Direct observation of charge state in the quasi-one-dimensional conductor Li0.9Mo6O17

The quasi-one-dimensional conductor Li0.9Mo6O17 has been of great interest because of its unusual properties. It has a conducting phase with properties different from a simple Fermi liquid, a poorly understood “insulating” phase as indicated by a metal-“insulator” crossover (a mystery for over 30 years), and a superconducting phase which may involve spin triplet Cooper pairs as a three-dimensional (p-wave) non-conventional superconductor. Recent evidence suggests a density wave (DW) gapping regarding the metal-“insulator” crossover. However, the nature of the DW, such as whether it is due to the change in the charge state or spin state, and its relationship to the dimensional crossover and to the spin triplet superconductivity, remains elusive. Here by performing 7Li-/95Mo-nuclear magnetic resonance (NMR) spectroscopy, we directly observed the charge state which shows no signature of change in the electric field gradient (nuclear quadrupolar frequency) or in the distribution of it, thus providing direct experimental evidences demonstrating that the long mysterious metal-“insulator” crossover is not due to the charge density wave (CDW) that was thought, and the nature of the DW gapping is not CDW. This discovery opens a parallel path to the study of the electron spin state and its possible connections to other unusual properties.

Scientific RepoRts | 6:20721 | DOI: 10.1038/srep20721 Most recent thermopower measurements show extreme thermoelectric effect anisotropy 24,25 , and theoretical studies 22,23 suggest that when B 0 is applied perpendicular to the lattice b-axis (B 0 ⊥ 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 field 20,21 , in which the metal-"insulator" crossover is viewed as the evidence of a DW gap (either CDW or SDW) formation 20,21,26 . 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 superconductivity [20][21][22][23] . However, controversy exists 27 in view of some of the same sets of experimental data presented previously, and also the authors with the μ sR data 28 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 7 Li-/ 95 Mo-NMR spectroscopy measurements on a single crystal of Li 0.9 Mo 6 O 17 . 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 7 Li and 95 Mo 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 10 2 -10 3 times smaller than the known values previously reported in other Q1D materials 29,30 , 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 B 0 used in our NMR measurements, where the angle θ = 0 o corresponds to B 0 parallel to the a-axis (B 0 || a). As we know, Li 0.9 Mo 6 O 17 has a highly anisotropic conductivity 20,21 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 P2 1 /m) crystal structure 28 , as shown in Fig. 1b. More experimental details are described in the Methods section.  Figure 2a shows the 7 Li-NMR spectra at a typical temperature T = 275 K with B 0 = 9 T, at various angles, plotted as the 7 Li-NMR free-induction decay (FID) absorption amplitude versus the MMR frequency shift ν − ν L , where ν is the NMR resonance frequency of the 7 Li nucleus. Here ν L is called the Larmor frequency, a constant determined by the value of B 0 and the gyromagnetic ratio of 7 Li. As expected theoretically 29 , the 7 Li-NMR spectrum has a central line (P C ) plus two symmetric quadrupolar satellites (P S1 and P S2 ), due to the 7 Li 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 P2 1 /m symmetry.
Noticeably, as the angle θ varies, the satellites P S1 and P S2 exchange their positions across the angle θ = 54.7° (called "magic angle") 31,32 . Their frequency shifts (ν − ν L ≡ ν S ) have a rather strong angular dependence, which is in sharp contrast to that of the central line P C . 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 model 31,32 . 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 7 Li-NMR spectrum frequency shifts at various temperatures, from which we obtained the experimental value of 7 Li quadrupolar frequency ν Q , a measure 31,32 of the EFG tensor (V zz ), ν Q ≈ 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 (p z ) 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 ν Q (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 B 0 . This is shown in Fig. 3a, plotted as 7 Li-NMR quadrupolar split Δ ν s (Δ ν s ≡ ν s1 − ν s2 ) versus angle θ with B 0 = 12 T, where ν s1 and ν s2 are the frequency shifts of the satellites P S1 and P S2 , respectively (see Fig. 2b). For comparison, the data with B 0 = 9 T at various temperatures are also displayed. No magnetic field dependence on the value of ν Q (or EFG) is observed, which is also understandable since the satellites have a non-magnetic origin.
To further consolidate this observation, we performed similar NMR measurements at B 0 = 14.8 T with the 95 Mo nucleus (spin I = 5/2). The data are shown in Fig. 3b, where the values of ν s1 and ν s2 are the frequency shifts of the two inner NMR spectrum satellites (m − 1/2 = ± 1), and ν s3 and ν s4 are the two outer ones (m − 1/2 = ± 2) right next to the inner satellites. With the same analysis used above for the 7 Li, we obtained the 95 Mo quadrupolar frequency ν Q ≈ 65 kHz. The data also show a highly symmetric electric field environment, except that the z-component (p z ) 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 ν Q (or EFG) at the 95 Mo, either, upon cooling in temperature. These results are summarized in Fig. 4, together with those of the 7 Li nucleus, including the distribution of ν Q as a function of temperature (300-2 K) and/or magnetic field (2.7-14.8 T) (see discussions in the Supplemental Information).
Finally, the values of ν Q (EFG) obtained above with both 7 Li and 95 Mo nuclei can be theoretically calculated using the point-charge model 29,30 . Our theoretical estimation (detailed in the Supplemental Information) indicates that on the average at both nuclei, 1) the charge covalence contribution to ν Q (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 In summary, we presented a direct observation of the electron charge state in Li 0.9 Mo 6 O 17 . The parameters of the EFG (nuclear quadrupolar frequency) are found by our 7 Li-and 95 Mo-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 Li 0.9 Mo 6 O 17 , 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 Li 0.9 Mo 6 O 17 were grown using a temperature-gradient flux method 8,10 . 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 μ m diameter copper wire wound with ~30 turns. The 7 Li-NMR experiments were conducted with a spectrometer and probe built at UCLA Clarklab (W. G. Clark), and the 95 Mo-NMR measurements on the same sample were performed at the Grenoble High Magnetic Field Laboratory, France with field B 0 = 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 developed 33 by Clark et al. was used for the 7 Li-NMR measurements, with our consideration that the 7 Li spin-lattice relaxation time goes extremely long at low temperatures. The 95 Mo-NMR measurements used standard spin-echo techniques 31,32 , 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 95 Mo nucleus. Thus, noticeably, these are extremely difficult experiments.
The calibration of each applied magnetic field B 0 used for the 7 Li/ 95 Mo-NMR measurements was made at temperature T = 10 K with the 63 Cu free-induction decay (FID) signals from the sample coil. For example, the value of B 0 used for the measurements at the 12 T magnet is determined to be B 0 = 11.9948 T, and at the 14.8 T magnet is B 0 = 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 bronze 29 Rb 0.3 MoO 3 and in the TMTSF family 30 , respectively.