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.
Zeolites are an important family of materials with periodic arrays of aluminosilicate cages that are widely used in different industrial processes1. Moreover, they also show interesting electronic phenomena, when intercalated with alkali metals, associated with the electronic states localized within individual cages. For example, exotic magnetism with different magnetically ordered states has been reported in alkali-doped zeolites2,3,4,5,6,7. With more than 200 possible zeolite frameworks known today8, alkali-doped zeolites thus represent a unique playground to control and study the effects of geometry and dopant concentration on the electronic potential depth, electron-electron repulsion and electron-phonon coupling at different length-scales.
Since electronic states are associated to the alkali s-electrons, they remain confined to cages, just like alkali-metals that form clusters or superatoms. It is thus not surprising that the metallic zeolites have been elusive for many years with only one documented exception in rubidium doped zeolite rho, where the microwave conductivity measurements indicated the metallic ground state9. Very recently, the insulator-to-metal transition has been also reported in sodium loaded low-silica X (LSX) zeolite, Nan/Na12-LSX10,11. So far, experimental evidence for the metallic state was mainly limited to the observation of Drude reflection appearing in the infrared region10 and a drastic decrease in the resistivity11 for the heavily loaded samples. We stress that the measured resistivity is still very high and atypical of simple metals as it does not decrease with decreasing temperature. Additional hint of metallic ground state was provided by a precise x-ray diffraction analysis12, where it was shown that Na atoms make bonding network through the tunnel windows that connect zeolite cages and thus establish a precondition for a narrow conduction band. However, firm direct experimental evidence for the metallic state in Nan/Na12-LSX is still lacking.
Nuclear magnetic resonance (NMR) is a powerful local-probe experimental tool to investigate a state of matter even in powder and highly air-sensitive samples. By measuring the temperature dependence of the NMR shift and spin-lattice relaxation time it is in principle possible to distinguish between insulating, metallic and superconducting states13,14,15,16. Unfortunately, in alkali-doped zeolites, the spin-lattice relaxation rate, 1/T1, is dominated by strong fluctuations of local magnetic fields and electric field gradients originating from large amplitude atomic motion of alkali metals17,18 thus masking the conventional Korringa-like behaviour expected in the metallic state. Here we show for Nan/Na12-LSX that at room temperature the values of 23Na 1/T1 due to the Na motion indeed typically exceed by four orders of magnitude contributions from the coupling of nuclear magnetic moments to itinerant electrons in the metallic state. Cooling sample to cryogenic temperatures freezes out the atomic motions on the NMR time scale and 23Na 1/T1 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 Nan/Na12-LSX, which is here discussed within the correlation-driven and disorder-driven aspects of metal-to-insulator transition (MIT)19,20.
The optical reflectance spectra of the Nan/Na12-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(EF), 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 data10,11.
At 270 K, the 23Na NMR spectrum of insulating Na11.6/Na12-LSX powder comprises several overlapping peaks close to the Larmor frequency (Fig. 2a). The structure of 23Na NMR lineshape reflects the multitude of Na sites in the β cages and supercages of the LSX structure12,21. The contribution of different Na sites to the observed 23Na 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 tail11. Therefore, the predominately diamagnetic susceptibility of n = 11.6 sample suggests that the lineshape and the shift of the 23Na NMR spectrum are almost entirely determined by the nuclear chemical shift and quadrupole interactions. The insulating Na11.6/Na12-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 23Na 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 23Na 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 23Na 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 23Na 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 polarons18.
Unfortunately, the observation of polaronic SC for n ≥ 14.2 is only an indirect proof of metallic state. Additional complexity in the analysis of 23Na 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 23Na 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 23Na NMR spectra, we next discuss the spin-lattice relaxation data, where the Korringa behaviour (1/T1T = const.) is usually a signature of metallic state14,22. For all compositions RC has, compared to ZC and SC, by two orders of magnitude longer T1. 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 T1 component (Fig. 3a), has a pronounced maximum in 1/T1T, which can be between 100 and 350 K empirically modelled within the Bloembergen-Purcell-Pound (BPP)-type mechanism23
Here τc 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, Ea, for the local field fluctuations by assuming the Arrhenius type correlation time, τc = τ0 exp(Ea/kBT), where τ0 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 zeolites18 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 τc increases exponentially with decreasing temperature, we anticipate that according to Eq. (1) the BPP contribution to the total 23Na relaxation rate diminishes at low temperatures, i.e., the atomic-motion driven (1/T1T )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/T1)α] with a single effective T1, where a stretching exponent α ≈ 0.6 accounts for distribution of T1’s due to multiple sites. The most important observation arising from this analysis is that plotting 1/T1T versus temperature for samples with n ≥ 14.2, we finally find metallic temperature independent 1/T1T 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 expression14,22
Here γe and γNa are the electronic and 23Na gyromagnetic ratios, respectively. The phenomenological parameter β, called the Korringa factor, characterizes the extent of electron correlations13,14. The temperature independent isotropic Knight shift, Kiso, which is proportional to Pauli spin susceptibility, is a measure of DOS at the Fermi level, N(EF). Comparing the low-temperature 1/T1T values for different n, we find that in metallic samples 1/T1T 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/T1T is given by the Korringa relaxation mechanism, a monotonic increase of low-temperature 1/T1T with n for n ≥ 14.2 speaks for a monotonic increase of N(EF) 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(EF) and could thus hardly affect the deduced monotonic increase in N(EF) as a function of loading level.
In order to quantitatively extract (1/T1T )metal from the measured temperature dependence of 1/T1T, 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/T1T )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/T1T )metal values are by more than one order of magnitude smaller than that of bulk metallic Na thus indicating a relatively low N(EF) in these metallic samples. This conclusion is further supported, if we use (1/T1T )metal = 2.3 × 10−2 s−1 K−1 of n = 16.5 sample to calculate Kiso = 300 ppm from Eq. (2) and compare it to much larger value of 1120 ppm found in metallic sodium14. Surprisingly, the plateau-like low-temperature behaviour in 1/T1T 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/T1T clearly rules out the possibility that for this loading range the system can be discussed as a narrow-gap semiconductor. In this case, 1/T1T would be dominated by the exp(−Δ/kBT ) term for , which decays exponentially with decreasing temperature24, in disagreement with the experimental data.
Plotting the normalized N(EF) extracted from Eq. (2) versus the sodium loading level n (Fig. 4b), we find that N(EF) markedly increases with n for n ≥ 14.2, thus speaking for the enhancement of DOS at Fermi level N(EF) 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(EF) is by a factor of ~3 smaller than the corresponding value in bulk Na. Our study of a minimal single-orbital Hubbard model demonstrated25 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 theoretically26 and experimentally27,28 recognized for related potassium-loaded LTA and FAU zeolites. However, the correlation-driven MIT is expected to be of first order19, which is not directly supported by the present data. We recall that a finite N(EF) has been observed even in the nominally insulating samples of Nan/Na12-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 23Na NMR for this sample shows the finite N(EF), 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 temperatures29. 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 Nan/Na12-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 cages12, the disorder strength decreases and triggers the MIT.
However, at the critical loading densities yet another possibility of a percolation-type metal-to-insulator transition19 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 Na16.7/Na12-LSX, which connects the neighboring supercages12. This Na-Na connectivity is not formed in nominally insulating Na9.4/Na12-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 threshold19. 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 Nan/Na12-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.
Using NMR as a local probe of sodium loaded low-silica X zeolite (Nan/Na12-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.
The LSX zeolites have a chemical formula A12Al12Si12O48, where A stands for alkali-metal cations that are required for charge compensation of the aluminosilicate framework1. 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 rule30 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 Na12-LSX, are exposed to Na vapour following the standard procedure described elsewhere11, a controlled amount of Na is additionally loaded yielding a targeted composition Nan/Na12-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 study18. 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.
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 terminals11.
Here we present detailed 23Na NMR experiments on Nan/Na12-LSX samples in the Na-loading range 9.4 ≤ n ≤ 16.5. The 23Na (I = 3/2) NMR spectra and T1 were measured in a magnetic field of 4.7 T in the temperature range between 6 K and 340 K. The 23Na reference frequencies of 52.9055 MHz was determined from NaCl aqueous solution standards.
23Na 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.
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We thank Dr. T. Ikeda for helpful discussions about the structure of Nan/Na12-LSX zeolite. MI especially thanks to Dr. T. Shimizu, Dr. A. Goto, Dr. K. Hashi and Mr. S. Ohki. This study was partially supported by Grants-in-Aid for Scientific Research (KAKENHI) [Grants No. 24244059(A) and No. 26400334(C)] from Japan Society for the Promotion of Science.
The authors declare no competing financial interests.
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Igarashi, M., Jeglič, P., Krajnc, A. et al. Metal-to-insulator crossover in alkali doped zeolite. Sci Rep 6, 18682 (2016). https://doi.org/10.1038/srep18682
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