered phases in other strongly ger role. That seems to correlate with our observations. correlated systems, other (TM)2X salts as well as the The c-axis term, Ec (~k)= t (cos k + cos(k +2πq )), recently discovered iron-pnictide superconductors23. anti − c c c c survives: even if qc is not well determined, for all data ACKNOWLEDGMENTS q = 1/218,20 - there are no major terms to fix it as it c 6 was for qb. Therefore, most functions of the SDW de- This work was supported by the European Commu- struction, formation of the solitonic midgap state or of nity under the project CoMePhS (grant no. NMPT4-CT- spill-over pockets, and finally of stabilization of initially 2005-517039). N. K. and B.S. also acknowledge financial fragmented solitonic walls, - all are maintained by elec- support from this grant. S.B. acknowledges supports of tronic hybridization in the nominally weakest c direction. the ANR program (project BLAN07-3-192276). This picture is coherent with our observation, at first

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