PHYSICAL REVIEW B 86, 085130 (2012) Magnetic field induced lattice effects in a quasi-two-dimensional organic conductor close to the Mott metal-insulator transition Mariano de Souza,1,2,* Andreas Brühl,1 Christian Strack,1 Dieter Schweitzer,3 and Michael Lang1 1Physikalisches Institut, Goethe-Universität Frankfurt, SFB-TR49, Max-von-Laue Strasse 1, D-60438 Frankfurt am Main, Germany 2Instituto de Geociências e Ciências Exatas - IGCE, Unesp - Univ Estadual Paulista, Departamento de Fı́sica, Caixa Postal 178, 13506-970 Rio Claro (SP), Brazil 33. Physikalisches Institut, Universität Stuttgart, D-70550 Stuttgart, Germany (Received 29 May 2012; revised manuscript received 1 August 2012; published 21 August 2012) We present ultra-high-resolution dilatometric studies in magnetic fields on a quasi-two-dimensional organic conductor κ-(D8-BEDT-TTF)2Cu[N(CN)2]Br, which is located close to the Mott metal-insulator (MI) transition. The obtained thermal expansion coefficient, α(T ), reveals two remarkable features: (i) the Mott MI transition temperature TMI = (13.6 ± 0.6) K is insensitive to fields up to 10 T, the highest applied field; (ii) for fields along the interlayer b axis, a magnetic field induced (FI) phase transition at TFI = (9.5 ± 0.5) K is observed above a threshold field Hc ∼ 1 T, indicative of a spin reorientation with strong magnetoelastic coupling. DOI: 10.1103/PhysRevB.86.085130 PACS number(s): 72.15.Eb, 72.80.Le, 74.70.Kn I. INTRODUCTION Currently, strong activities in condensed matter physics have been directed towards a better understanding of correla- tion effects in low-dimensional systems. The strong interaction between electrons in these systems gives rise to several inter- esting phenomena. Among them, the Mott metal-to-insulator (MI) transition can be considered one of the most prominent examples. Organic conductors of the κ-phase (BEDT-TTF)2X family [where BEDT-TTF, or simply ET, refers to the donor molecule bis(ethylenedithio)tetrathiafulvalene and X to a monovalent anion] have been recognized as appropriate systems for studying phenomena originating from the inter- play of electron-electron and electron-lattice interactions in reduced dimensions (for a recent review, see, e.g., Ref. 1). These substances are built by layers of interacting dimers, i.e., (ET)+2 , sandwiched by sheets of insulating polymeric counteranions X−, giving rise thus to a quasi-two-dimensional electronic structure. Their ground states can be tuned by chemical substitution and/or applying external pressure; see, e.g., the pressure-temperature (P -T ) phase diagram in Fig. 1. While the salt with X = Cu[N(CN)2]Cl (κ-Cl in short) is an antiferromagnetic Mott insulator (AFI) with TN ≈ 26 K, the salt with X = Cu[N(CN)2]Br (κ-H8-Br in short) is a superconductor (SC) with Tc ≈ 11 K, the highest Tc at ambient pressure among all ET-based organic compounds investigated to date. Interestingly enough, for X = Cu[N(CN)2]Br, the exchange of the hydrogen atoms of the ethylene end groups of the ET molecules by deuterium results in an antiferromagnetic insulating ground state, corresponding to a shift on the pressure axis towards lower pressure.9 The insulating state in the P -T phase diagram is separated from the metallic/superconducting range by an S-shaped first-order phase transition line (thick solid line in Fig. 1) which ends in a second-order critical point, indicated by (P0, T0) in Fig. 1 (see Ref. 7 and references therein for details). Hence, due to their close proximity to the MI boundary, fully deuterated salts of κ-(ET)2Cu[N(CN)2]Br, abbreviated to κ-D8-Br hereafter, have been recognized as suitable systems for exploring the Mott MI transition. The magnetic properties of the κ-phase (ET)2X family, especially the X = Cu[N(CN)2]Cl salt, have been investigated by various experimental techniques (see, e.g. Refs. 10,11, and 12). From the analysis of the NMR line shape, relaxation rate, and magnetization data, Miyagawa et al.12 were able to describe the spin structure of this state. Below TN = 26–27 K, they found a commensurate antiferromagnetic ordering with a magnetic moment of (0.4–1.0)μB/dimer. The observation of an abrupt jump in the magnetization curves for magnetic fields applied perpendicular to the conducting layers, i.e., along the b axis, was attributed to a spin-flop (SF) transition. Furthermore, a detailed discussion about the spin reorientation, taking into account the Dzialoshinskii-Moriya interaction, was presented by Smith et al.13,14 By resistance measurements under control of temperature, pressure, and magnetic field, a magnetic field induced Mott MI transition was observed by Kagawa et al.15 Interestingly enough, similar to this finding for the pressurized κ-Cl salt, a magnetic field induced MI transition was also observed in partially deuterated κ-(ET)2Cu[N(CN)2]Br.16 Fur- thermore, from 12C NMR studies evidence for phase separation into metallic/superconducting and magnetic phases in κ-D8-Br was reported in the literature.17 From temperature-dependent measurements of the coefficient of thermal expansion, the role of the lattice degrees of freedom for the Mott transition7 and the Mott criticality18 were studied. The latter results were found to be at odds with the Mott criticality derived from conductivity19 and NMR20 studies on pressurized κ-Cl. In order to gain more insight into the nature of the state on the insulating side of the Mott transition for the present κ-D8-Br material, we have performed thermal expansion measurements in magnetic fields. In this communication, we present expansivity data on single-crystal κ-D8-Br in magnetic fields up to 10 T and explore the field effects on the various phases in the vicinity of the MI line. II. EXPERIMENT High-quality single crystals of fully deuterated κ-(D8- ET)2Cu[N(CN)2]Br were prepared according to an alternative procedure as described in Refs. 21 and 22. The single crystal 085130-11098-0121/2012/86(8)/085130(5) ©2012 American Physical Society http://dx.doi.org/10.1103/PhysRevB.86.085130 DE SOUZA, BRÜHL, STRACK, SCHWEITZER, AND LANG PHYSICAL REVIEW B 86, 085130 (2012) 0 10 20 30 40 0 10 20 30 40 Z = Cl (P0,T0) TMI TC "H8-Br" Paramagnetic Insulator Antiferromagnetic Insulator Perco- lative SC Metal Bulk SC T ( K ) P (MPa) or (W/U eff ) Z = Br, "D8-Br" TN FIG. 1. Pressure-temperature (P -T ) phase diagram of κ- (ET)2Cu[N(CN)2]Z at zero magnetic field. The dashed line labeled TN indicates the paramagnetic-to-antiferromagnetic transition, the dash-dotted line labeled Tc corresponds to the transition into bulk superconductivity, and the thick solid line labeled TMI marks the first-order metal-to-insulator transition. D8-Br and H8-Br (position estimated according to Ref. 2) refer to the position of the deuterated and protonated single crystals of κ-(ET)2Cu[N(CN)2]Br, respectively. The vertical dotted line indicates the performed T sweeps for “D8-Br” crystals, illustrating a crossing of the S-shaped line. Open symbols refer to literature data for the critical end point (P0, T0): � (Ref. 3), � (Ref. 4), © (Ref. 5), � (Ref. 6), and � (Ref. 7). The position of the solid circle, corresponding to TMI for the present crystal, implies that at this point in the phase diagram TMI coincides with TN (cf. Ref. 8). studied here, labeled as 3 (batch A2907), is identical to the one studied in Ref. 2. The linear thermal expansion coeffi- cient, α(T) = l−1(∂l/∂T) (where l is the sample length), was measured by employing an ultra-high-resolution capacitance dilatometer with a maximum resolution of �l/l = 10−10, built after Ref. 23. Samples of the organic charge-transfer salts studied here are very sensitive to the quasiuniaxial pressure exerted by the dilatometer.24 In fact, the uniaxial pressure acting on the crystal, typically a few bars, can be adjusted by setting the starting capacitance. In order to reduce the strain exerted by the dilatometer on the sample to a minimum, a very small starting capacitance was chosen. The experimental data presented were corrected only for the thermal expansion of the dilatometer cell with no further data processing. The alignment of the crystal was guaranteed with an error margin of ±3◦. In all measurements, the magnetic field is parallel to the measuring direction. Resistance measurements were carried out by employing the standard four-terminal ac technique. In order to reduce cooling-rate-dependent effects associated with disorder of the ethylene end groups of the ET molecules, a cooling rate of ∼−3 K/h (thermal expansion) and ∼−6 K/h (resistance) through the glasslike transition around 77 K (Ref. 25) was applied. After the initial con- trolled cooldown, the sample was kept at temperatures below 40 K. Measurements of α(T ,B = const) were performed at temperatures ranging from 4.5 K up to about 14 K except for B = 0.5 T, where the measurements were limited to T � 11 K. III. RESULTS AND DISCUSSION The thermal expansion coefficient along the interplane b axis in zero magnetic field is displayed in Fig. 2. Upon cooling, an anomaly at Tg ≈ 77 K is observed. This anomaly has been attributed to a glasslike transition, which has been discussed in the literature in connection with the freezing out of the ethylene end groups25 and anion ordering.24,26 Upon further cooling, a second anomaly around TP = 30 K is observed. This feature has been assigned to critical fluctuations associated with the second-order critical end point of the first-order line,7,18 indicated by the solid triangle in Fig. 1. Further decreasing of the temperature reveals a pronounced anomaly around TMI = 13.6 K. As discussed in Ref. 7, this pronounced negative expansivity peak reflects the b-axis lattice effect upon crossing the first-order MI transition line; cf. the inset of Fig. 2, showing the anomaly in αb(T ) at T = TMI, which coincides with the metal-insulator transition revealed by resistivity. The peak of the anomaly in αb(T ) was taken as the thermodynamic transition temperature. The first-order character of the transition was confirmed by the observation of hysteresis in both R(T ) and relative length changes (�l/l) around TMI for another crystal.7 The drop of the resistance at Tc = 11.6 K, accompanied by a tiny kink (indicated by the arrow) in αb(T ), are signatures of a percolative SC in minor portions of the sample volume coexisting with the AFI state (see, e.g., Refs. 27 and 28). In what follows is a discussion on the effects of magnetic fields in the vicinity of the Mott MI transition. Figure 3 shows 0 2 0 4 0 6 0 8 0 1 0 0 -2 0 -1 0 0 1 0 2 0 3 0 4 0 5 0 6 0 6 8 10 12 14 16 18 20 -25 -20 -15 -10 -5 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Tc α b (1 0-6 K -1 ) T (K) TMI R (T )/ R (3 00 K ) TMI α b (1 0-6 K -1 ) T (K) Tg TP FIG. 2. Values of α(T ) along the b axis for single-crystal κ- (D8-ET)2Cu[N(CN)2]Br. Inset: magnification of the low-temperature αb(T ) data (left scale) together with results of the resistance normalized to the room-temperature value (right scale). TMI refers to the MI transition temperature and Tc denotes the critical temperature to percolative SC. 085130-2 MAGNETIC FIELD INDUCED LATTICE EFFECTS IN A . . . PHYSICAL REVIEW B 86, 085130 (2012) 4 8 1 2 1 6 -80 -60 -40 -20 0 TFI Zero-field 10T 4T 0.5T 1T 2T 6T T (K) α b (1 0-6 K -1 ) TMI FIG. 3. (Color online) Values of α(T ) for single-crystal κ-(D8- ET)2Cu[N(CN)2]Br measured along the b axis at low temperatures under selected fields, as indicated. Solid lines are a guide for the eyes. TFI refers to the magnetic field induced transition temperature and TMI to the metal-to-insulator transition temperature. Data taken at 0.5, 1, 2, 4, 6, and 10 T are shifted vertically for clarity. the zero field thermal expansion coefficient along the b axis at low temperatures on expanded scales together with data taken in magnetic fields of 0.5, 1, 2, 4, 6, and 10 T. The first information obtained from these data sets is that, upon cooling under magnetic field up to 10 T, TMI remains virtually unaffected within the resolution of our experiment. Upon further cooling under a weak field of 1 T, however, a second negative peak, centered around TFI = 9.5 K, can be observed. This second peak becomes more pronounced at 2 T and saturates in size at a field of about 4 T. A closer inspection of the data in Fig. 3 reveals the existence of a double-peak structure for fields exceeding 1 T. The latter has been reproduced in several runs performed under varying magnetic fields so that the possibility of experimental artifact can be ruled out. It is worth mentioning that the field induced phase transitions manifest themselves in kinks in the relative length changes (not shown), indicative of second-order phase transitions. The physical origin of this double-peak structure remains unclear and requires further investigations. It is well known that, under certain conditions, an antiferromagnet exposed to a magnetic field can become unstable against a state where the sublattice magnetization aligns approximately perpendicular to the field: the so-called spin-flop (SF) phase. The SF transition occurs when the magnetic field is applied parallel to the easy axis of the antiferromagnet and exceeds a critical value (critical field). As we discuss below in more detail, the field dependence of αb(T ) in the present case is indicative of a SF transition with strong coupling between the spin and lattice degrees of freedom. As can be seen in Fig. 3, Hc < 1 T (Hc refers to the critical field) for κ-D8-Br, which is consistent with a critical field Hc ∼ 0.4 T for the κ-Cl salt deduced in Ref. 12. However, the growth of the anomaly in αb(T) with increasing fields H > Hc at a virtually constant transition temperature TFI = 9.5 K is not expected for a SF transition and requires an explanation. In this respect we mention the results of resistance measurements on 50% and 75% deuterated κ-phase (ET)2Cu[N(CN)2]Br samples performed under field sweep (field applied along the b axis) at T = 5.50 and 4.15 K, respectively, where a transition from SC to a low-resistive state was found for fields exceeding about 1 T.29 This state was found to transform into a high-resistive state via jumplike increases in the resistance upon further increasing the field to 10 T.29 This behavior was interpreted by the authors as a field induced first-order SC-to-insulator transition and related to the theoretical scheme based on the SO(5) symmetry for superconductivity and antiferromagnetism, proposed by Zhang30 for the high-Tc cuprates. Likewise, a drastic B- induced increase in the resistance was observed also for the κ-(ET)2Cu[N(CN)2]Cl system when tuned close to the MI transition by hydrostatic pressure.6 Here it was argued that the marginally metallic/superconducting phases near the Mott transition undergo a field induced localization transition in accordance with theoretical predictions (see, e.g., Ref. 31 and references cited therein). Hence, based on these observations we expect that close to the Mott MI transition in the present fully deuterated κ-(ET)2Cu[N(CN)2]Br salt the electronic states may undergo drastic changes upon increasing the field. In fact, the initial rapid growth of the anomaly in αb and the tendency to saturation above about 4 T is very similar to the evolution of the resistance, i.e., the increase of R(B,T = const) with field revealed in the aforementioned transport studies.6,29 In this process, those electrons which are involved in the localization no longer contribute to the chemical binding and, as a consequence, the lattice expands. Hence, it is natural to associate the growth of the anomaly in αb(T) upon increasing fields H > Hc with the field induced localization transition.31 The observation of a field induced transition at TFI < TMI raises a question on the nature of the intermediary phase that forms in the temperature window between TMI and TFI for fields H > Hc. In the present stage of the investigations, i.e., lacking a detailed microscopic magnetic characterization of this state, we consider that this phase represents a paramagnetic insulator (PI), consistent with the notion of the SF transition. This assumption is in line with the magnetic phases proposed for κ-(ET)2Cu[N(CN)2]Cl in Refs. 13 and 14. In Fig. 4, a preliminary H ‖ b versus T phase diagram for fully deuterated κ-(ET)2Cu[N(CN)2]Br based on the expansivity data is shown. We stress that no such field induced effects were observed for fields along the a and c axes (not shown), also corroborating our claim of a SF transition. In fact, in Ref. 13 the authors pointed out that the nature of the interlayer magnetic ordering depends on the direction of the applied magnetic field. In particular, based on a detailed analysis of NMR and magnetization data, taking into account the Dzialoshinskii-Moriya interaction, they found that antiferromagnetic ordering between planes can be observed only for magnetic fields above Hc applied along the b axis. 085130-3 DE SOUZA, BRÜHL, STRACK, SCHWEITZER, AND LANG PHYSICAL REVIEW B 86, 085130 (2012) 0 5 10 15 20 0 2 4 6 8 10 SF + Perc. SC Spin-reoriented phase AFI + Perc. SC PI PM H // b -a xi s ( T ) T (K) FIG. 4. Schematic B-T diagram for κ-D8-Br. Symbols refer to the peak anomaly in αb(T ). Diamonds: peak position of the anomaly in αb associated with the metal-to-insulator transition, AFI + Perc. SC refers to the antiferromagnetic insulating phase coexisting with percolative superconductivity, while SF + Perc. SC indicates the spin- flopped phase coexisting with percolative superconductivity. Lines represent the various phase transitions discussed in the main text. PM and PI denote paramagnetic metal and paramagnetic insulator, respectively. The hatched region indicates the T window in which a double-peak structure in αb(T ) is observed. The spin-reoriented phase refers to the region where M† A and M† B are antiparallel, giving rise to an interplane antiferromagnetic ordering as discussed in the main text (cf. Ref. 14). At this point, it is worth mentioning that the term “interplane AFM ordering” is used here as defined in Figs. 4 and 5 of Ref. 13. Hence, given the absence of lattice effects at TFI for magnetic fields applied along the a and c axes, our findings indicate a close relation between interplane antiferromagnetic ordering and the lattice effects observed at TFI. Following the notation used by the authors in Ref. 13, the magnetization of the + (−) sublattice at the layer l is M+(−)l . The staggered and ferromagnetic moments are given by M† l = (M+l − M−l)/2 and MF l = (M+l + M−l)/2, respectively. For fields above Hc applied along the b axis, MF l is along b and M† l is in the a-c plane. M† A and M† B are antiparallel, giving rise to an interplane antiferromagnetic ordering. Our observation of a negative peak anomaly in αb(T ) at T = TFI thus suggests that, in order to achieve this particular spin configuration, the gain in exchange energy forces the layers formed by the (ET)+2 dimers to move apart from each other. Similar dilatometric experiments were carried out on two other κ-D8-Br single crystals. For both crystals, in contrast to the sharp anomaly at TFI ≈ 9.5 K under magnetic fields shown in Fig. 3, the effects of magnetic fields result in a smooth change of αb(T ) around the same temperature. Two factors should be considered as a possible explanation: (i) The crystal alignment upon mounting the sample in the dilatometer. As reported in the literature (see, e.g., Ref. 32), SF transitions are strongly dependent on the direction of the applied magnetic field. A minute misalignment of the material’s easy axis with respect to the applied magnetic field can cause a suppression of the transition. (ii) Sample inhomogeneities and/or the effect of the pres- sure exerted by the dilatometer on the sample. For one of these single crystals, we studied the effect of quasiuniaxial pressure exerted by the dilatometer on the sample and observed that a quasiuniaxial pressure of some of a few bars is enough to change the shape of the thermal expansion curves considerably: upon the application of uniaxial pressure of about 65 bar the transition was smeared out over a very wide temperature range.24 Our thermal expansion results at magnetic fields along the b- axis are summarized in the schematic H versus T diagram depicted in Fig. 4. The dashed line around ∼0.5 T separates the AFI from the SF phase, while the thick line marks the suppression of percolative SC together with the appearance of the spin-reoriented phase. The latter was first observed for κ-(ET)2Cu[N(CN)2]Cl and reported in Ref. 14. IV. SUMMARY In conclusion, our thermal expansion studies on fully deuterated κ-(BEDT-TTF)2Cu[N(CN)2]Br under magnetic field reveal the insensitivity of the Mott metal-to-insulator transition temperature under fields up to 10 T, which is in accordance with the proposal of a Mott insulating state with a π hole localized in a dimer. A field induced phase transition at TFI = (9.5 ± 0.5) K is observed, indicative of a spin reorientation with strong magnetoelastic coupling. Further experiments, including magnetostriction measurements both below and above TFI as well as magnetic measurements with B thoroughly aligned along the b axis, will help to better understand the behavior of almost localized strongly correlated electrons in this interesting region of the phase diagram of the κ-phase (BEDT-TTF)2X charge-transfer salts. 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