Band Ordering and Dynamics of Cu2–xTe and Cu1.98Ag0.2Te - The

Jun 24, 2016 - 63Cu, 65Cu, and 125Te NMR measurements are reported for Cu2–xTe and Cu1.98Ag0.2Te. The results demonstrate an onset of Cu-ion hopping...
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Band Ordering and Dynamics of Cu2−xTe and Cu1.98Ag0.2Te Ali A. Sirusi,*,† Sedat Ballikaya,§,¶ Jing-Han Chen,† Ctirad Uher,¶ and Joseph H. Ross, Jr.†,‡ †

Department of Physics and Astronomy, ‡Department of Materials Science and Engineering, Texas A&M University, College Station, Texas 77843, United States § Department of Physics, Istanbul University, Vezneciler, Istanbul, 34134, Turkey ¶ Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, United States S Supporting Information *

ABSTRACT: 63Cu, 65Cu, and 125Te NMR measurements are reported for Cu2−xTe and Cu1.98Ag0.2Te. The results demonstrate an onset of Cu-ion hopping below room temperature, including an activation behavior consistent with high-temperature transport measurements but with a significant enhancement of the hopping barriers with Ag substitution. We also separated the Korringa behavior by combining NMR line shape and relaxation measurements, thereby identifying large negative chemical shifts for both nuclei, as well as large Cu and Te s-state contributions in the valence band. Further comparison was obtained through heat capacity measurements and chemical shifts computed by density functional methods. The large diamagnetic chemical shifts coincide with behavior previously identified for materials with topologically nontrivial band inversion, and in addition, the large metallic shifts point to analogous features in the valence band density of states, suggesting that Cu2Te may have similar inverted features.

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per cell was proposed,18 in space group P6/mmm with lattice parameters a0 = 4.237 Å, c0 = 7.274 Å. Subsequently, an orthorhombic superstructure19,20 and also a mixture of both orthorhombic and hexagonal phases21 were reported. Recently, an adaptive genetic algorithm predicted Cu2Te to have a monoclinic22 structure with four formula units per cell. However, the detailed atomic positions are not known. In this report, we used NMR as a local probe, along with heat capacity measurements and all-electron calculations, to obtain physical insight into features of Cu2−xTe and Cu2−xAgyTe. Ag substitution is shown to have a substantial effect on the activated hopping processes. Furthermore, identification of the charge-carrier contributions to the NMR shifts and relaxation behavior, combined with density functional calculations, provides understanding of the hole bands contributing to the transport. Starting with these results, we also identify large negative chemical shifts in these materials, which supported by computational modeling, we show to be consistent with an inversion of the orbital occupation of the hole bands.

INTRODUCTION Copper-based chalcogenide compounds have gained much attention because of their intriguing potential applications. Cu2Te and Cu2Se compounds find themselves as components of efficient solar cells in which Cu2Te is used as a back contact for CdTe,1 and there has recently been enhanced interest because of high thermoelectric efficiency.2−6 Additionally, these materials can form a wide variety of two-dimensional structures which can lead to new physics.7,8 Moreover, the copper chalcogenide compounds are well-known superionic conductors,9 having structural phase transitions at high temperature. These and related materials also include well-known topological insulators that are due in part to the presence of heavy atoms.10−12 Transport measurements show that Cu2Te is metallic5,13,14 but with an apparent optical band gap of about 1 eV.15 These results correspond to heavily doped semiconducting behavior, with transport dominated by holes due to native Cu vacancies, and intrinsic insulating behavior expected for the ideal Cu2Te stoichiometry. At high temperatures, superionic transport also appears, as noted earlier, because of the presence of the relatively mobile Cu ions. Cu2Te has been reported to have five successive phase transitions13,16,17 at 548, 593, 638, and 848 K. The last phase (ϵ) has a cubic fluorite structure, the same as the hightemperature phase of Cu2Se. The low-temperature structures of Cu2Te are complex and, in some cases, are not yet understood. Initially, a hexagonal structure with two Cu2Te formula units © 2016 American Chemical Society

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EXPERIMENTAL AND COMPUTATIONAL METHODS Synthesis and Sample Characterization. Samples with the nominal compositions Cu2Te and Cu1.98Ag0.2Te are from Received: May 11, 2016 Revised: June 24, 2016 Published: June 24, 2016 14549

DOI: 10.1021/acs.jpcc.6b04785 J. Phys. Chem. C 2016, 120, 14549−14555

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contribution (quadrupole mechanism) and carrier dominated term (magnetic) obey 1/T1Q ∝ Q2 and 1/T1M ∝ γ2, respectively, the data for the two nuclei could be fitted to 1/(63,65)T1 = Aγ2(63,65) + BQ2(63,65), where A and B are constants to be fitted at each temperature. Thus, measurements for the two Cu nuclei can be used to determine the separated values with the uncertainties determined by those of the T1 measurements. Computational Methods. First-principles calculations were performed using the L/APW+lo method27 as implemented in the WIEN2k code.28 Calculations were performed with the generalized gradient approximation (GGA) using the widely used PBE exchange potential29 and also using the modified Becke-Johnson (mBJ)30 exchange potential. Calculations of the NMR chemical shift were performed using the formalism in the WIEN2k for evaluating paramagnetic and diamagnetic shielding currents.31 Experimental lattice parameters were used for the CuCl and ZnTe NMR standards as well as for Cu2Se (a = 5.763 Å) and Cu2Te (a = 6.004 Å)20 in the cubic fluorite structure. Fifty thousand k-points were used for all quoted results, with linearity checks also performed when computing NMR shifts. Computations for Cu2Se and Cu2Te follow the methods of ref 32, where it was shown that mBJ + U with Cu-d Ueff = 4 eV successfully models the band edge properties of these Cu-based semiconductors. To calculate NMR chemical shifts, we also computed shifts for CuCl (Cu standard) and ZnTe (for Te shifts). ZnTe was chosen as a secondary Te NMR standard for WIEN2k calculation; recently,33 the ZnTe 125Te resonance was measured to be δ = −875 ppm in a sample believed to have relatively small carrier-induced Knight shift. A separate study34 identified a similar value, δ = −888 ppm, however, with no discussion of charge carriers. Therefore, we took δcs = −875 ppm to be the ZnTe chemical shift relative to the (CH3)2Te primary standard. The calculated values have been corrected correspondingly to (CH3)2Te.

the same preparation batches as described in ref 5, using a combination of solid-state reaction and annealing followed by spark plasma sintering. Room-temperature powder X-ray diffraction (PXRD) and wavelength-dispersive spectroscopy (WDS) measurements5 showed that the Cu2Te sample forms a single phase with the space group P6̅m2 (#187). Similar to the behavior of Cu2−xAgxSe, Ag in Cu2Te is well-known to partially segregate to form the CuAgTe phase at ambient temperature,5 and the Cu1.98Ag0.2Te sample was found to be composed of two phases: Cu2AgxTe (0.01 ≤ x ≤ 0.03) and a small amount of CuAgTe. The Hall coefficients, thermal conductivities, and electrical conductivities were reported below 400 K in ref 5, showing that both samples are heavily doped p-type semiconductors, with p = 2.84 × 1021 and 1.25 × 1021 cm−3 for Cu2Te and Cu1.98Ag0.2Te at room temperature, respectively. In ref 6, the carrier density of the Cu2Te sample was misreported by a factor of about 3. Assuming all holes to be due to Cu vacancies gives the composition Cu1.85Te for the Cu2Te sample which is in good agreement with the phase diagram20 according to the hexagonal structure fitted in PXRD. The same calculation for the Ag-doped sample gives 0.08 vacancies per formula unit on the basis of its reduced hole density. NMR and Heat Capacity Measurements. The heat capacity measurements were performed in a Quantum Design Physical Property Measurement System, while NMR experiments were carried out using a custom-built pulse spectrometer at a fixed field near 9 T. 63Cu, 65Cu, and 125Te spectra were measured with solid CuCl and aqueous Te(OH)6 as the standard Cu and Te references, respectively. Te(OH)6 had a 707 ppm parametric shift compared to the primary standard of dimethyltelluride.23 Using this value, we corrected 125Te spectral shifts to dimethyltelluride, while the Cu NMR shifts were reported relative to the CuCl standard. The powder samples were mixed with crushed quartz to allow radio frequency (rf) penetration. Measurements utilized spin−echo integration versus frequency to record the wide-line spectra with t90 = 7 μs and t90 = 16 μs used for Cu and Te, respectively, after optimizing the spin−echo integral at the peak positions, and with tdelay = 100 and 150 μs between pulses for Cu and Te, respectively. The 63Cu NMR spectra were fitted using the DmFit package.24 For magnetic shift contributions δtotal = δcs + K, we followed the convention δcs = ( f − f 0)/f 0 for chemical shifts, with f 0 the standard reference frequency and with positive shifts having paramagnetic sign, while the Knight shifts (K) have an analogous definition. NMR spin−lattice relaxation measurements used a standard three-pulse sequence including an inversion pulse, a time twait, and then a two-pulse spin−echo for signal measurement. The results were analyzed with the relaxation time, T1, as fitting parameter using a standard25 multiexponential magnetic relaxation function [M(twait)/M(0) = 1 − α(0.1e−twait/T1 + 0.9e−6twait/T1)] for the central transition for 63Cu and 65Cu or, in some cases, a sum of such curves. For 125Te relaxation measurements, we used the single exponential [M(twait)/M(0) = 1 − αe−twait/T1] as appropriate for the spin-1/2 nucleus. The Cu NMR quadrupole relaxation process entails a different relaxation function, and therefore an overall scaling of the quadrupole values of T1; however, this does not affect the dynamical fitting parameters described later. We used nuclear moment values reported in ref 26 [63Cu (I = 3/2), γ = 7.111789 × 107 rad s−1 T−1, and Q = −22.0 fm2; 65Cu (I = 3/2), γ = 7.60435 × 107 rad s−1 T−1, and Q = −20.4 fm2] for separating the magnetic and quadrupole contributions. Since the phonon

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RESULTS AND ANALYSIS Figure 1a shows 63Cu spectra for Cu2Te versus temperature. The overall features are similar for 65Cu spectra and for the Cu1.98Ag0.2Te sample, shown in the inset of Figure 1b. These line shapes are m = 1/2 to −1/2 transitions for I = 3/2 Cu nuclei. The gradual decrease of signal with temperature (Figure 1a) corresponds to the development of Cu ion dynamics similar to Cu2Se.35 Spin−lattice relaxation times (T1) were obtained at several positions at 77 K to help distinguish distinct Cu sites. At 0 ppm (the narrow center of the spectrum), a single T1 curve was found to give a good fit. For other positions, the recovery curves were best fitted to two T1 curves, with similar results for several positions on the broader part of the spectrum, for which the fitted amplitudes for the shorter T1 were more than 7 times larger than the long T1. We assumed the latter to be a lowoccupation site which we ignored in the T1 analysis. Table 1 shows resulting T1 values with magnetic and quadrupole contributions separated. On the basis of these results, we fitted the spectra at 77 K as a sum of two sites (Figure 1b). The narrow middle resonance (site A) has been found to have a magnetic shift δtotal = −50 ppm (dotted line), while site B has δtotal = 450 ppm (dashed line). Site A could be fitted with no quadrupole contribution, while the broad portion of the line was fitted with quadrupole parameters νq = 10.5 MHz and η = 0.59. The resulting spectral weights are 30% for site A and 70% for site B. The observation 14550

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The effects of atomic dynamics can be seen in the temperature dependence of the spectra as shown in Figure 1a. These spectra are obtained using a spin−echo sequence with tdelay = 100 μs between pulses. We multiply the spectra by T since the total spectral weight is proportional to T−1. Hopping during the time delay causes the echo signal to be reduced. To quantify these changes, we fit for each temperature using the same shift parameters obtained for 77 K. Figure 2

Figure 2. Fitted height of 63Cu NMR site A line, multiplying by T, for Cu2Te.

displays the resulting site A height versus temperature. The decrease above 200 K is accompanied by the disappearance of site B (Figure 1a). A similar temperature dependence is observed for Cu1.98Ag0.2Te (not shown). The spectra disappear above 340 K for both samples and cannot be detected by spin− echo or free-induction decay sequences. Similar features are seen in Cu2Se;35 however, the Cu2Se signal reappears as a motionally narrowed line above 260 K indicating faster motion. Further results showing development of atomic dynamics are shown through the spin−spin relaxation time (T2), described in the Supporting Information. 63 Cu T1 versus temperature is shown in Figure 3, measured at the center position of the line shape. Korringa behavior (T1T = constant) is seen at low temperatures consistent with the metallic behavior of these samples. 1/T1 can be fitted over the full range to an activation formula, f exp(−ΔE/KBT) + BT. The solid curves in Figure 3 show the results with activation

Figure 1. (a) 63Cu spectra (echo integral × T) vs temperature; (b) 77 K 63Cu spectrum with fit (solid curve) including the narrow (dotted) and broad (dashed) resonances denoted sites A and B, respectively. Inset: 63Cu spectra of both samples at 77 K. Positive shifts correspond to paramagnetic sign, with shift including both the magnetic and quadrupole parts.

Table 1. T1 Values at 77 K for 65Cu and 63Cu and the 63 −1 Separated Magnetic (63T−1 1M) and Quadrupole ( T1Q) Contributions Obtained from Measurements at Positions Indicated Cu2Te site site A (measured at 0 ppm) site B (measured at 1300 ppm)

63

T1 (ms)

65

T1 (ms)

172 ± 4

166 ± 4

99 ± 11

65 ± 8

63 −1 T1M

(s−1)

4.02 ± 0.68

63 −1 T1Q

(s−1)

1.67 ± 0.77

10.1 ± 1.1

of two Cu NMR sites (and three Te NMR sites as shown later) is consistent with the Cu2Te structure measurements; the hexagonal cell contains six Cu2Te units, with detailed crystallographic positions not known. The inset of Figure 1b compares the Cu spectra of the two samples. The fitting for Cu1.98Ag0.2Te is similar to Cu2Te with the shifts of sites A and B reduced to δtotal = −90 and 400 ppm, respectively. The smaller shifts for Cu1.98Ag0.2Te result from its lower carrier density, hence, a smaller Knight shift contribution. Also, we do not identify a separate CuAgTe peak for Cu1.98Ag0.2Te. The number of Cu nuclei in the CuAgTe phase should be around 8% of the total on the basis of the WDS compositions, and this signal is assumed to be hidden under the overall resonance line.

Figure 3. 63Cu 1/TT1 vs temperature for Cu2Te (circles) and Cu1.98Ag0.2Te (squares) measured at the spectral maximum. Solid curves are fits as explained in the text. Inset: 63Cu spectra at 290 K, with the same symbols. 14551

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yielded an electronic contribution γ = 0.44 mJ/(mol K2), per mole formula unit. Computational Results. To compare with experiment, we calculate NMR chemical shifts using the PBE and mBJ + U methods. This is done for Cu2Te as well as for the analogue material Cu2Se using the method of ref 32. For Cu2Se as a test material, in the mBJ + U case, we obtain δ = +205 ppm for Cu NMR in the high-temperature cubic phase. This is in excellent agreement with the result δcs = +220 ppm observed in the cubic phase above the structural transition.35 With the PBE method, for which the band gap collapses to give a semimetallic contact, a larger calculated shift of δ = +694 ppm results, an increase which is not surprising since the paramagnetic contribution38 is overestimated when the separation of bands becomes reduced. Thus, we find that Cu2Se has a Cu chemical shift in the normal range, which is correctly computed using WIEN2k with the band contact lifted using the mBJ + U method. For Cu2Te, the calculated shift is δ = +273 ppm for Cu in the high-temperature cubic phase, using mBJ + U and −260 ppm for 125Te. Using PBE, these become +1040 ppm and +1251 ppm, respectively, once again increased because of the collapsed gap as in Cu2Se. Calculated partial densities of states are shown in Figure 5 for the cases discussed earlier. These are

energies ΔE = 0.35 and 0.5 eV for Cu2Te and Cu1.98Ag0.2Te, respectively. We also measured 65Cu as well as 63Cu T1 at selected temperatures. We separated the magnetic and quadrupole contributions35 using (T1)−1 = (T1Q)−1 + (T1M)−1 with (T1Q)−1 ∝ Q2 and (T1M)−1∝ γ2. Results are given in Table 1 for Cu2Te at 77 K. Site B exhibits only a magnetic contribution, and for both sites, we find that the magnetic contributions dominate at 77 K, not unexpected since the compounds are metallic.13,14 On the other hand, at room temperature, 65T1/63T1 at site A is almost identical to (63Q/65Q)2, indicating a switch to a quadrupole mechanism as a result of ionic motion. Te NMR Results. Figure 4 shows a 125Te NMR spectrum for the Cu2Te sample. Measurements at 77 K, at 918, 1172, and

Figure 4. 125Te spectra for the Cu2Te sample. Dashed curves: Gaussian peaks fitted as explained in the text. The solid curve is the sum of these curves. Right axis: relaxation times (T1) at three distict positions (squares, with error bars smaller than symbols). Inset: 1/T1T vs temperature at the peak position corresponding to site D, with Korringa fit given by solid line.

1504 ppm (squares in Figure 4), yielded T1 = 7.2 ± 0.2 ms, T1 = 6.7 ± 0.2 ms, and T1 = 4.7 ± 0.2 ms, respectively. Given these results and the observed shape, we fitted the spectrum to the three Gaussian curves labeled as C, D, and E in Figure 4, having almost identical spectral weights. The inset of Figure 4 shows 1/T1T of site D versus temperature. The constant 1/T1T follows Korringa-like metallic behavior36 with no hopping behavior since spin 1/2 125Te is much less sensitive to atomic motion. For Cu1.98Ag0.2Te, the 125Te spectrum also has obvious features similar to Cu2Te, and it was fitted in the same way. We obtained T1= 7.2, 7.3, and 6 ms at 77 K, at positions corresponding to sites C (901 ppm), D (1177 ppm), and E (1498 ppm), respectively. The decrease of 125Te T1 with increasing shift in both samples is consistent with the Korringa behavior, showing that the Knight shift is the main factor responsible for shifted parts of the Te spectrum and, thus, the overall line shape. Heat Capacity. To further understand the carrier states contributing to the Knight shifts, we measured the heat capacity versus temperature for the Cu2Te sample. In many crystalline materials, the low-temperature contribution is37 CP = γT + βT3, where γ is the contribution due to metallic electrons and β is due to phonons. The results for Cu2Te (more details of which can be found in the Supporting Information) show, in addition, an Einstein oscillator contribution, presumably due to the loosely held ions also responsible for the initiation of lowtemperature hopping (Figure S2). Fitting to such a model

Figure 5. Partial densities of states for cubic Cu2Se and Cu2Te, using the models shown. Zero energy is the valence band maximum. Top: Cu s-states, per Cu atom; bottom: Te s-states, per Te atom.

shown for the Cu and Te s-orbits which determine NMR Knight shifts, in the upper valence band region containing the holes. In cubic symmetry, the materials have normal (noninverted) band structures with small s contributions for holes: for Cu2Te, gs(E) is zero at the band edge by symmetry, and for mBJ + U, the Cu + Te contributions increase to 8% of the total g(E) for E = −1 eV. The partial g(E) results do not include contributions from interstitial states outside of the WIEN2k atomic spheres; the interstitials contribute 17% to g(E) at E = −0.5 eV for Cu2Te, renormalizing by a small amount the relative gs(E) contributions, which, however, remain small. However, the s-fraction remains small, with the integrated gs(E) over the range of occupied valence states about 5% of the total g(E) . Using the result for a single hole pocket 14552

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2 π

2

(meff /ℏ2)3/2 (Ev − E)

method to calculate K and partition δtotal, the results are shown in Table 2 for the Cu2Te sample, along with (K2T1MT) values.

(1)

Table 2. Theoretical Korringa Product [K2T1MT in 10−6 sK], Total Fitted Shift (δtotal), Chemical Shift (δcs), and Knight Shift (K) at 77 K Derived from Data for the Cu2Te Sample As Explained in the Text

we also calculate effective masses for comparison with experiment. For Cu2Se in mBJ + U, we obtain meff = 1.2m0 for holes at E = −0.5 eV, where m0 is the bare electron mass. This is in good agreement with the experimental value extrapolated35 to 1.5m0 for the cubic phase at 390 K, helping to further confirm the validity of the mBJ + U approach for the band-edge states. For Cu2Te, we obtain 0.71m0 at E = −0.9 eV, the approximate Fermi energy position for p = 3 × 1021 cm−3, the hole density for the Cu2Te sample. We use the measured γ = 0.44 mJ/(mol K2) from specific heat quoted earlier, the relation37 γ = π2k2B g(EF)/3 yields g(EF) = 0.19 states/(eV formula unit), and meff/m0 = 0.49, which is close to the calculated value. Thus, the overall g(EF) for the valence band is not much changed in the low-temperature structure of Cu2Te.

site A (63Cu) 2

K T1MT δtotal (ppm) K (ppm) δcs (ppm)

3.7 −50 440 −490

site C (125Te) site D (125Te) site E (125Te) 2.6 918 2170 −1250

2.6 1172 2240 −1070

2.6 1504 2710 −1200

The same procedure for Cu site B yields K = 700 ppm and δcs = −250 ppm; however, the δtotal fit for this site includes a large model-dependent uncertainty because of the large quadrupole contribution, and so we did not include this site in Table 2. We also did not make the dense set of Cu NMR measurements needed to isolate T1M for Cu nuclei in the Ag-doped sample; however, its somewhat reduced Te relaxation rates yield a mean δcs = −1040 ppm for the Te sites. For both samples, a striking result of this analysis is the large and negative chemical shifts obtained in all cases. The Cu2Te Knight shift can also be estimated from the measured electronic part of the heat capacity (γ = 0.44 mJ/mol K2) with the assumption of a single hole pocket. The Knight HF shift is36 K = μBgs(EF)HHF s , where Hs is the contact hyperfine field and gs(EF) is the s-partial contribution. The value g(EF) = 0.19 states/(eV formula unit) was extracted from the specific heat, as noted earlier. If all states were s-states, equally distributed between Cu and Te, and using36 HHF = 260 and s 1720 T for Cu and Te, respectively, we obtain K = 930 ppm for Cu, and 6190 ppm for Te. The observed Cu and Te Knight shifts (Table 2) are smaller than these estimates by a factor of 0.47 for Cu and 0.38 for Te (taking the mean value for the latter). These correspond to a 9 times larger s-fraction than the calculated results described earlier, for which gs(E) is about 5% of the total g(E) . The ratio gs(E)/gtotal(E) is also essentially the same as Knight’s ξ factor,36 indicating the fraction of electrons in s-orbitals contributing to the Knight shift. While ξ can cover a large range, when properly considering only the s electrons, estimates using standard values of HHF s have been established to provide good estimates of K and T1, within a range of about 20%.41,42 Thus, there is some uncertainty in using such values to estimate gs(E) from T1, but it is much smaller than the factor of 9 difference from the calculated value. Further, the Korringa product can also have a contribution due to electron−electron interactions; this term would enhance the susceptibility (and hence the Knight shift) over the freeelectron value. This factor can be very significant for semiconductors near the metal−insulator transition, but it should be closer to unity for the present case, doped well into the metallic regime (as shown by the constant 1/125T1T, Figure 4) but with relatively small carrier density compared to that of a metal. In most cases, this effect leads to an enhancement of K relative to the Korringa value, but, for example, in P-doped silicon,43 the P NMR Korringa product approaches a value of about 62% of the free-electron value for carrier densities well into the metallic regime (e.g., K would be multiplied by a factor of 0.8). Comparing values in Table 2, we see that if K were reduced in this way, δcs for Cu becomes −400 ppm, while the smaller K yields δcs values for the three 125Te sites with mean

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DISCUSSION Atomic Hopping. For Cu2Te Cu NMR, the fitting parameters for 1/T1 versus T include ΔE = 0.35 eV and f = 7× 107 s−1. Likewise, the fit gives ΔE = 0.5 eV and f = 2 × 1010 s−1 for the Ag-doped sample. Both activation energies are larger than the results for Cu2Se (0.23 eV).35 Transport measurements39 on Cu2−xTe give ΔE = 0.4 ± 0.03 eV, in good agreement with the NMR. The prefactor f in the T1 fits corresponds in standard Bloembergen, Purcell, and Pound theory40 to f = f 0(ωloc/ωL)2, where f 0 is the atomic hopping attempt frequency and where the ratio is that of the line width to the center frequency of the NMR spectrum. This is for the situation where the population of mobile ions is fixed,9 which should be the case here because of the large density of vacancies. Because Cu ions hop between sites with different quadrupole widths, this ratio is difficult to determine precisely; however, using ωloc/ωL ≈ 0.007 on the basis of the observed spectrum width of Figure 1, the fitted prefactors correspond to an attempt frequency f 0= 1 × 1012 Hz for Cu2Te. This is comparable to ordinary phonon frequencies as expected for single-ion hopping processes.9 The larger f for Cu1.98Ag0.2Te presumably reflects sampling of sites with larger ωloc because of Ag alloying. The Cu NMR spin−echo results demonstrate that the hopping mechanism in unsubstituted Cu2Te remains unchanged below room temperature. Expressing the Arrhenius hopping rate as 1/τ = f 0 exp[−ΔE/kBT], and using f 0 = 1012 Hz and the fitted ΔE = 0.35 eV, τ is reduced to 200 μs (equal to the spin−echo time scale of twice the separation between pulses) when the temperature drops to 220 K, the same as the temperature below which static behavior takes hold in Figure 2. The Te NMR Korringa behavior (Figure 4), which remains constant versus temperature, also shows that during the slowing down process, the electronic behavior remains unchanged, in contrast to Cu2Se which exhibits a structure change.5 The enhanced activation energy of the Ag-substituted sample indicates that substitution is a way to stabilize the material against ionic motion, as may be needed for electronic applications. Electronic Behavior. The resonance shift (δtotal) is a sum of chemical shift (δcs) and Knight shift (K) contributions. Knight shifts can be obtained from the Korringa relation;36 since at 77 K both samples are in the metallic regime, the Korringa product [K2T1MT = ℏγ2e /(4πkBγ2n)] is realized. For Cu nuclei, T1M is the partitioned magnetic contribution described earlier. Using this 14553

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value −700 ppm. On the other hand, with an enhanced K2T1T, the δcs results become correspondingly more negative. This indicates the range of negative chemical shifts implied by the measured results. The Korringa T1 results thus point to a relatively large scontribution in the Cu2Te valence band, approximately 9 times larger than the contribution obtained in the calculation, the smaller result corresponding to a normal band structure with a p-dominated valence band edge. In contrast to Cu2Te, the Cu Knight shift and 1/T1M in p-type Cu2Se is shown35 to be much smaller and in good agreement with the calculations reported here. In addition to the s-state at the band edge, the observed negative chemical shifts in Cu2Te are also characteristic of systems with an inverted band structure. The Cu main for Cu2Te peak falls in a chemical shift range outside of what is normally expected44 for Cu, and the negative 125Te shift is also at the far end of the reported range. For comparison, recent reports have identified45,46 PbTe to have a 125Te shift corresponding to δ = −1150 ppm, more positive than Cu2Te, and other rock-salt-structure tellurides of which we are aware are reported to have more paramagnetic shifts. It was previously identified47 that negative chemical shifts tend to be observed in topological insulators. The hexagonal Cu2Te structure is believed to be a superstructure of the Nowotny structure,18 akin to hexagonal Ag2Te and Ag2Se, also known as topological insulators.10−12 Thus, there are several indicators that Cu2Te may have a topologically interesting electronic structure. Clearly, the band ordering and its orbital composition is significantly different from that of the parent cubic phase, as evidenced both by Knight shifts for both nuclei and by the chemical shifts.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +1 (979) 845 7823. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Robert A. Welch Foundation, Grant No. A-1526. Sedat Ballikaya kindly acknowledges financial support by Scientific Research Projects Coordination Unit of Istanbul University with project numbers of 20611 and 21272 and would also like to thank the Scientific and Technological Research Council of Turkey (TUBITAK) for financial support with project number 115F510. Synthesis of the Cu2Te and Cu1.98Ag0.2Te samples at the University of Michigan was supported as part of the Center for Solar and Thermal Energy Conversion, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Basic Energy Sciences, under Award DE-SC-0000957.

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REFERENCES

(1) Yun, J. H.; Kim, K. H.; Lee, D. Y.; Ahn, B. T. Back Contact Formation Using Cu2Te As A Cu-Doping Source And As An Electrode In CdTe Solar Cells. Sol. Energy Mater. Sol. Cells 2003, 75, 203−210. (2) Sridhar, K.; Chattopadhyay, K. Synthesis By Mechanical Alloying And Thermoelectric Properties Of Cu2Te. J. Alloys Compd. 1998, 264, 293−298. (3) Sklyarchuk, V.; Plevachuk, Y. Electronic Properties Of Liquid Tl2Te, Tl2Se, Ag2Te, Cu2Te, And Cu2Se Alloys. Semiconductors 2002, 36, 1123−1127. (4) Liu, H.; Shi, X.; Xu, F.; Zhang, L.; Zhang, W.; Chen, L.; Li, Q.; Uher, C.; Day, T.; Snyder, G. J. Copper Ion Liquid-Like Thermoelectrics. Nat. Mater. 2012, 11, 422. (5) Ballikaya, S.; Chi, H.; Salvador, J. R.; Uher, C. Thermoelectric Properties Of Ag-Doped Cu2Se And Cu2Te. J. Mater. Chem. A 2013, 1, 12478. (6) He, Y.; Zhang, T.; Shi, X.; Wei, S.-H.; Chen, L. High Thermoelectric Performance In Copper Telluride. NPG Asia Mater. 2015, 7, e210. (7) Xu, R.; Husmann, A.; Rosenbaum, T. F.; Saboungi, M.-L.; Enderby, J. E.; Littlewood, P. B. Large Magnetoresistance In NonMagnetic Silver Chalcogenides. Nature 1997, 390, 57. (8) Chi, H.; Kim, H.; Thomas, J. C.; Shi, G.; Sun, K.; Abeykoon, M.; Bozin, E. S.; Shi, X.; Li, Q.; Shi, X.; et al. Low-Temperature Structural And Transport Anomalies In Cu2Se. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 89, 195209. (9) Boyce, J.; Huberman, B. Superionic Conductors: Transitions, Structures, Dynamics. Phys. Rep. 1979, 51, 189−265. (10) Qi, X.-L.; Zhang, S.-C. Topological Insulators And Superconductors. Rev. Mod. Phys. 2011, 83, 1057−1110. (11) Hasan, M. Z.; Kane, C. L. Colloquium: Topological Insulators. Rev. Mod. Phys. 2010, 82, 3045−3067. (12) Lee, S.; In, J.; Yoo, Y.; Jo, Y.; Park, Y. C.; Kim, H.-J.; Koo, H. C.; Kim, J.; Kim, B.; Wang, K. L. Single Crystalline β-Ag2Te Nanowire As A New Topological Insulator. Nano Lett. 2012, 12, 4194−4199. (13) Miyatani, S.-Y.; Mori, S.; Yanagihara, M. Phase Diagram And Electrical Properties Of Cu2−δTe. J. Phys. Soc. Jpn. 1979, 47, 1152− 1158. (14) Wu, X.; Zhou, J.; Duda, A.; Yan, Y.; Teeter, G.; Asher, S.; Metzger, W.; Demtsu, S.; Wei, S.-H.; Noufi, R. Phase Control Of CuxTe Film And Its Effects On CdS/CdTe Solar Cell. Thin Solid Films 2007, 515, 5798−5803. (15) Sorokin, G.; Papshev, Y. M.; Oush, P. Photoconductivity Of Cu2S, Cu2Se And Cu2Te. Sov. Phys. Solid State 1966, 7, 1810.

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CONCLUSIONS Our investigations included 63Cu, 65Cu, and 125Te NMR measurements in Cu2Te and Cu1.98Ag0.2Te and showed that the hexagonal-structure material differs greatly in electronic structure from the cubic fluorite Cu2Te phase, with an inverted band ordering of Cu and Te s-states. This conclusion is supported both by NMR Knight shifts and by chemical shifts and is confirmed through heat capacity measurements and electronic structure calculations. These point to a very large ssymmetry participation in the valence band, in contrast to the behavior demonstrated for Cu2Se. The results coincide with behavior previously identified for materials with topologically nontrivial band inversion. The results also demonstrate the initiation of Cu-ion dynamics at low temperatures, in good agreement with conventional superionic behavior and hightemperature transport measurements. Even with the very small Ag substitution into the Cu2Te phase, the hopping barriers for ion motion significantly increase, which may be important for practical applications.

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The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b04785. Spin−spin relaxation times T2; heat capacity information (PDF) 14554

DOI: 10.1021/acs.jpcc.6b04785 J. Phys. Chem. C 2016, 120, 14549−14555

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The Journal of Physical Chemistry C (16) Vouroutzis, N.; Manolikas, C. Phase Transformations In Cuprous Telluride. Phys. Status Solidi A 1989, 111, 491−497. (17) Kashida, S.; Shimosaka, W.; Mori, M.; Yoshimura, D. Valence Band Photoemission Study Of The Copper Chalcogenide Compounds, Cu2S, Cu2Se And Cu2Te. J. Phys. Chem. Solids 2003, 64, 2357−2363. (18) Nowotny, H. Die Kristallstructur Yon Cu2Te. Z. Metallkd. 1946, 37, 40. (19) Patzak, I. Uber Die Dtruktur Und Die Lage Der Phasen Im System Kupfer-Tellur. Z. Metallkd. 1956, 47, 418. (20) Blachnik, R.; Lasocka, M.; Walbrecht, U. The System CopperTellurium. J. Solid State Chem. 1983, 48, 431−438. (21) Asadov, Y. G.; Rustamova, L. V.; Gasimov, G. B.; Jafarov, K. M.; Babajev, A. G. Structural Phase Transitions In Cu2−xTe Crystals (x = 0.00, 0.10, 0.15, 0.20, 0.25). Phase Transitions 1992, 38, 247−259. (22) Nguyen, M. C.; Choi, J.-H.; Zhao, X.; Wang, C.-Z.; Zhang, Z.; Ho, K.-M. New Layered Structures Of Cuprous Chalcogenides As Thin Film Solar Cell Materials: Cu2Te And Cu2Se. Phys. Rev. Lett. 2013, 111, 165502. (23) Inamo, M. 125Te NMR Evidence For The Existence Of Trinuclear Tellurate Ion In Aqueous Solution. Chem. Lett. 1996, 25, 17−18. (24) Massiot, D.; Fayon, F.; Capron, M.; King, I.; Le Calvé, S.; Alonso, B.; Durand, J.-O.; Bujoli, B.; Gan, Z.; Hoatson, G. Modelling One- And Two-Dimensional Solid-State NMR Spectra. Magn. Reson. Chem. 2002, 40, 70−76. (25) Narath, A. Nuclear Spin-Lattice Relaxation In Hexagonal Transition Metals: Titanium. Phys. Rev. 1967, 162, 320−332. (26) Harris, R. K.; Becker, E. D. NMR Nomenclature: Nuclear Spin Properties And Conventions For Chemical ShiftsIUPAC Recommendations. J. Magn. Reson. 2002, 156, 323. (27) Madsen, G. K. H.; Blaha, P.; Schwarz, K.; Sjöstedt, E.; Nordström, L. Efficient Linearization Of The Augmented Plane-Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 2001, 64, 195134. (28) Schwarz, K.; Blaha, P. Solid State Calculations Using WIEN2k. Comput. Mater. Sci. 2003, 28, 259−273. (29) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (30) Tran, F.; Blaha, P. Accurate Band Gaps Of Semiconductors And Insulators With A Semilocal Exchange-Correlation Potential. Phys. Rev. Lett. 2009, 102, 226401. (31) Laskowski, R.; Blaha, P.; Tran, F. Assessment Of DFT Functionals With NMR Chemical Shifts. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 87, 195130. (32) Zhang, Y.; Wang, Y.; Xi, L.; Qiu, R.; Shi, X.; Zhang, P.; Zhang, W. Electronic Structure Of Antifluorite Cu2X (X = S, Se, Te) Within The Modified Becke-Johnson Potential Plus An On-Site Coulomb U. J. Chem. Phys. 2014, 140, 074702. (33) Koumoulis, D.; Morris, G. D.; He, L.; Kou, X.; King, D.; Wang, D.; Hossain, M. D.; Wang, K. L.; Fiete, G. A.; Kanatzidis, M. G.; et al. Nanoscale β-Nuclear Magnetic Resonance Depth Imaging Of Topological Insulators. Proc. Natl. Acad. Sci. U. S. A. 2015, 112, E3645−E3650. (34) Edwards, T. G.; Gjersing, E. L.; Sen, S.; Currie, S. C.; Aitken, B. G. 125Te NMR Chemical Shifts And Tellurium Coordination Environments In Crystals And Glasses In The Ge−As−Sb−Te System. J. Non-Cryst. Solids 2011, 357, 3036−3041. (35) Sirusi, A. A.; Ballikaya, S.; Uher, C.; Ross, J. H., Jr. LowTemperature Structure And Dynamics In Cu2Se. J. Phys. Chem. C 2015, 119, 20293−20298. (36) Carter, G. C.; Bennett, L. H.; Kahan, D. J. Metallic Shifts In NMR. Prog. Mater. Sci. 1976, 20, 1. (37) Ashcroft, N.; Mermin, N. Solid State Physics; Saunders College: Philadelphia, 1976. (38) Calculation of NMR and EPR Parameters: Theory And Applications, 1st ed.; Kaupp, M., Bühl, M., Malkin, V. G., Eds.; Wiley-VCH: Weinheim, Germany, 2004.

(39) Yakshibaev, R. A.; Mukhamadeeva, N. N.; Almukhametov, R. F. Phase Transformations And Ionic Transport In The Cu2−δTe Superionic Conductor. Phys. Status Solidi (a) 1988, 108, 135−141. (40) Bloembergen, N.; Purcell, E. M.; Pound, R. V. Relaxation Effects In Nuclear Magnetic Resonance Absorption. Phys. Rev. 1948, 73, 679− 712. (41) van der Klink, J. J.; Brom, H. NMR In Metals, Metal Particles And Metal Cluster Compounds. Prog. Nucl. Magn. Reson. Spectrosc. 2000, 36, 89−201. (42) Saeed, M.; Wazumi, T.; Kumagai, K.-i.; Nakajima, Y.; Tamegai, T. NMR Study Of Two-Gap Superconductivity In Lu2Fe3Si5. J. Phys. Soc. Jpn. 2013, 82, 064705. (43) Hoch, M. J. R.; Holcomb, D. F. 31P Knight Shifts And Spin Dynamics In Si:P At Temperatures Comparable To The Fermi Temperature. Phys. Rev. B: Condens. Matter Mater. Phys. 2005, 71, 035115. (44) Günther, H. NMR Spectroscopy: Basic Principles, Concepts and Applications in Chemistry; Wiley-VCH: Siegen, Germany, 2013. (45) Koumoulis, D.; Chasapis, T. C.; Leung, B.; Taylor, R. E.; Stoumpos, C. C.; Calta, N. P.; Kanatzidis, M. G.; Bouchard, L.-S. SiteSpecific Contributions To The Band Inversion In A Topological Crystalline Insulator. Adv. Electron. Mater. 2015, 1, 1500117. (46) Njegic, B.; Levin, E.; Schmidt-Rohr, K. 125Te NMR ChemicalShift Trends In PbTe−GeTe And PbTe−SnTe Alloys. Solid State Nucl. Magn. Reson. 2013, 55−56, 79−83. (47) Nowak, B.; Kaczorowski, D. NMR As A Probe Of Band Inversion In Topologically Nontrivial Half-Heusler Compounds. J. Phys. Chem. C 2014, 118, 18021−18026.

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DOI: 10.1021/acs.jpcc.6b04785 J. Phys. Chem. C 2016, 120, 14549−14555