209Bi NMR in Topologically Trivial and Nontrivial Half-Heusler

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Article 209

Bi NMR in Topologically Trivial and Nontrivial Half-Heusler Bismuthides Bogdan Nowak, and Dariusz Kaczorowski J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b07135 • Publication Date (Web): 30 Aug 2016 Downloaded from http://pubs.acs.org on September 3, 2016

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The Journal of Physical Chemistry

209

Bi NMR in Topologically Trivial and Nontrivial Half-Heusler Bismuthides

Bogdan Nowak and Dariusz Kaczorowski* Institute for Low Temperature and Structure Research, Polish Academy of Sciences, P.O. Box 1410, 50-950 Wrocław, Poland

ABSTRACT 209

Bi NMR experiments were performed for half-Heusler compounds ScPtBi, LaPdBi and

LaPtBi. The resonance shifts in these materials as well as in a few isostructural RTBi (R = Sc, Y, Lu; T = Pd, Pt) phases were revealed to correlate linearly with the calculated band inversion strength that characterizes topological character of the systems. On the contrary, commonly accepted relationship between the NMR shifts and the average nuclear charge was found to be violated.

Corresponding author. E-mail address: [email protected] Phone number: (+48) 71 395 42 58

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1. INTRODUCTION Theoretical prediction of the formation of nontrivial topological states in rare-earthbased half-Heusler compounds,1-3 ignited substantial interest in studying this class of materials. In particular, detailed calculations

4,5

indicated a few bismuthides RTBi with T –

Pd, Pt and R = Y, La, or Lu to be putative topological insulators showing so-called band inversion effect, quantified by the band inversion strength (BIS) parameter, which was defined as an energy difference between the Γ6 and Γ8 energy levels at the Γ symmetry point in the Brillouin zone, ∆BIS = EΓ6 - EΓ8. Despite many efforts, unambiguous experimental verification of the occurrence of topologically nontrivial states in the RTBi phases is still lacking. While, the first angleresolved photoemission spectroscopy (ARPES) study yielded no firm conclusion as regards the presence of Dirac nodes in LuPtBi, DyPtBi and GdPtBi,

6

the most recent ARPES data

suggested the presence of topological surface states in YPtBi and LuPtBi. 7 On the other hand, numerous

electrical

magnetotransport

investigations

revealed

anomalous

features

characteristic of Weyl semimetals for several RTBi compounds 8-18 including those studied by ARPES. Most interestingly, the RPtBi phases with R = Y, La, and Lu as well as the RPdBi ternaries with R = Ho, Er, Tm, and Lu exhibit superconductivity at low temperatures that possibly has unconventional character due to nontrivial topology or/and noncentrosymmetric crystal structure. 9,13,16,17,19-23 Recently, we suggested

24,25

that nuclear magnetic resonance (NMR) can be utilized as a

simple technique probing the band inversion effect in half-Heusler bismuthides. Analyzing the NMR data obtained for RTBi compounds where R = Y and Lu, we noticed that inversion in the order of the electronic bands near the Fermi level manifests itself in an abrupt change in sign and magnitude of the

209

Bi resonance shift

209

δ as well as in a rapid drop in the nuclear

spin-lattice relaxation time. Our finding of negative nontrivial YPtBi, LuPdBi and LuPtBi,

4,5

209

Bi NMR shifts in topologically

and positive frequency shifts in topologically trivial

ScPdBi and YPdBi 4,5 was confirmed by the results reported by other research group.26 Most recently, another paper by the latter team appeared,27 in which the authors suggested for the RTBi (R = Sc, Y, Lu; T = Ni, Pd, Pt) phases a direct correlation of the 209Bi shift tensors with the average strength of spin-orbit coupling (SOC). The SOC strength was expressed as an energy difference ESOC = EΓ8 - EΓ7 and related to the average nuclear charge in the investigated systems. Indeed, the reported correlation should be expected if the band inversion in the RTBi

compounds is a consequence of strong SOC effect.28-31 However, some authors argued (see 2 ACS Paragon Plus Environment

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e.g. Ref.32) that in many materials with nontrivial topology scalar relativistic effects on the s electrons of heavy elements may play an essential role in the band inversion, instead of SOC. Therefore, resolving the actual origin of the band inversion effect in half-Heusler phases remains an essential objective in the studies on these materials. In this work we performed 209Bi NMR measurements on ScPtBi, LaPdBi and LaPtBi. To the best of our knowledge, this is the first report on the NMR data for the latter two phases, considered as topologically trivial and nontrivial, respectively.3-5 The obtained results, together with the previously reported data,24,25 were analyzed in terms of relationship between the 209Bi resonance shifts and the average nuclear charge or the band inversion strength in the RTBi compounds. While, no obvious correlation was found in the linear dependencies of

209

209

δ versus values,

δ on ∆BIS were established separately for the RPdBi and RPtBi

series.

2. EXPERIMENTAL DETAILS Polycrystalline samples of LaPdBi, LaPtBi and ScPtBi were obtained by arc-melting the appropriate amounts of the high-purity constituents on a water-cooled copper crucible in ultra-pure argon atmosphere. Some small excess of bismuth was taken in order to account for its high volatility above melting temperature. The buttons were flipped over and re-melted several times to promote homogeneity. Subsequently, the ingots were wrapped with tantalum foil, sealed in evacuated (vacuum 10-4 torr) quartz tubes and annealed at 800oC for two weeks. The products were characterized at room temperature by powder x-ray diffraction (PXRD) carried out using an X’pert Pro PANanalitical diffractometer with Cu-Kα radiation. The theoretical PXRD pattern calculations and the crystal structure refinements were done employing the FULLPROF program package.33 The chemical composition of the samples were examined by energy-dispersive X-ray (EDX) spectroscopy on a FEI scanning electron microscope equipped with an EDAX Genesis XM4 spectrometer. NMR measurements were performed at 293 K on fine-pulverized specimens using a Bruker Avance DSX 300 spectrometer operating at a field of 7.05 T. The 209Bi line shapes of NMR spectra and their shifts were obtained. In the case of ScPtBi, the

209

Bi NMR spectra

were acquired by Fourier transforming the free induction decay (FID) signal following a single radio-frequency (RF) pulse. For LaPdBi and LaPtBi, a nuclear spin echo was excited



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by means of two pulse sequence (α±x −τ − β±y) with α±x = 1µs < 90°±x and β±y = 1µs < 90°±y , interpulse delay τ ≈ 30 µs and repetition time t ≈ 500 ms. Such a technique is frequently applied for materials exhibiting inhomogeneously broadened resonance lines.34-36 Quadrature detection and phase cycling procedures were used for removal of baseline artifacts from the spin-echo data.37 The second half of the spin echo was Fourier-transformed and different spectra for different frequency settings were overlayed (frequency-sweep spectra,34,35 called also variable offset cumulative spectra (VOCS).36 According to the IUPAC unified δ scale,38 the

209

Bi and

value of

45

Sc NMR frequency shifts were determined with reference to the respective

209

Ξ or 45Ξ, defined as the ratio of the isotope-specific frequency to that of 1H in

tetramethylsilane (TMS) in the same magnetic field .

3. RESULTS AND DISCUSSION The EDX results revealed that the prepared LaPdBi and LaPtBi samples were homogeneous, essentially free of foreign phases, with the chemical compositions close to the ideal ones. The PXRD refinements indicated the crystal structure of the MgAgAs-type with the cubic lattice parameter a = 685.0(1) pm for LaPdBi and a = 685.9(2) pm for LaPtBi, in very good agreement with the literature data.18, 39-41 In contrast, the obtained Sc-Pt-Bi alloy was found by EDX and PXRD to be Bideficient and composed of two cubic phases, namely ScPtBi (MgAgAs-type) and ScPt (CsCltype), in proportion of about 1:1. The lattice parameter a = 643.9(1) pm derived for the ScPtBi phase, is slightly larger than that of ScPdBi (a = 643.2(1) pm,25 in concert with the unit cell volume relationships observed within the pairs YPdBi – YPtBi, LaPdBi – LaPtBi, and LuPdBi – LuPtBi.24,25,40 For the ScPt phase, the PXRD data analysis yielded a = 326.8(1) pm, in perfect agreement with the previous report.42 The presence of two Sc-based phases in the studied Sc-Pt-Bi alloy was corroborated by the 45Sc NMR experiment that gave two welldefined signals in nearly equal proportion (not shown). In turn, only one sharp 209Bi NMR line was recorded for this alloy with the positive isotropic shift 209δ = 340(40) ppm (see Figure 1) that can be ascribed to the ScPtBi phase.27,43 In striking contrast to narrow 209Bi NMR spectra observed for the Sc-, Y- and Lu-based half-Heusler bismuthides 24,25 and the present work, in the case of LaPdBi and LaPtBi the

209

Bi spin echoes recorded by traditional technique were

very narrow, signaling that the NMR powder pattern spectra are very broad, likely extending over a range of few MHz. This finding implied that the full spectral resonance could not be 4 ACS Paragon Plus Environment

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acquired in a single spectrum.

Therefore, the

209

Bi VOCS spectra were collected, as

exemplified in Figure 2 for LaPtBi. The obtained line is very broad, and its overall shape hints at the presence of structural defects in the measured specimen. The likely atomic disorder (anti-sites, vacancies, etc.) results in breaking the nominally cubic symmetry of the Bi site in the MgAgAs-type unit cell, and hence the electric field gradient (EFG) tensor at this position becomes finite. This feature may lead to broadening the NMR signal of the quadrupolar 209Bi nuclei (I = 9/2) through the nuclear electric quadrupole interaction. The effect is especially significant in the case of LaPtBi and LaPdBi, however it is worth recalling here that also for the Y- and Lu-based half-Heusler bismuthides some structural disorder, yet of lesser degree, was anticipated before from the fact of the absence of Solomon echoes in their NMR spectra, Ref.24,25, in contrast to the case of the respective antimonides. 44 The observed large broadening of the 209Bi NMR signal in LaPtBi correlates well with the

139

La nuclear quadrupole resonance (NQR) experiment reported in Ref.45. Despite the

nominally cubic symmetry of the La site, three NQR lines centered at 2.49, 4.98, and 7.47 MHz were observed at T = 4.2 K, and ascribed to the transitions between the adjacent energy levels (±1/2 ↔ ±3/2), (±3/2 ↔ ±5/2) and (±5/2 ↔ ±7/2). This result can be naturally rationalized by assuming creation of EFG’s due to structural disorder that effectively lowers the local symmetry in the measured sample. It is well known that in nominally cubic compounds inhomogeneous broadening of the NMR signal due to structural disorder is usually symmetrical, leaving the position of a central transition ½ ↔ – ½ and its isotropic shift unchanged. In fact, the shapes, linewidths and shifts for several independently prepared samples of LaPtBi and LaPdBi were found repeatable. The obtained shifts are 209δ = – 435(50) ppm in LaPtBi and 209δ = 4200(50) ppm in LaPdBi. Large errors in the 209δ values result mainly from large linewidths and in minor part are determined by unknown concentration of carriers. In Figure 3, the

209

Bi resonance shifts in the RTBi (R = Sc, Y, La, Lu; T = Pd, Pt)

compounds are plotted against the average nuclear charge < Z > = (ZR +ZT+ZBi)/3 (panel a) and the band inversion strength ∆BIS, calculated in Ref. 4 (panel b). While no systematic dependence of 209δ on is observed for neither of the two series, clear correlation between 209

δ and ∆BIS manifests itself in a form of two nearly parallel straight lines corresponding to

the Pt- and Pd-bearing materials, respectively. The observed separation of the 209δ versus ∆BIS data into two branches likely originates from the fact that in the RTBi materials the electronic 5 ACS Paragon Plus Environment


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band structures near the Fermi level are determined mainly by the TBi frameworks, with little participation of the states due to the R atoms.31 The slopes of the two lines are nearly the same because all the considered compounds are isostructural and isoelectronic.

4. CONCLUSIONS The measured resonance shifts of 209Bi nuclei in the RPdBi and RPtBi ( R = Sc, Y, La, and Lu) half-Heusler compounds have been shown to depend linearly on the calculated bands inversion strength (BIS). On the other hand, no clear correlation between the NMR shifts and the average nuclear charge has been found, at variance with common believe that BIS in these materials is controlled by strong spin-orbit coupling (SOC) being proportional to . Actually, contrary to naïve expectation for pairs ScPtBi and LaPtBi or ScPdBi and LaPdBi, in which the partners have distinctly different , the measured

209

Bi NMR shifts and the

calculated ∆BIS values are quite similar. Another key outcome from the present study is challenging the statement made in our own previous research24,25 and then corroborated by other authors26 that topological character of the half-Heusler compounds is directly reflected in the sign of the resonance shift. At odds with our expectation of negative

209

Bi shift in topologically nontrivial ScPtBi,4,27,43 the

measured 209δ value appeared slightly positive.

ACKNOWLEDGEMENT The authors acknowledge support from the National Science Centre (Poland) under research grant 2015/18/A/ST3/00057.

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FIGURE CAPTIONS

Fig.1. Single-pulse NMR spectrum for 209Bi nuclei in ScPtBi measured at T = 293 K.

Fig.2. Examples of

209

Bi NMR subspectra acquired at different radio frequency transmitter

offsets and the resulting VOCS spectrum obtained for LaPtBi at T = 293 K. The central transition ½ ↔ – ½ and unresolved overlapping satellites, characteristic for other transitions of the I = 9/2 system are clearly seen, hence indicating the presence of EFG’s due to some structural disorder.

Fig.3. The NMR frequency shift of

209

Bi nuclei in RTBi (R = Sc, Y, La, Lu; T = Pd, Pt) half-

Heusler compounds plotted versus (a) average nuclear charge, and (b) band inversion strength. The 209δ data were measured here or taken from Refs. 24 and 25. The values of ∆BIS were taken from Ref. 4 (for ScPtBi, a modified value ∆BIS ≈ – 0.55 eV was applied, corresponding to the difference in the lattice parameter calculated in Ref. 4 and that derived experimentally in the present work). The Pd- and Pt-bearing compounds are denoted by triangles and circles, respectively. The topologically nontrivial compounds are marked by full symbols, while the topologically trivial ones by open symbols.



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Fig.1. Single-pulse NMR spectrum for 209Bi nuclei in ScPtBi measured at T = 293 K. Fig. 1 153x119mm (300 x 300 DPI)

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Fig.2. Examples of 209Bi NMR subspectra acquired at different radio frequency transmitter offsets and the resulting VOCS spectrum obtained for LaPtBi at T = 293 K. The central transition ½ ↔ – ½ and unresolved overlapping satellites, characteristic for other transitions of the I = 9/2 system are clearly seen, hence indicating the presence of EFG’s due to some structural disorder. Fig. 2 280x170mm (300 x 300 DPI)



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Fig. 3 The NMR frequency shift of 209Bi nuclei in RTBi (R = Sc, Y, La, Lu; T = Pd, Pt) half-Heusler compounds plotted versus (a) average nuclear charge, and (b) band inversion strength. The 209δ data were measured here or taken from Refs. 23 and 24. The values of ∆BIS were taken from Ref. 4 (for ScPtBi, a modified value ∆BIS ≈ – 0.55 eV was applied, corresponding to the difference in the lattice parameter calculated in Ref. 4 and that derived experimentally in the present work). The Pd- and Pt-bearing compounds are denoted by triangles and circles, respectively. The topologically nontrivial compounds are marked by full symbols, while the topologically trivial ones by open symbols. Fig. 3a 172x145mm (300 x 300 DPI)


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Fig. 3 The NMR frequency shift of 209Bi nuclei in RTBi (R = Sc, Y, La, Lu; T = Pd, Pt) half-Heusler compounds plotted versus (a) average nuclear charge, and (b) band inversion strength. The 209δ data were measured here or taken from Refs. 23 and 24. The values of ∆BIS were taken from Ref. 4 (for ScPtBi, a modified value ∆BIS ≈ – 0.55 eV was applied, corresponding to the difference in the lattice parameter calculated in Ref. 4 and that derived experimentally in the present work). The Pd- and Pt-bearing compounds are denoted by triangles and circles, respectively. The topologically nontrivial compounds are marked by full symbols, while the topologically trivial ones by open symbols. Fig. 3b 166x189mm (300 x 300 DPI)



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TOC graphic 57x42mm (300 x 300 DPI)


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209Bi NMR in Topologically Trivial and Nontrivial Half-Heusler

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