Metal-to-insulator crossover in alkali doped zeolite

We report a systematic nuclear magnetic resonance investigation of the 23Na spin-lattice relaxation rate, 1/T1, in sodium loaded low-silica X (LSX) zeolite, Nan/Na12-LSX, for various loading levels of sodium atoms n across the metal-to-insulator crossover. For high loading levels of n ≥ 14.2, 1/T1T shows nearly temperature-independent behaviour between 10 K and 25 K consistent with the Korringa relaxation mechanism and the metallic ground state. As the loading levels decrease below n ≤ 11.6, the extracted density of states (DOS) at the Fermi level sharply decreases, although a residual DOS at Fermi level is still observed even in the samples that lack the metallic Drude-peak in the optical reflectance. The observed crossover is a result of a complex loading-level dependence of electric potential felt by the electrons confined to zeolite cages, where the electronic correlations and disorder both play an important role.

itinerant electrons in the metallic state. Cooling sample to cryogenic temperatures freezes out the atomic motions on the NMR time scale and 23 Na 1/T 1 finally discloses Korringa behaviour below 25 K thus proving the metallic ground state for n ≥ 14.2. Surprisingly, a small portion of density of states (DOS) at the Fermi level persists deep into the insulating state. This important finding that was not possible before with bulk-property measurements, holds important clues about the metal-to-insulator crossover in Na n /Na 12 -LSX, which is here discussed within the correlation-driven and disorder-driven aspects of metal-to-insulator transition (MIT) 19,20 .

Results
The optical reflectance spectra of the Na n /Na 12 -LSX samples included in this study clearly demonstrate the emergence of Drude peak at lower photon energies for n ≥ 14.2 as shown in Fig. 1a. Moreover, the temperature dependence of resistivity reveals finite low-temperature values for n = 16.5, but diverges for n = 11.6 as displayed in Fig. 1b. The measured resistivity may be affected by the constriction resistance at the connection between powder particles, which can result in a misleading negative temperature coefficient of the resistivity for n = 16.5. Nonetheless, finite value of ρ at 2 K for n = 16.5 demonstrates a finite DOS at the Fermi level, N(E F ), consistent with the metallic state. These two standard characterization techniques thus comply with the MIT as a function of Na-loading at a critical loading concentration between n = 11.6 and n = 14.2, in full agreement with the literature data 10,11 .
At 270 K, the 23 Na NMR spectrum of insulating Na 11.6 /Na 12 -LSX powder comprises several overlapping peaks close to the Larmor frequency (Fig. 2a). The structure of 23 Na NMR lineshape reflects the multitude of Na sites in the β cages and supercages of the LSX structure 12,21 . The contribution of different Na sites to the observed 23 Na NMR components is discussed in Methods section. The bulk magnetic susceptibility of this sample shows a diamagnetic response, although the presence of diluted localized magnetic moments is evident from a characteristic low-temperature Curie tail 11 . Therefore, the predominately diamagnetic susceptibility of n = 11.6 sample suggests that the lineshape and the shift of the 23 Na NMR spectrum are almost entirely determined by the nuclear chemical shift and quadrupole interactions. The insulating Na 11.6 /Na 12 -LSX sample can be set thus as a suitable NMR reference against which all changes of NMR parameters when crossing the MIT are compared.
Indeed, for samples with n ≥ 14.2, a Lorentzian line [hereafter named as a shifted component (SC)] appears in the metallic samples on the high-frequency side of the 23 Na NMR spectrum, well separated from the diamagnetic frequency range (Fig. 2a). The appearance of SC is limited to samples that show metallic-like response in optical and resistivity measurements (Fig. 1) and is completely absent in insulating samples, e.g. as for n = 11.6 shown in Fig. 2b. The SC is optimally detected with an echo pulse sequence with precisely two times longer pulse length than that optimized for the residual diamagnetic 23 Na spectral component centered around zero shift -hereafter we call it a residual component (RC) as it is reminiscent to that described above for the insulating n = 11.6 sample. We conclude that the electric field gradient for Na atoms contributing to this SC is averaged out on the time scale of 23 Na NMR measurements, ~10 −5 s. Motional effects also explain the Lorentzian lineshape of SC. EFG averaged to zero and the Lorentzian lineshape are clear signatures that at elevated temperatures Na atoms undergo large amplitude displacements. Temperature dependence of 23 Na NMR spectra shown for metallic n = 16.5 sample in Fig. 2b, reveals that with increasing temperature the intensity of SC increases significantly above ≈ 150 K. This means that such states must be thermally excited from the ground state. We can rationalize the appearance and the strong temperature dependent shift of SC within a polaron model, where thermally activated behavior is associated with the creation/annihilation of localized small polarons from the bath of (conducting) large polarons 18 . Unfortunately, the observation of polaronic SC for n ≥ 14.2 is only an indirect proof of metallic state. Additional complexity in the analysis of 23 Na spectra arises for n ≤ 14.4, where we observe another non-shifted component (see Fig. 2), which has the optimal pulse lengths the same as SC detected at n ≥ 14.2. Using the same arguments as for SC, we conclude that Na atoms contributing to this line must perform large amplitude jumps between different sites in the same cage. However, unlike to SC, this line has no hyperfine interaction with unpaired electron spins, therefore we call it zero component (ZC), implying that it has a completely different, most likely non-magnetic bipolaronic, origin. It is interesting to note that the 23 Na NMR spectrum for n = 14.4 (Fig. 2a) shows a coexistence of ZC and SC, which may indicate an inhomogeneous distribution of sodium atoms throughout the zeolite cages.
Since the metallic state cannot be unambiguously confirmed from the analysis of 23 Na NMR spectra, we next discuss the spin-lattice relaxation data, where the Korringa behaviour (1/T 1 T = const.) is usually a signature of metallic state 14,22 . For all compositions RC has, compared to ZC and SC, by two orders of magnitude longer T 1 . This distinction is manifested over a wide range of temperatures as two separate nuclear magnetization recoveries with long and short time constants. The temperature dependence of the short ZC/SC T 1 component (Fig. 3a), has a pronounced maximum in 1/T 1 T, which can be between 100 and 350 K empirically modelled within the Bloembergen-Purcell-Pound (BPP)-type mechanism 23 Here τ c is the correlation time for the local field fluctuations at the nucleus, ω is the Larmor angular frequency and C is a measure of the fluctuating local fields magnitude. We estimated the activation energy, E a , for the local field fluctuations by assuming the Arrhenius type correlation time, τ c = τ 0 exp(E a /k B T), where τ 0 is a constant. For the activation energies we obtained a value of around 0.1 eV for all loading densities investigated. The estimated activation energy is typical for atomic motion in zeolites 18 and provides yet another independent proof that sodium motion is present in both insulating and metallic state. However, the strong relaxation due to the atomic motion completely masks the weaker metallic Korringa contribution to the spin-lattice relaxation.
Since τ c increases exponentially with decreasing temperature, we anticipate that according to Eq. (1) the BPP contribution to the total 23 Na relaxation rate diminishes at low temperatures, i.e., the atomic-motion driven (1/T 1 T ) BPP → 0 as temperature decreases. In addition, the relaxation rates for RC and ZC/SC become comparable below ~100 K thus implying that other relaxation mechanisms, which are only moderately site dependent, set in. Therefore, the low temperature relaxation curves were fitted with stretched exponential model ~exp[− (τ/T 1 ) α ] with a single effective T 1 , where a stretching exponent α ≈ 0.6 accounts for distribution of T 1 's due to multiple sites. The most important observation arising from this analysis is that plotting 1/T 1 T versus temperature for samples with n ≥ 14.2, we finally find metallic temperature independent 1/T 1 T below ~25 K (Fig. 3b). This is a hallmark of the nuclear spin-lattice relaxation via the itinerant electrons and is accounted for by the Korringa expression 14,22 Here γ e and γ Na are the electronic and 23 Na gyromagnetic ratios, respectively. The phenomenological parameter β, called the Korringa factor, characterizes the extent of electron correlations 13,14 . The temperature independent isotropic Knight shift, K iso , which is proportional to Pauli spin susceptibility, is a measure of DOS at the Fermi level, N(E F ). Comparing the low-temperature 1/T 1 T values for different n, we find that in metallic samples 1/T 1 T is enhanced relative to insulating samples by an order of magnitude. If the system can be treated as a simple metal and the plateau in 1/T 1 T is given by the Korringa relaxation mechanism, a monotonic increase of low-temperature 1/T 1 T with n for n ≥ 14.2 speaks for a monotonic increase of N(E F ) with Na loading level. This holds true as long as the relevant electronic bandwidth does not change significantly as a function of loading level. Because these compounds are far away from any magnetic instability, we expect that the electron correlations could be well taken into account by the Korringa factor. As a result, the electron correlation can only renormalize the extracted values of N(E F ) and could thus hardly affect the deduced monotonic increase in N(E F ) as a function of loading level. In order to quantitatively extract (1/T 1 T ) metal from the measured temperature dependence of 1/T 1 T, we assumed that the relaxation rate has two contributions, the BPP and Korringa, described by Eqs. (1) and (2), respectively. That is, the data was fitted to where between 30 K and 80 K another sodium motion likely sets in with an estimated activation energy of around 22 meV for all sodium loading densities investigated (except for n = 9.4, where we obtained a slightly higher value of 32 meV). Table 1 summarizes the values of (1/T 1 T ) metal for all n in the range between 9.4 and 16.5 and is compared to the related value measured in bulk metallic Na. We note that the (1/T 1 T ) metal values are by more than one order of magnitude smaller than that of bulk metallic Na thus indicating a relatively low N(E F ) in these metallic samples. This conclusion is further supported, if we use (1/T 1 T ) metal = 2.3 × 10 −2 s −1 K −1 of n = 16.5 sample to calculate K iso = 300 ppm from Eq. (2) and compare it to much larger value of 1120 ppm found in metallic sodium 14 . Surprisingly, the plateau-like low-temperature behaviour in 1/T 1 T is also seen for n = 11.6 and 11.3, where the Drude term is not observed and resistivity diverges at low temperature. We stress that the observed low-temperature 1/T 1 T clearly rules out the possibility that for this loading range the system can be discussed as a narrow-gap semiconductor. In this case, 1/T 1 T would be dominated by the exp(− Δ /k B T ) term for ∆  k T B , which decays exponentially with decreasing temperature 24 , in disagreement with the experimental data.

Discussion
Plotting the normalized N(E F ) extracted from Eq. (2) versus the sodium loading level n (Fig. 4b), we find that N(E F ) markedly increases with n for n ≥ 14.2, thus speaking for the enhancement of DOS at Fermi level N(E F ) with doping, which is in qualitative agreement with the enhancement of optical reflectance (Fig. 1a). We note that for the most loaded sample (n = 16.5), the extracted N(E F ) is by a factor of ~3 smaller than the corresponding value in bulk Na.    Our study of a minimal single-orbital Hubbard model demonstrated 25 that the experimentally observed strong variation of Drude peak in optical conductivity cannot be explained solely by band filling effects. In fact, it showed that the variation of electron-electron repulsion U divided by a bandwidth W, is much more relevant, meaning that the main effect of sodium loading is to define the electronic potential and the Coulomb repulsion felt by the electrons in the zeolite cages. Similarly, the importance of electron correlations has been theoretically 26 and experimentally 27,28 recognized for related potassium-loaded LTA and FAU zeolites. However, the correlation-driven MIT is expected to be of first order 19 , which is not directly supported by the present data. We recall that a finite N(E F ) has been observed even in the nominally insulating samples of Na n /Na 12 -LSX. For example, the n = 11.3 sample exhibits a resistivity diverging at low temperatures and is described by an energy band gap of 0.2 eV. At the same time, the local probe 23 Na NMR for this sample shows the finite N(E F ), more precisely ~8% of the value found in metallic sodium. The phase diagram shown in Fig. 4 is more reminiscent of a metal-to-insulator crossover rather than the sharp transition thus calling for considerations of other relevant microscopic factors.
In the alternative picture, where disorder is the driving mechanism for MIT, a continuous metal-to-insulator is typically found at finite temperatures 29 . The physical reason is that at finite temperatures the electrons can escape the trapping potential through the thermal activation. Indeed, the alkali-doped zeolites can be viewed as a strongly disordered system for several reasons. First, by a careful analysis of the spectral intensities belonging to SC and ZC as a function of sodium loading level (Fig. 4c), we identify a region around n = 14.4 where both spectral components coexist, implying an inhomogeneous Na distribution in the cages that is responsible for a cage-to-cage variation in the electric potential depths. Second, as pointed out in the x-ray study by Ikeda et al. 12 , in Na n /Na 12 -LSX the coordinates of available sodium sites in the zeolite framework remain the same as a function of sodium loading level. What is changing with n is the average occupancy of these sites. Local variations in the Na arrangements in the neighbouring cages are responsible for the variations in the local potential depth and thus for the disorder. For low carrier densities, the trapping potential of disordered sodium clusters within the cages is expected to become comparable or larger than the Fermi level, and the electrons get localized. At higher loading densities not only the carrier density increases, but since the loaded sodium atoms reach the limit of the highest possible occupancy in the cages 12 , the disorder strength decreases and triggers the MIT.
However, at the critical loading densities yet another possibility of a percolation-type metal-to-insulator transition 19 opens. Although, the disorder-driven scenario in the presence of varying correlation effects seems plausible, we should be aware that the variation of alkali atom loading level not only changes the electron correlation energies and disorder strength, but also strongly determines the electric potential felt by the electrons. Electron-density distribution analysis showed a formation of the chain-like Na cation distribution in metallic Na 16.7 /Na 12 -LSX, which connects the neighboring supercages 12 . This Na-Na connectivity is not formed in nominally insulating Na 9.4 /Na 12 -LSX. In the percolation picture of a random (disordered) potential a small metallic regions of connected supercages are formed at low sodium loading densities separated by insulating areas. When the electron density increases the metallic regions grow and eventually become connected at the percolation threshold 19 . Although our observation of the crossover regime and the inhomogeneous distribution of sodium atoms throughout the zeolite lattice tentatively support the percolation picture, we leave the important question of the true nature of MIT in alkali doped zeolites open for further studies. However, what is made clear from present results is that for the Na n /Na 12 -LSX zeolites the concentration of sodium atoms strongly affects in a very complex way the electronic properties by simultaneously changing the band filling, the electronic potential depth, the electron-electron repulsion and the amount of disorder.

Conclusions
Using NMR as a local probe of sodium loaded low-silica X zeolite (Na n /Na 12 -LSX), we have unambiguously confirmed a metallic ground state for higher loading densities of n ≥ 14.2. By extracting the DOS at the Fermi level as a function of sodium loading level, we have discovered a continuous (crossover like) evolution across the metal-to-insulator transition. Most importantly, a finite DOS at the Fermi level for nominally insulating samples and a clear indication of inhomogeneous Na distribution in the neighboring cages in the crossover region, put some constraints on the driving mechanism of electron localization and the nature of MIT in alkali-doped zeolites.

Methods
Samples. The LSX zeolites have a chemical formula A 12 Al 12 Si 12 O 48 , where A stands for alkali-metal cations that are required for charge compensation of the aluminosilicate framework 1 . The main structural motif is comprised of truncated octahedral β cages, which are arranged in a diamond structure by doubly connecting their 6-membered rings. This way additional supercages are formed with a diameter approximately twice of that of β cages. Following the Lowenstein's rule 30 the Si and Al atoms alternatingly occupy the framework sites resulting in structurally ordered LSX zeolite framework. When sodium-based parent structures, i.e. A = Na, hereafter abbreviated as Na 12 -LSX, are exposed to Na vapour following the standard procedure described elsewhere 11 , a controlled amount of Na is additionally loaded yielding a targeted composition Na n /Na 12 -LSX. Here n denotes the loading density of guest Na atoms per supercage. The values of n were for the purpose of this study recalibrated by inductively coupled plasma technique. Particularly for higher density levels, the calibrated values substantially exceed those calculated from known amount of starting materials used in our preliminary NMR study 18 . For example, the loading levels of "n = 10" and "n = 12" studied in ref. 18 correspond to the recalibrated values of n = 9.4 and n = 16.7, respectively.
Bulk-property measurements. Optical reflectance spectra were measured by conventional apparatus.
Since we were dealing with powder samples with a grain diameter of few μm, the resistivity, ρ, was measured by pinching the powder between two metallic plates acting also as terminals 11 .
Scientific RepoRts | 6:18682 | DOI: 10.1038/srep18682 NMR measurements. Here we present detailed 23 Na NMR experiments on Na n /Na 12 -LSX samples in the Na-loading range 9.4 ≤ n ≤ 16.5. The 23 Na (I = 3/2) NMR spectra and T 1 were measured in a magnetic field of 4.7 T in the temperature range between 6 K and 340 K. The 23 Na reference frequencies of 52.9055 MHz was determined from NaCl aqueous solution standards. 23 Na NMR signal assignment to the sodium crystallographic sites. According to ref. 12, the occupancies of Na1, Na2, Na3 and Na6 crystallographic sites remain the same for n = 9.4 and n = 16.7. These sites are located near the inner wall of the zeolite framework and are responsible for the framework charge compensation. They can be naturally attributed to the RC component present at all sodium loading levels. On other hand, the occupancies of Na5, Na7, Na8 and Na9 sites, which are located near the centre of the supercage, increase substantially from n = 9.4 to n = 16.7. Based on this observation we tentatively attribute the SC to this set of sites. Next we recall that the ZC and SC behave very similarly since both signals are influenced by sodium motion and the only difference is the absence of NMR shift for ZC. As proposed in ref. 18, the SC detects small polarons excited from the bath of large polarons, whereas the ZC could be explained by the non-magnetic bipolaronic nature of electronic states at lower loading levels.