Introduction

The physical properties of quasi-low-dimensional (Q1D) conductors have been the subject of numerous investigations since these materials allow many fundamental theories of one- and two-dimensional systems to be directly tested1,2,3,4. It has been found4,5 that one-dimensional (1D) electron gas is not stable at low temperatures and correlation effects (interactions/fluctuations among the electron charges and/or spins) can lead to a rich variety of phase transitions and to different collective modes of condensate phase excitations. Depending on the details6,7 of the electron-electron and/or electron-phonon interactions, various quantum ground states, such as CDW, spin-density wave (SDW) and singlet (s-wave or d-wave) or triplet (p-wave) superconductivity may occur. Among which, CDW or SDW appears to be a precursor which sets the stage for superconductivity4,5,8. These nature phenomena have been observed1,2,3,4,6,7 in a number of low dimensional organic and non-organic conductors including cuprate and Fe-based high-Tc superconductors where the Fermi surface is highly anisotropic, suggesting a peculiarity of their electron charge and/or spin state associated with the formation of each of these long-range ordered phases.

In this paper we present an nuclear magnetic resonance (NMR) study of the low temperature metal-“insulator” crossover9,10,11,12,13,14, which is one of the most mysterious properties5,14,15,16,17 of the Q1D paramagnetic conductor lithium purple bronze, Li0.9Mo6O17. Even though intensive experimental studies have been performed since 1980s, the mechanism of this crossover remains unsolved, while four completely different mechanisms9,10,11,12,13,14,15,17,18,19 have been theoretically proposed: CDW, SDW, localization due to disorder (Anderson type) and Luttinger liquid. When the applied magnetic field B0 = 0, the crossover appears at temperature TMI = 24 K, while when B0 ≠ 0 this temperature can shift somewhat depending on the direction of it13,19. As for the superconductivity, the transition is at temperature Tc = 2.2 K8,9,20,21 and the superconductivity has been found to be three dimensional (3D)20,21,22,23. Thus this indicates that there is also an electron Q1D to 3D dimensional crossover. According to the thermal expansion data8, here the Q1D to 3D dimensional crossover of the conducting electrons is also found to take place gradually starting at or near the metal-“insulator” crossover temperature.

Most recent thermopower measurements show extreme thermoelectric effect anisotropy24,25 and theoretical studies22,23 suggest that when B0 is applied perpendicular to the lattice b-axis (B0 ⊥ b) and along the c-axis (in the sample bc-plane), there is a re-entrant superconductivity at high fields. These studies agree with those of the resistivity measurements in the applied magnetic field20,21, in which the metal-“insulator” crossover is viewed as the evidence of a DW gap (either CDW or SDW) formation20,21,26. They may shed new light on the understanding of the unknown properties, as they imply the significance of the electron charge and/or spin state, as well as its possible changes, associated with the metal-“insulator” crossover and its possible connection to the dimensional crossover as well as to the 3D superconductivity20,21,22,23. However, controversy exists27 in view of some of the same sets of experimental data presented previously and also the authors with the μsR data28 argue that SDW is not supported. Moreover, direct electron charge and/or spin state evidences, which are key important toward resolving the mysteries, have not been reported.

Here we provide a direct observation of the electron charge state for the low temperature metal-“insulator” crossover phenomenon, with our detailed temperature, field and angular dependences of the 7Li-/95Mo-NMR spectroscopy measurements on a single crystal of Li0.9Mo6O17. It is well-known that NMR is a versatile local probe capable of directly measuring the local electric and magnetic field including the electron charge and spin statics & dynamics at the atomic scale. Here we focus on the electron charge dynamics & statics surrounding the 7Li and 95Mo nucleus, which serve as the direct probes for the observation, with the experimental data that has the contributions from all types of sources including the lattice (electron-phonon coupling)6 and non-lattice contributions (such as the argument of possible electron-electron repulsion as that in the regime of a Luttinger liquid theory, a purely electronic origin)8. Our measurement has a sensitivity of 0.01 kHz in frequency, which allows us to be able to detect the local electric and/or magnetic field changes in the order of 102–103 times smaller than the known values previously reported in other Q1D materials29,30, associated with a possible CDW or SDW formation, or if any other state change occurs.

Figure 1a is the schematic of the experimental set-up with sample rotations around the lattice b-axis in the applied field B0 used in our NMR measurements, where the angle θ = 0o corresponds to B0 parallel to the a-axis (B0 || a). As we know, Li0.9Mo6O17 has a highly anisotropic conductivity20,21 of 250:10:1 along the lattice b, a and c axes, respectively (i.e., b is the conducting axis), with a monoclinic (space group P21/m) crystal structure28, as shown in Fig. 1b. More experimental details are described in the Methods section.

Figure 1
figure 1

Sample set-up in the NMR experiment and the crystal structure.

(a) Schematic of the sample rotation around the lattice b-axis in the applied magnetic field B0 (B0 ⊥ b). That the value of the angle θ = 0° is for B0 || a and θ is “+” if the sample rotation is clockwise [viewed along the b-axis (+)]. Otherwise, θ is “−”. For convenience, the values of the lattice constant of Li0.9Mo6O17 [Ref. 34] are also shown on the side. (b) The crystal structure of Li0.9Mo6O17 viewed along ~a –axis.

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Figure 2a shows the 7Li-NMR spectra at a typical temperature T = 275 K with B0 = 9 T, at various angles, plotted as the 7Li-NMR free-induction decay (FID) absorption amplitude versus the MMR frequency shift ν − νL, where ν is the NMR resonance frequency of the 7Li nucleus. Here νL is called the Larmor frequency, a constant determined by the value of B0 and the gyromagnetic ratio of 7Li. As expected theoretically29, the 7Li-NMR spectrum has a central line (PC) plus two symmetric quadrupolar satellites (PS1 and PS2), due to the 7Li spin quantum m = +1/2 ↔ −1/2 (central) and ±3/2 ↔ ±1/2 (satellites) transitions, respectively, as a spin I = 3/2 nucleus. Only three NMR lines are observed because all the Li sites are equivalent due to the space group P21/m symmetry.

Figure 2
figure 2

7Li-NMR spectrum and frequency shift.

(a) Angular dependence of the 7Li-NMR spectrum of Li0.9Mo6O17, plotted as the 7Li-NMR free-induction decay (FID) absorption amplitude versus the NMR frequency shift, at temperature T = 275 K with sample rotations around the b-axis in the applied magnetic field B0 = 9 T. (b) Angular dependence of the 7Li-NMR frequency shift of Li0.9Mo6O17 at various temperatures with sample rotations around the b-axis at B0 = 9 T. The dashed curves are the theoretical fit. The vertical dashed lines are for the directions of the a- and c-axes, the magic angle and the principle Z-axis (with quadrupole moment component pz) of the EFG determined from the experiment.

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Noticeably, as the angle θ varies, the satellites PS1 and PS2 exchange their positions across the angle θ = 54.7° (called “magic angle”)31,32. Their frequency shifts (ν − νL ≡ νS) have a rather strong angular dependence, which is in sharp contrast to that of the central line PC. This is because, generally, NMR spectrum satellites and central line have different origins: the central line is magnetic, while the satellites are quadrupolar – because of the quadrupolar interaction of the probe nucleus’s quadrupole moment (Q) with the electric field gradient (EFG) at the probe nucleus (under the high field limit)29. The EFG comes from the surrounding charges at all the lattice sites (called contribution of ligand lattice), plus electron orbital overlaps and charge covalence, according to the well-known point-charge model31,32. The quadrupolar interaction contribution to the satellites is dominant as it is in the first order, while to the central line is in the second order and thus usually negligible. Therefore, an NMR spectrum satellite of a probe nucleus can be used as a direct probe for the observation of the electron charge state, an intrinsic electronic behavior.

Figure 2b shows the angular dependence of the 7Li-NMR spectrum frequency shifts at various temperatures, from which we obtained the experimental value of 7Li quadrupolar frequency νQ, a measure31,32 of the EFG tensor (Vzz), νQ ≈ 44 kHz (detailed analysis can be found in the Supplementary Information). These data also indicate a highly symmetric electric field environment, where the z-component (pz) of the EFG principle axes is found to be ⊥ b and along the lattice a-axis at the Li site. But it shows no signature of change in the value of νQ (or EFG), upon cooling over a wide range of temperatures (including the crossover temperature at ~24 K).

In order to examine possible field effect on the observed EFG, we varied the magnitude of the magnetic field B0. This is shown in Fig. 3a, plotted as 7Li-NMR quadrupolar split Δνs (Δνs ≡ νs1−νs2) versus angle θ with B0 = 12 T, where νs1 and νs2 are the frequency shifts of the satellites PS1 and PS2, respectively (see Fig. 2b). For comparison, the data with B0 = 9 T at various temperatures are also displayed. No magnetic field dependence on the value of νQ (or EFG) is observed, which is also understandable since the satellites have a non-magnetic origin.

Figure 3
figure 3

7Li-NMR quadrupolar split frequency and 95Mo-NMR quadrupolar satellite frequency.

(a) Temperature and angular dependences of the 7Li-NMR quadrupolar split frequency of Li0.9Mo6O17 at the applied magnetic field B0 = 9 T and 12 T. The dashed curves are the theoretical fit. (b) Angular dependence of the 95Mo-NMR spectrum satellite frequency at a typical temperature T = 30 K with B0 = 14.8 T. The dashed curves are the theoretical fit with spin quantum m − 1/2 = ±1 for the inner satellites which have frequency shifts νs1 and νs2 and m − 1/2 = ±2 for the outer satellites which have frequency shifts νs3 and νs4. The dashed vertical lines indicate the positions of the lattice a- and c-axes and the magic angle, as well as the position of the principle Z-axis (pz) of the EFG at the Mo site obtained from the experiment.

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To further consolidate this observation, we performed similar NMR measurements at B0 = 14.8 T with the 95Mo nucleus (spin I = 5/2). The data are shown in Fig. 3b, where the values of νs1 and νs2 are the frequency shifts of the two inner NMR spectrum satellites (m − 1/2 = ±1) and νs3 and νs4 are the two outer ones (m − 1/2 = ± 2) right next to the inner satellites. With the same analysis used above for the 7Li, we obtained the 95Mo quadrupolar frequency νQ ≈ 65 kHz. The data also show a highly symmetric electric field environment, except that the z-component (pz) of the EFG principle axis at the Mo sites is along the lattice c-axis (note, the conduction electrons come from the Mo atoms). There is no signature of change in the value of νQ (or EFG) at the 95Mo, either, upon cooling in temperature. These results are summarized in Fig. 4, together with those of the 7Li nucleus, including the distribution of νQ as a function of temperature (300–2 K) and/or magnetic field (2.7–14.8 T) (see discussions in the Supplemental Information).

Figure 4
figure 4

7Li- and 95Mo-NMR quadrupolar frequency νQ (EFG) and distribution of νQ (EFG).

(a) Temperature dependence of the 7Li- and 95Mo-NMR quadrupolar frequency νQ (EFG) and/or the distribution of it at the applied magnetic field B0 = 9 T and/or 14.8 T. (b) Magnetic field-dependence of the 7Li-NMR quadrupolar frequency νQ (EFG) and the distribution of νQ (EFG). The values of ΔfQ for the distribution of νQ are obtained from the 7Li-NMR spectra at B0 ~ || a, where the total internal magnetic field at the Li site is ~0. The dashed lines are the guides to the eye.

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Finally, the values of νQ (EFG) obtained above with both 7Li and 95Mo nuclei can be theoretically calculated using the point-charge model29,30. Our theoretical estimation (detailed in the Supplemental Information) indicates that on the average at both nuclei, 1) the charge covalence contribution to νQ (EFG) has a similar magnitude as that from the ligand lattice, while the contribution of the orbital overlap is negligible and 2) among the ligand lattice the charges from the Mo electrons have a contribution ~1.5 times larger than that of the charges from the oxygen. This indicates the effectiveness of the observation probes using 7Li and/or 95Mo nuclei.

In summary, we presented a direct observation of the electron charge state in Li0.9Mo6O17. The parameters of the EFG (nuclear quadrupolar frequency) are found by our 7Li- and 95Mo-NMR measurements and also theoretically estimated. We showed no sign of change in the EFG or in the distribution of it at the atomic scale, as a function of temperature and/or applied magnetic field, i.e., there is no possibility for a lattice-driven or a purely electronic CDW. Thus, we provided a direct experimental evidence demonstrating that the long mysterious metal-“insulator” crossover is not due to the CDW and the nature of the observed DW gapping is not a CDW. Our discovery lays the foundation for the understanding of the unusual properties of Li0.9Mo6O17 and opens a parallel path to the study of the electron spin state at the metal-“insulator” crossover and of its potential connection to the electron dimensional crossover as well as to the spin triplet superconductivity in low dimensional electron systems in general.

Methods

High quality single crystals of Li0.9Mo6O17 were grown using a temperature-gradient flux method8,10. The sample used for the measurement has a length ~1.7 mm and a width ~1.0 mm, while the thickness at one end is 0.3 mm and at the other end is ~0.6 mm. The sample mass is 1.5 mg. The NMR coil was made from 50 μm diameter copper wire wound with ~30 turns. The 7Li-NMR experiments were conducted with a spectrometer and probe built at UCLA Clarklab (W. G. Clark) and the 95Mo-NMR measurements on the same sample were performed at the Grenoble High Magnetic Field Laboratory, France with field B0 = 14.8 T. The sample was fixed on the goniometer in the NMR probe during the measurements so that it can rotate around the lattice b-axis.

The “smash tickle” method developed33 by Clark et al. was used for the 7Li-NMR measurements, with our consideration that the 7Li spin-lattice relaxation time goes extremely long at low temperatures. The 95Mo-NMR measurements used standard spin-echo techniques31,32, with number of averages up to 10,000 for the signal recording, due to the very small gyromagnetic ratio and the very small natural abundance of the 95Mo nucleus. Thus, noticeably, these are extremely difficult experiments.

The calibration of each applied magnetic field B0 used for the 7Li/95Mo-NMR measurements was made at temperature T = 10 K with the 63Cu free-induction decay (FID) signals from the sample coil. For example, the value of B0 used for the measurements at the 12 T magnet is determined to be B0 = 11.9948 T and at the 14.8 T magnet is B0 = 14.7427 T. Using the standard Fourier transform (FFT) algorithm in the spectrum analysis, our NMR spectrometer system has a high resolution enabling us to detect a frequency change of 0.01 kHz because of a local electric and/or magnetic field at the atomic scale, as a consequence of CDW, SDW, superconductivity, lattice structure change or any other phase transitions. Noticeably, this is highly sensitive as the honor of the role of an NMR spectrum normally plays. As an example, for a CDW or a charge ordering, it has been experimentally observed that across the transition there is a local field change, which corresponds to a change (spectrum splitting) in NMR frequency to be in the order of ~5–10 kHz, as seen in the blue bronze29 Rb0.3MoO3 and in the TMTSF family30, respectively.

Additional Information

How to cite this article: Wu, G. et al. Direct observation of charge state in the quasi-one-dimensional conductor Li0.9Mo6O17. Sci. Rep. 6, 20721; doi: 10.1038/srep20721 (2016).