NMR as a Probe of Band Inversion in Topologically Nontrivial Half

Article pubs.acs.org/JPCC

NMR as a Probe of Band Inversion in Topologically Nontrivial HalfHeusler Compounds Bogdan Nowak and Dariusz Kaczorowski* W. Trzebiatowski Institute for Low Temperature and Structure Research, Polish Academy of Sciences, P.O. Box 1410, 50-950 Wrocław, Poland ABSTRACT: 209Bi nuclear magnetic resonance (NMR) was studied in half-Heusler compounds YPdBi and YPtBi. The observed NMR spectra exhibit low intensity because of short nuclear transverse relaxation time (T2) governed by sizable structural disorder. In both compounds, the frequency shift of the 209Bi bulk nuclei is dominated by the chemical shielding (δcs) contribution. Remarkably, it is positive for topologically trivial YPdBi yet strongly negative for topologically nontrivial YPtBi. At the same time, the spin−lattice relaxation rate (1/T1) is distinctly larger in YPtBi due to stronger spin−orbit coupling and postulated inversion of the electronic bands near the Fermi level. The unique features of δcs and 1/T1 established for YPtBi can be considered as possibly universal fingerprints of topologically nontrivial state in similar materials.

1. INTRODUCTION Ternary compounds YPdBi and YPtBi belong to a large family of the so-called half-Heusler phases MTX (M = Y, La−Lu; T = Ni, Pd, Pt; X = Sb, Bi), which crystallize in a noncentrosymmetric cubic structure (space group F4̅3m, no. 216) with atoms occupying the positions 4a (0, 0, 0), 4b (1/2, 1/2, 1 /2), and 4c (1/4, 1/4, 1/4) and all having the same sitesymmetry −43m.1 The family is a subject of current interest due to indications from ab initio electron structure calculations of possible band inversion near the Fermi level and thus formation of a topologically nontrivial state.2−9 The band inversion near the Fermi level is a key to realize the state of topological insulator (TI). It is characterized by insulating band gap in the bulk while having a gapless surface state that is protected by time-reversal symmetry.10−12 The topology of the electronic band structure in the crystal structure of half-Heusler phases is defined by the so-called band inversion strength (Δ) defined as an energy difference between the Γ6 and Γ8 energy levels at the Γ symmetry point in the Brillouin zone.2,3,5,6 It is generally believed that strong spin−orbit coupling (SOC) gives rise to the band inversion10−12 and is generally responsible for the semimetallic properties.13 However, some authors argue that scalar relativistic effects on the s electrons of heavy elements play an essential role for the band inversion in many materials, including HgTe-like materials, instead of SOC.14 The electronic structure calculations based on a fullpotential linearized-augmented-plane-wave method with modified Becke−Johnson local-density-approximation (MBJLDA) of exchange-correlation potential5,6 show that YPtBi, LaPtBi, LuPdBi, and LuPtBi exhibit the band inversion effect and may be thus topologically nontrivial. The same calculations indicate that YPdBi is topologically trivial.5,6 Obviously, the s/p © 2014 American Chemical Society

inversion which is responsible for the topological order is also absent in YPdSb and YPtSb, the compounds isostructural and isoelectronic with YPtBi. Though the topological classification of the half-Heusler phases is still a matter of controversy,15−17 detailed experimental characterization of these materials becomes highly desirable. Additional motivation for comprehensive studies of MTX ternaries comes from the recent findings of low-carrier superconductivity that sets in YPtBi,18−20 LaPtBi,21 and LuPtBi22 and may have a topological nature. In order to verify the topological character of these materials, first one requires an experimental probe for the band inversion effect. It seems that nuclear magnetic resonance (NMR) could be here a very appropriate technique as NMR as a local-probe method is sensitive to the electronic band structure in the vicinity of the Fermi energy εF. Advantages of NMR also include the ability to reliably probe the properties of lesser quality or even amorphous materials, which may appear not suitable to study by conventional macroscopic techniques. In particular, studies of the NMR resonance shift in metals have an inherent advantage over bulk properties (e.g., magnetic susceptibility, electrical conductivity, heat capacity) measurements because the presence of foreign phases generally does not affect the resonance shift. In the past, the significance of NMR was demonstrated in numerous investigations of classical semiconductors such as PbTe.23−25 More recently, just for PbTe a powerful approach combining experimental NMR results with ab initio calculations was developed.26 The first NMR study on Hg1−xCdxTe that is presently known as an archetypal two-dimensional (2D) TI Received: May 30, 2014 Revised: July 21, 2014 Published: July 21, 2014 18021

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Figure 1. Powder X-ray diffraction patterns of annealed (a) YPdBi (sample 2) and (b) YPtBi (sample 4). Below the experimental data are shown the theoretical PXRD patterns calculated for two different atom distributions: model (1) Y atoms at 4a (0, 0, 0), Pd or Pt atoms at 4c (1/4, 1/4, 1/4), Bi atoms at 4b (1/2, 1/2, 1/2), and model (2) Y atoms at 4c (1/4, 1/4, 1/4), Pd or Pt atoms at 4a (0, 0, 0), Bi atoms at 4b (1/2, 1/2, 1/2). For simplicity, in both models, full site occupancies were assumed.

were obtained by Fourier transforming the free induction decay (FID) signal following single radio frequency (RF) pulse. Quadrature detection and extended phase cycling procedures were used. For uniform saturation of the resonance line the nuclear magnetization recovers exponentially, independently of magnitude of the nuclear spin. Indeed, the recovery of the FID amplitude after the saturation of nuclear spins by a comb of RF pulses seems to be of single exponential form for 209Bi nuclei. For each composition we measured several samples from different batches and realized that the results are slightly sample dependent. In particular, a trace of extra line of 209Bi NMR with a resonance shift ≈0.27%, characteristic of binary compound YBi, was observed35 despite this impurity was hardly visible in the PXRD data.

system was reported in ref 27. The bulk properties of wellrecognized 3D-TI systems, Bi2Se3, Bi2Te3, and some ordered ternaries, were studied by 77Se and 125Te NMR28−30 as well as by 209Bi NMR.31,32 In the present work, we performed 209Bi NMR studies on the bismuthides YPdBi and YPtBi using samples containing native defects and impurities. The results were compared with the 121,123 Sb NMR data obtained recently for the respective antimonides33 and discussed in the context of the possible band inversion that is a prerequisite for the formation of TI states.

2. EXPERIMENTAL METHODS Polycrystalline samples of YPdBi (samples 1 and 2) and YPtBi (samples 3 and 4) were prepared by arc-melting the appropriate amounts of the elemental constituents with the purity not less than 99.9 wt %, performed in ultrapure argon atmosphere on a water-cooled copper crucible. The buttons were flipped over and remelted several times to ensure homogeneity. Subsequently, the ingots were wrapped with tantalum foil, sealed in evacuated (vacuum 10−4 Torr) quartz tubes, and annealed at 800 °C for 2 weeks. The obtained samples were characterized at room temperature by powder X-ray diffraction (PXRD) carried out using an X’pert Pro PANanalitical diffractometer with monochromatized Cu Kα radiation. The crystal structure refinements and the theoretical PXRD pattern calculations were done employing the FULLPROF program package.34 The chemical compositions of the samples were examined on a FEI scanning electron microscope equipped with an EDAX Genesis XM4 spectrometer. The materials were found homogeneous, nearly free of foreign phases, and with the stoichiometry close to 1:1:1. NMR measurements of 209Bi nuclei with nuclear spin 209I = 9 /2 and natural abundance 209A = 100% were performed at 293 K using a Bruker Avance DSX 300 spectrometer operating at a field of 7.05 T. The 209Bi NMR spectra of YPdBi and YPtBi

3. RESULTS AND DISCUSSION 3.1. Crystal Structure. Figure 1 displays the PXRD patterns obtained for the studied samples of YPdBi and YPtBi. They can be easily indexed within the MgAgAs-type crystal structure, characteristic of half-Heusler phases. The refined cubic lattice parameter of the former compound was 6.641 Å (sample 1) and 6.630 Å (sample 2), in good agreement with the literature data: 6.639 Å36 and 6.640 Å.37 The Rietveld refinement yielded the composition Y1.04PdBi0.96 with the 4a (0, 0, 0) position occupied by a mixture of 0.91 Y + 0.09 Bi atoms, the 4b (1/2, 1/2, 1/2) position filled with a mixture of 0.87 Bi + 0.13 Y atoms, and the 4c (1/4, 1/4, 1/4) position being fully occupied solely by Pd atoms. Most importantly, our result markedly differs from the model recently suggested by Wang et al.38 in which Y atoms are located at the unique 4c site. As displayed in Figure 1a, the latter atom distribution results in distinctly different relative intensities of the PXRD lines (note especially the two first Bragg reflections) and thus must be ruled out in the present case. It is also worth noting that the lattice parameter of 6.68 Å38 is significantly larger than all the 18022

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For comparison, Figure 2b displays the 121Sb NMR data acquired for the respective Sb-based compounds YPdSb and YPtSb.33 Notably, the observed resonance lines are much stronger and distinctly narrower than those of the 209Bi nuclei in the bismuthides. Moreover, as reported in ref 33, in the 121Sb and 123Sb NMR spectra of YPdSb and YPtSb it was possible to observe quadrupolar (Solomon) echoes, which could not be excited for YPdBi and YPtBi. Taking into account that the nuclear spin 123I = 7/2 and the quadrupolar moment 123Q = −49 fm2 of the 123Sb nuclei42 have similar values to those of the 209Bi nuclei (121Sb nucleus is characterized by 121I = 5/2 and 121Q = −36 fm2 42), one may infer that in the investigated compounds EFG at the Bi position is remarkably larger than that at the Sb sites. Larger EFG at nominally −43m crystallographic position implies higher level of intrinsic structural disorder. Another support for the latter conjecture comes from our inability to detect any 195Pt NMR signal in YPtBi. The Pt resonance is expected to be weaker than that of Bi by about an order of magnitude, generally because of 195I = 1/2 and small abundance 195A ≈ 34%. Alike in the present case, it was also not found for the half-Heusler phase YbPtBi.43 Nevertheless, it should be stressed that 195Pt NMR signal was effortlessly measured in the antimonide YPtSb33 that probably exhibits a much lesser degree of atomic disorder. To summarize our findings, the 209Bi and 195Pt NMR results concurrently manifest an electronically inhomogeneous character of the investigated samples of YPdBi and YPtBi. Qualitatively, they are consistent with the macroscopic PXRD data. In this context, it seems worth recalling that crystallographic disorder in single-crystalline YPdBi was suggested also by the authors of ref 38 to be a likely source of the observed linear magnetoresistance. Neither NMR nor PXRD could provide an unambiguous determination of the type of disorder in the studied specimens. Deviation from the ideal structure may be associated with some site interchange in the distribution of atomic constituents, as mentioned above, but it may also be similar to that reported for the half-Heusler antimonides ScTSb (T = Ni, Pd),44 where vacancies in the T atom sublattice were revealed. In each case one should take into account the presence of impurities and other spurious defects in the crystal structures of real samples. 3.3. 209Bi Resonance Shifts. Generally, the NMR frequency shift is defined as δ = (νsample − νref)/νref, where νsample stands for the frequency position of the measured resonance line and νref is the frequency of the resonance of the given nuclei in a reference material.42 According to the IUPAC unified δ scale, the reference standard for NMR of 209Bi nuclei is Bi(NO3)3 in HNO3, and 209Bi NMR frequency shifts are determined with reference to the related value of 209Ξ, where 209 Ξ is defined as the ratio of the isotope-specific frequency to that of 1H in tetramethylsilane (TMS) measured in the same magnetic field.42 In the case of YPdBi, the so-defined 209Bi resonance shift is positive and equal to +0.113%. In contrast, the resonance shift derived for YPtBi is negative, and its absolute value is markedly larger being δ = −0.178%. To interpret this striking result, one should first recall that the principal contributions to the NMR signal shift are the chemical shielding (δCS) and the Knight shift (K), δ = δCS + K.23−26 The chemical shielding is dependent on local structure and electronic environment of the nucleus. In turn, the Knight shift probes the interaction of nuclear spins with charge carriers (electrons or holes). The chemical and Knight shifts are normally distinguished through studies of the resonance

values quoted above. Here, it is worth recalling that a similar degree of occupational disorder on the crystallographic sites of the Y and pnictogen atoms as that found in our study for YPdBi was established for the corresponding antimonide with the refined composition Y0.97PdSb1.03.39 A similar model of the atom distribution, with Pt atoms placed at the 4c (1/4, 1/4, 1/4) position (note entirely different relative intensities of the low-angle Bragg peaks for the Y atom located at this site), was found appropriate for YPtBi (see Figure 1b). The refined chemical composition was Y0.99PtBi1.01, and the lattice parameter was 6.638 Å (sample 3) and 6.648 Å (sample 4), i.e., close to that reported in the literature: 6.652,18 6.650,19 6.66,40 and 6.640 Å.41 The PXRD data refinement converged at a mixture of 0.92 Y + 0.08 Bi atoms at the 4a (0, 0, 0) position, a mixture of 0.93 Bi + 0.07 Y atoms at the 4b (1/2, 1 /2, 1/2) site, with the 4c (1/4, 1/4, 1/4) position fixed at full occupancy by Pt atoms. 3.2. NMR Spectra. The experimental 209Bi NMR data obtained at room temperature for YPdBi (sample 2) and YPtBi (sample 4) are presented in Figure 2a. For both bismuthides a

Figure 2. Frequency shifts and the relaxation times of (a) 209Bi NMR in YPdBi and YPtBi and (b) 121Sb NMR in YPdSb and YPtSb measured at T = 293 K. The same scale (in ppm) is used for both resonances. Note that topologically trivial/nontrivial materials are represented by green/red lines, respectively. The data for YPdSb and YPtSb were taken from ref 33.

single yet broadened and resonance of rather weak intensity was revealed. Its line width appeared slightly sample dependent and equal to about 20−25 kHz, which is much larger than can be expected for dipolar or pseudodipolar lines. Moreover, the 209 Bi resonance line of YPdBi is slightly asymmetric. Generally, in half-Heusler phases with perfect structural ordering, the electric field gradient (EFG) at each atom site is equal to zero due to the tetrahedral symmetry. However, any structural disorder in nominally cubic materials is known to broaden the NMR resonance of nuclei with I > 1/2 over pure dipolar value, and it happens mainly because of quadrupolar interaction. Especially, the resonance of 209Bi nuclei is very sensitive in this respect, due to their very large nuclear spin 209I = 9/2 and large quadrupolar moment 209Q = −51.6 fm2.42 The broadness of the NMR lines recorded for YPdBi and YPtBi can thus be attributed to the presence of atomic disorder in the unit cells of the samples measured. In turn, the weakness of the 209Bi resonance implies short (comparable with a dead time of a receiver) spin−spin relaxation time, T2, which probably also arises because of structural disorder. 18023

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frequency as a function of temperature and carrier concentration, followed by extrapolation of the shift to zero carrier concentration. For classical semiconductors, the sign of K measured relative to the resonance of a “carrier-free” sample is different for p- and n-type materials; namely, it is negative for the former and positive for the latter ones. Additionally, assuming a parabolic band with unipolar carriers, it was found that K scales with N1/3, where N is the carrier concentration.23,25 The experimental studies on the Sb-based phases YPdSb and YPtSb indicated a p-type conductivity and weakly temperature dependent N ≈ 1019 cm−3 near room temperature.39,45−47 The 121,123 Sb resonance shifts determined for these two compounds were positive and of nearly same value (δ = +0.092% and +0.089% for YPdSb and YPtSb, respectively).33 This finding can be attributed to the chemical shielding terms, which dominate over the Knight shift effects. The same type of electronic transport as it the antimonides yet with an order of magnitude larger carrier concentration was reported for YPdBi.36 Also in this case, the Knight shift makes probably a minor contribution to the measured total resonance shift. This conjecture is supported by our observation of nearly same NMR line widths, resonance shifts, and relaxation times for samples taken from different batches, which probably contained only somewhat different concentration of native carriers. Most importantly, by analogy to the other compounds, the dominant role of δCS can be expected in YPtBi that was characterized as a p-type conductor with N ≈ 2 × 1019 cm−3 at 300 K.18,19 Consequently, the prominent negative difference (−2900 ppm) between the frequency shifts in topologically trivial YPdBi and in topologically nontrivial YPtBi must be attributed to a substantial difference between their chemical shifts δCS with only some minor correction for the actual Knight shift values K. Thus, it seems very likely that the observed large negative 209Bi resonance shift in YPtBi is a crucial experimental fingerprint of the band inversion near the Fermi energy, postulated theoretically to occur in this material.2,3,5,6 3.4. Spin−Lattice Relaxation. The nuclear magnetization recovery function in NMR measurement performed on 209Bi nuclei that experience nonzero EFG can be generally expressed as48

As demonstrated in Figure 3, for both compounds, this function provides a good description of the experimental data

Figure 3. Recovery curves of nuclear magnetization obtained at T = 293 K for 209Bi nuclei in topologically trivial YPdBi (sample 2) and topologically nontrivial YPtBi (sample 4).

collected within two decades in the factor 1 − M(t)/M(∞). The so-derived values of the T1 constant are T1 = 66 ms for YPdBi and T1 = 26 ms for YPtBi. For comparison, the nuclear spin−lattice relaxation times determined by a similar method for the Sb-based counterparts were T1 = 101 ms and T1 = 96 ms for YPdSb and YPtSb, respectively.33 Commonly, the spin−lattice relaxation rate 1/T1 of quadrupolar nuclei can be expressed as a sum of two independent contributions 1/T1 = (R1)M + (R1)Q, where the first term represents magnetic interactions and the second one results from interaction of quadrupolar moment of the given nucleus with crystalline electric field gradient at its crystallographic site. In semiconductors, 1/T1 usually increases monotonously with increasing the carrier density.49 Another important factor is the magnitude of relativistic effects, namely strengthening of SOC brings about an increase in 1/T1.30 As noted above, the charge carrier concentrations in YPdSb and YPtSb are practically the same. Consequently, the difference between the measured spin−lattice relaxation times is almost negligible. Additional justification for the similar relaxation rate in these two compounds comes from the fact that their T1 was found to be dominated by quadrupolar relaxation via phonons,33 which is hardly dependent on the carrier density.31 As regards the bismuthides, it seems likely that similar mechanism is the prevailing relaxation channel, but this hypothesis cannot be verified in the NMR studies because of the 100% abundance of the 209Bi isotope. The observed substantial shortening of the relaxation time T1 on going from YPdBi to YPtBi can result from both the increase in the charge carriers concentration (see above) and strengthening the SOC interaction. Then, in view of the similar carried density in the two bismuthides,18,19,36 the distinct drop in the value of T1 on proceeding from YPdBi to YPtBi should be attributed nearly solely to the relativistic effects, in line with the theoretically predicted2,3,5,6 band inversion in the latter compound. Thus, the extremely fast nuclear spin−lattice relaxation of the 209Bi nuclei in YPtBi seems to be another experimental fingerprint of the topologically nontrivial character of the electronic ground state in this material.

M(t ) = M(∞){1 − C[c1 exp( −45t /T1) + c 2 exp( −28t /T1) + c3 exp( −15t /T1) + +c4 exp( −6t /T1) + c5 exp( −t /T1)]}

where M(∞) stands for the signal intensity at thermal equilibrium, the terms weighted by the coefficients c1−5 account for saturation of the particular excitations in an I = 9/2 system, and the parameter T1 represents the nuclear spin−lattice relaxation time. The constants C and c1−5 are dependent on initial saturation conditions, and they are usually treated as adjustable parameters. In the experiments performed for YPdBi and YPtBi, a train of short saturation pulses was applied, and this procedure was established to uniformly saturate nearly all the allowed transitions. Though we did not succeed in achieving the complete saturation (the C coefficient was estimated to be about 92%), an important part of the magnetization was found to recover in a manner described by the simplified expression M(t ) = M(∞)[1 − C exp( −t /T1)] 18024

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(7) Ouardi, S.; Shekhar, C.; Fecher, G. H.; Kozina, X.; Stryganyuk, G.; Felser, C.; Ueda, S.; Kobayashi, K. Electronic Structure of Pt Based Topological Heusler Compounds with C1b Structure and “Zero Band Gap”. Appl. Phys. Lett. 2011, 98, 211901−1−3. (8) Zhang, X. M.; Wang, W. H.; Liu, E. K.; Liu, G. D.; Liu, Z. Y.; Wu, G. H. Influence of Tetragonal Distortion on the Topological Electronic Structure of the Half-Heusler Compound LaPtBi from First Principles. Appl. Phys. Lett. 2011, 99, 071901−1−3. (9) Nourbakhsh, Z. Three Dimensional Topological Insulators of LuPdBixSb1‑x Alloys. J. Alloys Compd. 2013, 549, 51−56. (10) Hasan, M. Z.; Kane, C. L. Colloquium: Topological Insulators. Rev. Mod. Phys. 2010, 82, 3045−3067. (11) Qi, X.-L.; Zhang, S.-C. Topological Insulators and Superconductors. Rev. Mod. Phys. 2011, 83, 1057−1110. (12) Ando, Y. Topological Insulator Materials. J. Phys. Soc. Jpn. 2013, 82, 102001−32. (13) Oguchi, T. Electronic Band Structure and Structural Stability of LaBiPt. Phys. Rev. B 2001, 63, 125115−1−5. (14) Zhu, Z.; Cheng, Y.; Schwingenschlögl, U. Band Inversion Mechanism in Topological Insulators: A Guideline for Materials Design. Phys. Rev. B 2012, 85, 235401−1−5. (15) Liu, C.; Lee, Y.; Kondo, T.; Mun, E. D.; Caudle, M.; Harmon, B. N.; Bud’ko, S. L.; Canfield, P. C.; Kaminski, A. Metallic Surface Electronic State in Half-Heusler Compounds RPtBi (R = Lu, Dy, Gd). Phys. Rev. B 2011, 83, 205133−1−6. (16) Vidal, J.; Zhang, X.; Luo, J.-W.; Zunger, A. GW Identification of False-Positive and False-Negative Assignments of Topological Insulators and Semimetals in Density-Functional Calculations. arXiv:1101.3734v2 [cond-mat.mtrl-sci], 21 Jan 2011, 1−11. (17) Vidal, J.; Zhang, X.; Yu, L.; Luo, J.-W.; Zunger, A. False-Positive and False-Negative Assignments of Topological Insulators in Density Functional Theory and Hybrids. Phys. Rev. B 2011, 84, 041109(R)-1− 4. (18) Butch, N. P.; Syers, P.; Kirshenbaum, K.; Hope, A. P.; Paglione, J. Superconductivity in the Topological Semimetal YPtBi. Phys. Rev. B 2011, 84, 220504(R)-1−5. (19) Bay, T.; Naka, T.; Huang, Y. K.; de Visser, A. Superconductivity in Noncentrosymmetric YPtBi under Pressure. Phys. Rev. B 2012, 86, 064515−1−5. (20) Bay, T. V.; Jackson, M.; Paulsen, C.; Baines, C.; Amato, A.; Orvis, T.; Aronson, M. C.; Huang, Y. K.; deVisser, A. Low Field Magnetic Response of the Non-Centrosymmetric Superconductor YPtBi. Solid State Commun. 2014, 183, 13−17. (21) Goll, G.; Marz, M.; Hamann, A.; Tomanic, T.; Grube, K.; Yoshino, T.; Takabatake, T. Thermodynamic and Transport Properties of the Non-Centrosymmetric Superconductor LaBiPt. Physica B 2008, 403, 1065−1067. (22) Tafti, F. F.; Fujii, T.; Juneau-Fecteau, A.; de Cotret, S. R.; Doiron-Leyraud, N.; Asamitsu, A.; Taillefer, L. Superconductivity in the Noncentrosymmetric Half-Heusler Compound LuPtBi: A Candidate for Topological Superconductivity. Phys. Rev. B 2013, 87, 184504−1−5. (23) Hewes, C. R.; Adler, M. S.; Senturia, S. D. Nuclear-MagneticResonance Studies in PbTe and Pb1‑xSnxTe: An Experimental Determination of k·p Band Parameters and Magnetic Hyperfine Constants. Phys. Rev. B 1973, 7, 5195−5212. (24) Sapoval, B.; Leloup, J. Y. Knight Shift in Multivalley Semiconductors, I. Theory of Contact, Orbital, and Dipolar Shift and Relativistic Effects. Phys. Rev. B 1973, 7, 5272−5276. (25) Leloup, J. Y.; Sapoval, B.; Martinez, G. Knight Shift in Multivalley Semiconductors. II. Determination of the Hyperfine Coupling Constants in N- and P-Type PbSe and PbTe. Phys. Rev. B 1973, 7, 5276−5284. (26) Taylor, R. E.; Alkan, F.; Koumoulis, D.; Lake, M. P.; King, D.; Dybowski, C.; Bouchard, L.-S. A Combined NMR and DFT Study of Narrow Gap Semiconductors: The Case of PbTe. J. Phys. Chem. C 2013, 117, 8959−8967. (27) Vieth, H. M.; Vega, S.; Yielin, N.; Zamir, D. Temperature Dependence of the NMR Line Shift and T1 Relaxation Times of 125 in

4. CONCLUSIONS The crystal structure of the half-Heusler compounds YPdBi and YPtBi consists of three interpenetrating face-centered-cubic lattices with Pd/Pt atoms located at the unique site, where they are double-tetrahedrally coordinated by Y and Bi atoms. The latter atoms form two other fcc sublattices and exhibit mutually mixed occupancies at their crystallographic sites. The 209Bi NMR measurements confirmed that both materials are somewhat electronically inhomogeneous on the microscopic scale, which gives rise to broadening of NMR lines and fairly enhanced spin−spin relaxation rates 1/T2. The key findings from the performed NMR measurements of YPtBi are the very short 209Bi spin−lattice relaxation time T1 = 26 ms and anomalously large negative 209Bi resonance shift δ = −0.178% with respect to that in the reference material. Most importantly, both these NMR characteristics distinctly differ from the values derived for the isostructural bismuthide YPdBi (T1 = 66 ms and δ = +0.113%). The likely origin for the observed dissimilarity is in principal interactions between 209Bi nuclear spins and spins of polarized electrons from the bands near the Fermi energy. Thus, the obtained NMR data are perfectly in concert with the results of the electronic band structure calculations, which predicted for YPtBi the band inversion effect. It seems plausible that short T1 and negative δ are universal features of the band inversion in topologically nontrivial materials. If so, NMR measurements may appear an efficient method of probing the band inversion effect, which is a prerequisite condition for the emergence of topological insulator states.

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AUTHOR INFORMATION

Corresponding Author

*Tel +48 71 395 42 58; Fax +48 71 344 10 29; e-mail D. [email protected] (D.K.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Centre of Science (Poland) under research grant 2011/01/B/ST3/04466. REFERENCES

(1) Graf, T.; S. Parkin, S. P.; Felser, C. Simple Rules for the Understanding of Heusler Compounds. Prog. Solid State Chem. 2011, 39, 1−50. (2) Chadov, S.; Qi, X.-L.; Kübler, J.; Fecher, G. H.; Felser, C.; Zhang, S.-C. Tunable Multifunctional Topological Insulators in Ternary Heusler Compounds. Nat. Mater. 2010, 9, 541−545. (3) Lin, H.; Wray, L. A.; Xia, Y.; Xu, S.; Jia, S.; Cava, R. J.; Bansil, A.; Hasan, M. Z. Half-Heusler Ternary Compounds as New Multifunctional Experimental Platforms for Topological Quantum Phenomena. Nat. Mater. 2010, 9, 546−549. (4) Xiao, W. D.; Yao, Y.; Feng, W.; Wen, J.; Zhu, W.; Chen, X.-Q.; Stocks, G. M.; Zhan, Z. Half-Heusler Compounds as a New Clas of Three-Dimensional Topological Insulators. Phys. Rev. Lett. 2010, 105, 096404−1−4. (5) Al-Sawai, W.; Lin, H.; Markiewicz, R. S.; Wray, L. A.; Xia, Y.; Xu, S.-Y.; Hasan, M. Z.; Bansil, A. Topologic Electronic Structure in HalfHeusler Topological Insulators. Phys. Rev. B 2010, 82, 125208−1−5. (6) Feng, W.; Xiao, D.; Zhang, Y.; Yao, Y. Half-Heusler Topological Insulators: A First-Principles study with the Tran-Blaha Modified Becke-Johnson Density Functional. Phys. Rev. B 2010, 82, 235121−1− 5. 18025

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The Journal of Physical Chemistry C

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