Intermetallics 40 (2013) 28e35
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Nonmetallic behaviour in half-Heusler phases YPdSb, YPtSb and LuPtSb Bogdan Nowak*, Dariusz Kaczorowski W. Trzebiatowski Institute for Low Temperature and Structure Research, Polish Academy of Sciences, P.O. Box 1410, 50-950 Wrocław, Poland
a r t i c l e i n f o
a b s t r a c t
Article history: Received 8 February 2013 Received in revised form 29 March 2013 Accepted 2 April 2013 Available online 3 May 2013
We present the results of combined macroscopic [magnetic susceptibility, heat capacity, electrical resistivity] and microscopic [nuclear magnetic resonance (NMR)] studies of half Heusler phases YPdSb, YPtSb and LuPtSb. The bulk results indicated diamagnetic and nonmetallic behaviours. The Solomon quadrupolar echoes revealed for all three materials the presence of some static electric ﬁeld gradients, and thus some small deviation from the perfect cubic symmetry. The spin-lattice relaxation rates of the 121,123 Sb nuclei were shown to be nonmetallic, quadrupolar in nature and due to the dominant twophonon Raman processes. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: A. Rare-earth intermetallics B. Electrical resistance and other electrical properties B. Magnetic properties B. Thermodynamic and thermochemical properties
1. Introduction Ternary compounds YPdSb, YPtSb and LuPtSb belong to a large family of the so-called half-Heusler phases MTX (M ¼ Y, La-Lu; T ¼ Ni, Pd, Pt; X ¼ Sb, Bi) , which crystallize in a noncentrosymmetric cubic structure (space group F-43m, nr 216) with all the atoms having the same site-symmetry 43 m . The halfHeusler compounds exhibit diverse physical properties suitable for green-energy and spintronic applications [1,2]. In particular, they have been intensively studied in recent years, for their potential use in novel thermoelectric converters or devices based on giant magnetoresistance effect . The magnetic behaviour in most rareearth (RE) bearing MTX materials is governed by the presence of sizeable magnetic moments on the lanthanide atoms due to welllocalized 4f electronic states [3e7]. In the case of YPdSb and YPdBi, which contain no 4f electrons, simple diamagnetic behaviour was found [3e6]. All the MTX ternaries exhibit semimetallic or narrow-gap semiconducting behaviour in their electronic transport [3e7]. The very intriguing case constitutes YbPtBi that possesses a heavy-fermion ground state characterized by a huge value of the electronic speciﬁc heat coefﬁcient g ¼ 8 J/(mol K2) [7,8]. In turn, the compound CePtBi exhibits enhanced thermoelectric characteristics being prospective for real-world applications . The nonmagnetic
* Corresponding author. E-mail address: [email protected]
t.pan.wroc.pl (B. Nowak). 0966-9795/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.intermet.2013.04.001
counterpart to the latter bismuthide, namely LaPtBi, was reported to be a non-centrosymmetric low-carrier superconductor with Tc ¼ 0.8 K , and an unconventional superconductivity below Tc ¼ 0.77 K was discovered also for YPtBi [11,12]. The interest in half-Heusler phases has recently been boosted by the theoretical prediction that a few of them may belong to a class of topological insulators [13e17]. Though the topological classiﬁcation of these materials is still a matter of controversy , detailed experimental characterization of the less-studied compound seems highly desirable and may possibly result in new discoveries. To the best of our knowledge only the Pd-bearing compound was hitherto studied in quite some detail, primarily in the context of being a nonmagnetic counterpart to the heavy-rare-earth REPdSb phases [3e5,19]. The electronic transport behaviours of YPtSb and LuPtSb were already brieﬂy reported in Refs. [19e21]. The valence states of YPtSb  and LuPtSb  were investigated by means of hard X-ray photoelectron spectroscopy (HAXPES) as a bulk sensitive method and compared with the ab initio electronic structure calculations . The data have been interpreted in a model of zero band gap between the valence and conduction bands at the Fermi energy, ℇF. Combined with sufﬁciently strong spinorbit coupling (SOC) it can lead to a band inversion (nontrivial state) which is the key to realize the state of topological insulator in some of the half-Heusler compounds containing heavy metals . However, in other theoretical studies carried out by two independent groups [16,17] YPdSb and YPtSb were shown to be regular
B. Nowak, D. Kaczorowski / Intermetallics 40 (2013) 28e35
semiconductors with ﬁnite band gap (trivial state), while LuPtSb was situated at the borderline between trivial and nontrivial case. In this paper, we report on the magnetic and electrical transport properties of YPdSb, YPtSb and LuPtSb, investigated by bulk (magnetic susceptibility, heat capacity, electrical resistivity) and local-probe (nuclear magnetic resonance; NMR) methods. In particular, NMR of heavy nuclei with nuclear spin I > 1/2 is a very useful and sensitive tool in the determination of sample quality (breaking of local symmetry, imperfections of chemical composition, defects etc.). The main aim of our study was to verify the electronic ground states in these compounds. 2. Experimental details Polycrystalline samples of YPdSb, YPtSb and LuPtSb were prepared by arc-melting the appropriate amounts of elemental constituents (purities: 99.9 wt.% Y, 99.9 wt.% Lu, 99.9 wt.% Pd, 99.9 wt.% Pt and 99.99 wt.% Sb) performed on a water-cooled copper crucible in an ultra-pure argon atmosphere. The buttons were ﬂipped over and remelted several times to ensure homogeneity. The ﬁnal weight losses were below 0.5%. Subsequently, the ingots were wrapped with tantalum foil, sealed in evacuated (vacuum 104 torr) quartz tubes and annealed at 800 C for two weeks. From the annealed ingots, bulk specimens of appropriate sizes were cut using a wire saw to be used in magnetic, electrical and heat capacity measurements. The only exception was resistivity measurement of YPtSb that was made on as cast sample because heat treatment was established to bring about large amount of micro- and macrocracks, which notably inﬂuenced the magnitude of the measured resistance. The remaining pieces of each compound were ﬁnepulverised in an MBraun argon glove box with continuously controlled partial pressures of O2 and H2O to be lower than 1 ppm, placed in glass ampoules, and then sealed for heat treatment in a tube resistance furnace at 300 C for 3 h, in order to remove strains introduced during the sample powdering. These powders were used in NMR measurements. The quality of the obtained material was checked by X-ray powder diffraction using an X’pert Pro PANalytical diffractometer with CuKa radiation and by energy dispersive X-ray (EDX) analysis employing a Philips 515 scanning electron microscope equipped with an EDAX PV 9800 spectrometer. Both techniques proved the single-phase character of the samples. The diffraction experiments were performed both before and after annealing at 800 C. No substantial differences in the recorded X-ray spectra were observed. After annealing, the X-ray lines were only slightly sharper and respective CuKa1/CuKa2 lines (if applied) were better resolved. As an example, the X-ray diffraction pattern obtained for the annealed sample of YPtSb is shown in Fig. 1. The lattice parameters reﬁned from the X-ray data using the program FULLPROF  were: a ¼ 6.5324(8) A for YPdSb, a ¼ 6.533(1) A for YPtSb and a ¼ 6.4469(7) A for LuPtSb. These values are very similar to those reported in the literature [5,19,21,22,24]. The magnetic measurements were performed using a Quantum Design SQUID magnetometer in the temperature range 2e400 K and in magnetic ﬁelds up to 7 T. The heat capacity was measured in zero magnetic ﬁeld from room temperature down to 2 K by the thermal relaxation method using a Quantum Design Physical Property Measurement System. The electrical resistivity was studied down to 4.2 K by the conventional four-point DC technique employing a home-made setup. The nuclear magnetic resonance (NMR) measurements were performed between 50 K and 293 K using a Bruker Avance DSX 300 spectrometer operating at a ﬁeld of 7.05 T and temperature controller ITC-503 (Oxford Instruments Co Ltd.). The 121Sb, 123Sb, 175 Lu and 195Pt NMR spectra in YPdSb, YPtSb and LuPtSb were
Fig. 1. Powder X-ray diffraction pattern of annealed YPtSb together with Rietveld ﬁt (thin red line) and difference plot (bottom). Vertical ticks indicate the positions of Bragg reﬂections. (For interpretation of the references to colour in this ﬁgure legend, the reader is referred to the web version of this article.)
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. The line widths, deﬁned as the full width at half maximum (FWHM), are designated as D1/2 .The possibility of quadrupolar broadening was checked by looking for quadrupole echo effects. The Solomon echoes [25,26] produced by a sequence of two pulses ax s by have been observed in YPdSb, YPtSb and LuPtSb for half-integer quadrupolar nuclei of 121Sb with spin I ¼ 5/2 and 123Sb nuclei with spin I ¼ 7/2 but not for 175Lu (I ¼ 7/2). According to IUPAC uniﬁed d scale the 121,123Sb, 175Lu and 195Pt chemical shift (Knight shift) d (K) should be determined with reference to the respective values of X, where X is deﬁned as the ratio of the isotope-speciﬁc frequency to that of 1H in tetramethylsilane (TMS) in the same magnetic ﬁeld [27,28]. This convention is also used here. However, according to the discussion presented in Ref.  and references therein, the 195Pt Knight shifts (in ppm) should be expressed rather as: 195K ¼ 195K (X 195Pt) þ 6300. 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 was found to
Fig. 2. Temperature dependencies of the molar magnetic susceptibility of YPdSb, YPtSb and LuPtSb.
B. Nowak, D. Kaczorowski / Intermetallics 40 (2013) 28e35
be of single exponential form for both platinum and antimony nuclei. Then, the spin-lattice relaxation time T1 can be determined by ﬁtting the data to the three-parameter magnetization recovery function M(t) ¼ M(N)[1 C,exp(t/T1)], where M(t) and M(N) represent, respectively, the signal intensity at time t after saturation and at thermal equilibrium. The quantities T1, M(N) and C z 1 are treated as adjustable parameters.
temperature QD ¼ 275 K. It was also shown in Ref.  that over the entire temperature range studied (1.8e300 K), the speciﬁc heat of YPdSb follows the formula
3. Results and discussion
¼ gT þ bT 3
with the electronic contribution to the speciﬁc heat g ¼ 0.2 mJ/ (mol K2) and the coefﬁcient b ¼ 0.28 mJ/(mol K4) that implies via the relation QD ¼ ð12Rp4 n=5bÞ1=3 (n is the number of atoms per molecule and R is the gas constant) the characteristic Debye
¼ gT þ 9 1 k nR
The magnetic behaviour of YPdSb, YPtSb and LuPtSb is presented in Fig. 2. All three compounds are diamagnetic with the intrinsic molar magnetic susceptibility of the order of 104 emu/ mol (the values measured at 400 K are 5.2 105, 5.6 105, and 7.7 105 emu/mol for YPdSb, YPtSb and LuPtSb, respectively). Some upturns in c(T) observed at low temperatures likely arise from the presence in the samples studied of small amounts of undeﬁned paramagnetic impurities. The result obtained for YPdSb is similar to that reported in Ref. . The heat capacity of YPdSb was communicated in Ref. . In the low temperature region (below 10 K), the experimental C(T) curve was successfully described by a Debye model
3.1. Bulk properties
3 ZT 0
x4 ex ðex 1Þ2
3 2 QE QE 1 ; exp exp T T T
in which the lattice contribution to the speciﬁc heat is represented by both the Debye function (second term) and the Einstein function (third term) weighted by the parameter k that ensures the proper quantity of the oscillator modes involved. The parameters derived from this more advanced approach were: g ¼ 0.3 mJ/(mol K2), QD ¼ 270 K, QE ¼ 110 K, and k ¼ 0.08, in good agreement with the low-temperature analysis, apparently due to almost negligible contribution of the Einstein oscillations to the total speciﬁc heat of YPdSb. Fig. 3(a) displays the experimental C(T) data obtained for YPtSb, evaluated in terms of Eq. (1) (see the inset) and Eq. (2) (note the solid line in the main panel). The Sommerfeld coefﬁcient and the Debye temperature derived from the low-temperature ﬁt are g ¼ 0.1 mJ/(mole K2) and QD ¼ 270 K, respectively. Notably, both values are very similar to those found for YPdSb. The other ﬁt yielded the parameters: g ¼ 0.3 mJ/(mol K2), QD ¼ 282 K, QE ¼ 130 K, and k ¼ 0.05, again very close to those evaluated for the isostructural counterpart YPdSb.
Fig. 3. Temperature dependencies of the speciﬁc heat of (a) YPtSb and (b) LuPtSb. The solid curves represent the least squares ﬁts of Eq. (2) to the experimental data. Insets: the lowtemperature data plotted as C/T vs T2. The solid lines are the ﬁts according to Eq. (1). (c) The low-temperature speciﬁc heat of YPtSb and LuPtSb plotted as C/T3 vs T to emphasize the Einstein contribution.
B. Nowak, D. Kaczorowski / Intermetallics 40 (2013) 28e35
Fig. 4. Temperature dependencies of the electrical resistivity of YPtSb and LuPtSb. The solid curves represents the ﬁts discussed in the text.
The speciﬁc heat data of LuPtSb is presented in Fig. 3(b). Analogous analysis of the experimental data by means of Eq. (1) provided the parameters: g ¼ 0.4 mJ/(mole K2) and QD ¼ 252 K, In turn, the least-squares ﬁt of Eq. (2) resulted in the values: g ¼ 0.7 mJ/(mol K2), QD ¼ 258 K, QE ¼ 117 K, and k ¼ 0.04. Apparently, alike in YPdSb, the Einstein term gives minute contributions to the total speciﬁc heat of YPtSb and LuPtSb. Nevertheless, as displayed Fig. 3(c), for both Pt-bearing phases it brings about a distinct maximum in the C/T3 vs T plot at a temperature Tmax z 20 K that scales fairly well with the Einstein temperatures, derived from Eq. (2), (QE z 5Tmax ). In all three compounds studied the contributions due to electrons are very
small. This ﬁnding hints at semiconducting character of the electronic transport in these materials. The temperature dependencies of the electrical resistivity of YPtSb and LuPtSb are shown in Fig. 4. Both compounds exhibit nonmetallic (semimetallic or semiconducting) behaviour. At room temperature, the resistivity of the Y-based material amounts to about 1.88 mU cm, while that of LuPtSb it is about 1.46 mU cm. With decreasing temperature, r(T) of the latter compound shows a monotonic rise up to 1.93 mU cm at 5 K, with a nearly linear increase down to about 70 K and some ﬂattening at lower temperatures. In the case of YPtSb, the resistivity achieved at the lowest temperature studied is 2.06 mU cm, however the overall variation in r(T) is less distinct and is made up of a very broad hump around 80 K. In general, the electrical conductivity in both compounds, both as regards its magnitude and the temperature dependencies, is similar to that reported for YPdSb . Therefore, by analogy to the latter phase, it seems justiﬁed to presume that r(T) of YPtSb and LuPtSb is governed by an interplay of semiconductor-like thermal activation of charge carriers over a small energy gap Eg and variable range hopping processes, quantiﬁed by the Mott temperature TM that is related to localization energy of the carriers. As a result, the two-channel electrical conductivity should vary as 
1=4 Eg 1 T þ shop exp M ¼ sact exp rðTÞ 2kB T T (3)
Fitting Eq. (3) to the experimental data of YPtSb yielded a fairly reasonable description over the entire range studied (the broad hump in r(T) could not be accounted for within this simple model). The so-derived parameters are: sact ¼ 3.7 104 (mU cm)1, shop ¼ 4.9 104 (mU cm)1, Eg ¼ 110 meV, and TM ¼ 0.3 K. Similar
Fig. 5. Multiple quadrupolar echoes of 121Sb (I ¼ 5/2) in YPdSb, YPtSb and LuPtSb recorded at spectrometer frequency of 71.887 MHz (B0 ¼ 7.05 T) and T ¼ 293 K. The excitation consists of two 2.5 ms pulses. The second pulse is RF phase-shifted by p/2. The nRF z 100 kHz .The remnants of the free-induction decay after the excitation pulses produce the asymmetry. The two radio-frequency pulses are separated by interpulse delay s ¼ 100 ms in (a), s ¼ 50 ms in (b) and s ¼ 40 ms in (c). Number of scans NS ¼ 4000. The allowed echoes are observed at times t ¼ 3s/2, 2s and 3s. Weak signals at t ¼ 5s/2 and t ¼ 4s present in (a) and (b) coincide with predicted position of forbidden echoes.
B. Nowak, D. Kaczorowski / Intermetallics 40 (2013) 28e35
analysis of the experimental data of LuPtSb gave the parameters: sact ¼ 6.2 104 (mUcm)1, shop ¼ 5.3 104 (mUcm)1, Eg ¼ 71 meV, and TM ¼ 1.1 K. These results are comparable to those obtained before for YPdSb : sact ¼ 5.3 105 (mUcm)1, shop ¼ 1.75 104 (mUcm)1, Eg ¼ 250 meV, and TM ¼ 0.6 K. The Mott temperatures are similar to the values determined for halfHeusler compounds TbNiSb and HoNiSb , while the energy gaps derived for YPdSb and YPtSb are close to those reported in Ref.  (270 meV and 160 meV, respectively). 3.2. NMR results 3.2.1. NMR spectra and sample quality In half-Heusler phases with perfect structural order, the electric ﬁeld gradient (EFG) at each atom site is equal to zero due to the tetrahedral symmetry, and thus no quadrupolar effects are expected in NMR signal of any nuclei. However, as can be inferred from Fig. 5 and Fig. 6, in the case of YPdSb, YPtSb and LuPtSb well resolved quadrupolar (Solomon) echoes could be excited for both 121 Sb and 123Sb isotopes. It must be stressed that well resolved Solomon echoes can only be generated for quadrupolar nuclei occupying the sites with nominally tetrahedral or cubic local symmetries and exhibiting small electric ﬁeld gradients. This implies very weak disorder; its type cannot be elucidated from the NMR data only. The Solomon echo pulse sequence includes two RF pulses separated by a time delay s and is applied to powder samples to generate the spectrum due to satellite transitions which are usually lost in dead-time of the receiver during one pulse experiment. Contrary to the Hahn echoes , for Solomon echoes s must be much shorter than FID of the central transition, on which are superimposed the echoes. Multiple Solomon echoes arise from refocusing of off-resonance single quantum (1Q) and multiple quantum (MQ) coherences generated by the ﬁrst pulse. The occurrence of quadrupolar Solomon echoes in the measured
Fig. 7. Quadrupolar echo of 175Lu (I ¼ 7/2) in LuPtSb recorded at spectrometer frequency of 34.011 MHz (B0 ¼ 7.05 T) and T ¼ 293 K. The excitation consists of two 2 ms pulses. The second pulse is RF phase-shifted by p/2. Number of scans NS ¼ 8000.
samples of YPdSb, YPtSb and LuPtSb (EFGs0) indicates some deviation from the perfect tetrahedral symmetry, although our experimental X-ray diffraction patterns for LuPtSb and YPtSb are in excellent agreement with the theoretical ones, calculated assuming full atomic ordering (see Fig. 1). It should be recalled, however, that small level of disorder in nominally ordered compound is usually hardly detectable by standard X-ray diffraction methods . Our results, even not supported by metallographic and microprobe analyses, are reliable and conclusive. The X-ray data show that the compounds are cubic but deviation is likely associated with defects possibly similar to that reported for scandium based half-Heusler antimonides ScTSb (T ¼ Ni, Pd) , where the vacancies in the lattice of T-atoms were observed. The non-intentional magnetic impurities found in our magnetic studies and anti-site effects can
Fig. 6. Multiple quadrupolar echoes of 123Sb (I ¼ 7/2) in YPdSb, YPtSb and LuPtSb recorded at spectrometer frequency of 38.925 MHz (B0 ¼ 7.05 T) and T ¼ 293 K. The excitation consists of two 3.1 ms pulses. The second pulse is RF phase-shifted by p/2. The nRF z 80 kHz. The two radio-frequency pulses are separated by an interpulse delay s ¼ 150 ms in (a), s ¼ 100 ms in (b) and s ¼ 40 ms in (c). Number of scans NS ¼ 4000. The allowed echoes are observed at times t ¼ 4s/3, 3s/2, 5s/3, 2s, 5s/2, 3s and 4s.
B. Nowak, D. Kaczorowski / Intermetallics 40 (2013) 28e35
Fig. 8. The 195Pt NMR spectra in YPtSb and LuPtSb. Zero on the frequency scale corresponds to the zero Knight shift value of 195Pt nuclei determined with reference to X 195 Pt ¼ 0.21496784 [26,27].
also be probable sources of EFG. However, their identiﬁcation needs independent experimental techniques. Generally, the echo amplitudes depend on the two pulse durations and the vQ/nRF ratio. The larger the vQ/nRF ratio, the weaker the echo amplitudes. Here, nQ ¼ 3e2qQ/2I(2I 1)h is so-called quadrupole frequency. For the data presented on Fig. 6 the amplitude of the RF pulses, vRF ¼ 80.6 kHz, and associated p/2 pulse duration was equal to 3.1 ms. Essentially the same picture (not shown) was obtained for vRF ¼ 23.8 kHz, (p/2 ¼ 10.5 ms) thus suggesting that in both cases vQ << nRF applied. The observation presented herein strongly indicates that in our samples any chemical or structural imperfections must be very small, and the associated quadrupolar interactions at the Sb site are very weak. Fortunately, both the homo- and hetero-dipolar interactions are also weak. Of course, any quantitative analysis of the EFG at the Sb site is strongly sample dependent. We estimate the nQ values in our samples are of the order of few kHz. In Fig. 7 the quadrupolar echo of 175Lu nuclei (I ¼ 7/2) in LuPtSb is shown. Here, no Solomon echoes are observed, probably because of severe shortening of the spinespin relaxation time T2 and equivalent line broadening. The measured signal agrees qualitatively with the spectrum obtained for LuPtSb by frequency sweeping at constant ﬁeld of 5.5 T . Even for relatively weak EFG at the Lu site the quadrupole coupling constant CQ ¼ e2Qqzz/h (qzz stands for the component of the EFG tensor along the principal z-axis) and quadrupole frequency vQ of 175Lu nuclei are not small due to considerably large value of the quadrupole moment 175 Q ¼ 349 fm2 [27,35]. We note, however, that well resolved Solomon echoes of 175Lu nuclei can be observed, e.g., for cubic com_ private communication). pounds LuB12 and LuAs (O.J.Zoga1, Usually, in a one pulse experiment the line widths of 121Sb, 123 Sb,175Lu and 195Pt nuclei in cubic, non-magnetic intermetallics come mainly from the dipolar homonuclear interaction 121Sb-121Sb and heteronuclear interactions 123Sbe121Sb, 175Lue121Sb and 195Pte 121 Sb, respectively. However, in YPdSb, YPtSb and LuPtSb no agreement is observed between the calculated (dipolar only) and experimental line-widths, taken with single pulse sequence for 195 Pt as well as 121Sb, 123Sb or 175Lu nuclei. This ﬁnding implies the presence of structural disorder and/or other mechanisms of interactions. The single-pulse and Fourier transform of the p/2-s-p/2 or p/2-s-p spin echoes in LuPtSb reveal at room temperature very similar line shapes of the 195Pt NMR with line width 195D1/ 195 Pt nuclei measured directly 2 ¼ 19.0(7) kHz. The chemical shift of
with respect to X 195Pt is equal to 3875(10) ppm. The line shapes are, however, slightly asymmetric. In the case of YPtSb the linewidth of the 195Pt NMR signal is of the order of 15.5(5) kHz at room temperature and slightly increases with decreasing temperature, while the chemical shift of 195Pt nuclei is temperature independent and equal to about 3825(10) ppm. The 195Pt NMR spectra in YPtSb and LuPtSb (see Fig. 8) are about one order of magnitude larger than the calculated dipolar one and cannot be explained solely by structural disorder, since for 195Pt(I ¼ ½ and Q ¼ 0) the spectra are unaffected by EFG. Possible structural disorder and distribution of chemical shifts in a powdered nonmagnetic sample can broaden the line-width only slightly . Thus, pseudodipolar and/or scalar interactions 195Pte121,123Sb and 121,123 Sbe195Pt must be taken into consideration. Similar effects were observed in 195Pte119Sn and 119Sne195Pt magic-angle-spin (MAS) NMR performed for half-Heusler compounds TiPtSn and ZrPtSn . At T ¼ 293 K, the line-width in YPtSb equals to 5.3 kHz and 2.8 kHz for 121Sb and 123Sb NMR resonance, respectively. Both values are much larger than the dipolar ones but are in good agreement with the expected relation 121D1/2/123D1/2 f J (121Sbe 195 Pt)/J(123Sbe195Pt) f (121g/123g) ¼ 1.847 (J is a spin coupling constant describing scalar interaction), valid when dipolar and pseudodipolar interactions are weak and quadrupolar broadening can be neglected. Veriﬁcation of this hypothesis requires detailed MAS experiments, especially that any structural disorder in nominally cubic materials broadens the resonance of antimony and lutetium nuclei over pure dipolar value mainly by the quadrupolar interaction. The resonance of 175Lu nuclei is very sensitive in this respect, since the 175Lu nuclei have extremely large quadrupole moment 175Q ¼ 349 fm2 compared with 121Q ¼ 36 fm2 and 123 Q ¼ 49 fm2 [27,35]. Interestingly, at room temperature our static 121 Sb line-widths in YPdSb (3.4 kHz) and YPtSb (5.3 kHz) are only about 1.2 kHz larger than the respective 121Sb MAS line-widths in ScPdSb and ScPtSb . However, for the latter compound the 121Sb MAS NMR experiment did not reveal any scalar interaction 121Sbe 195 Pt and the compound was characterized as a metal , in contrast to the semimetallic/semiconducting behaviour of YPdSb, YPtSb and LuPtSb. Table 1 presents a collection of the 121Sb chemical shifts determined for a few half-Heusler antimonides. The values of diso systematically decrease on going from Sc to Y to Lu. The line-width of 121 Sb in YPtSb changes from 5.3 to 9.5 kHz with decreasing temperature from T ¼ 292 K to T ¼ 50 K, and simultaneously the chemical shift increases slightly from 885 ppm to 977 ppm. It is also worth mentioning that the line-widths of 121Sb, 175Lu and 195Pt in LuPtSb were found weakly temperature dependent, while no such dependency was reported in the literature . 3.2.2. Spin-lattice relaxation rate The recovery curves of the nuclear magnetisation obtained for 121 Sb, 123Sb and 195Pt nuclei in YPtSb at T ¼ 293 K are shown in Fig. 9. They are single exponential and intercept the ordinate axis at [M(N) M(t)]/M(N) close to 1, what indicates near perfect saturation of nuclear spins system. As expected, the quadrupolar 121Sb and 123Sb nuclei relax faster than 195Pt nuclei. Generally, the spinTable 1 121 Sb chemical shifts at T ¼ 293 K. Compound
diso [ppm] a
Taken from Ref. .
B. Nowak, D. Kaczorowski / Intermetallics 40 (2013) 28e35
quadrupolar mechanism of the spin-lattice relaxation in both compounds. It is known  that
io n h 2 e2 qQ =h : ðR1 ÞQ f ð2I þ 3Þ= I 2 2I 1
Fig. 9. The recovery curves of nuclear magnetisation obtained for 121Sb, 123Sb and 195Pt nuclei in YPtSb at T ¼ 293 K.
lattice relaxation rate of antimony nuclei is expected to be the sum of three independent contributions:
1=T1 hR1 ¼ ðR1 Þdip þ ðR1 Þimp þ ðR1 ÞQ
where (R1)dip results from nuclear dipolar coupling, (R1)imp results from the dipolar coupling to the electronic magnetic dipole moment of the magnetic impurity ions, and (R1)Q results from interaction of quadrupole moment (Q) of 121Sb or 123Sb nucleus with the crystalline electric ﬁeld gradient (q) at its site. The ﬁrst two terms in Eq. (4) represent magnetic interactions (R1)M. Therefore, each such a term is proportional to square of the nuclear magnetogyric ratio of the respective nucleus.
ðR1 ÞM fg2
At 293 K, the measurements gave T1(121Sb) ¼ 101(2) ms and T1( Sb) ¼ 125(2) ms in YPdSb and T1(121Sb) ¼ 96(2) ms and T1(123Sb) ¼ 123(5) ms in YPtSb. If the observed rates 121(R1) and 123 (R1) were due entirely to magnetic processes they would be in a ratio of (121g/123g)2 ¼ 3.41. Instead, the observed ratio is 1.24(7) for YPdSb and 1.28(7) for YPtSb, hence strongly indicating a dominant 123
Then, the ratio hQ ¼ 121(R1)Q/123(R1)Q will be proportional to the ratio of the squares of the quadrupole moments multiplied by the appropriate ratio of spin factors. The calculated value hQ ¼ 1.27 is in very good agreement with the experimental values. It is based on the nuclear moments 121Q ¼ 36 fm2 and 123Q ¼ 49 fm2, reported in IUPAC documents [27,35] and differs considerably from hQ ¼ 1.447 used in old works on NMR of antimony [39,40]. The magnetic relaxation is mainly due to spin diffusion to paramagnetic impurities and is expected to be important at low temperatures. The occurrence of quadrupolar echoes mentioned above is the ﬁngerprint of the deviation from perfect cubic symmetry of the structure and presence of some static EFG in the studied half-Heusler phases. Moreover, even in crystals with cubic symmetry, quadrupole relaxation process may be effective by way of the lattice vibrations. They might cause the electric ﬁeld at the position of the nucleus to ﬂuctuate from cubical symmetry leading to effective electric quadrupole interaction. Thus, the quadrupolar relaxation could originate from both static EFG and lattice degrees of freedom through nuclear quadrupole-phonon couplings [41,42]. For 121Sb nuclei in YPtSb, the measurements of the spin-lattice relaxation time T1 were made between 50 and 292 K at a magnetic ﬁeld of 7.05 T. In that temperature range, the recovery function was single exponential, hQ z 1.27, and the temperature dependence was found to be of the form 121(R1) f T2 (see Fig. 10). These characteristics indicate that 121(R1) is entirely quadrupolar [121(R1) ¼ 121(R1)Q] and is due to the dominant ﬁrst-order Raman process (1R process) and/or an “anharmonic” Raman process (aR process) as derived theoretically in Ref. [41,42], based on the Debye model for the lattice vibrations. For this mechanism, the T-dependence of the relaxation rate may be calculated as [39,41,42]
R1 T fT*2 E* T*
with T* ¼ T/QD, where QD is the Debye temperature. E*(T*) is a numerical function connecting the high temperature region (T* > 1) in which R1 f T2 to the low temperature region (T* < 0.02) in which R1 f T7. For the NaCl-type crystals, E*(T*) could be expressed as E*(T*) ¼ 1 b/T*2 for T* > 0.5 [41,42]. Interestingly, also in the case of 121Sb in YPtSb, the E(T) is proportional to 1/T2 with a positive constant b in the temperature range studied. This ﬁnding is fully consistent with the magnitude of QD determined for YPtSb from the speciﬁc heat data. 4. Conclusions
Fig. 10. Temperature dependencies of the nuclear spin-lattice relaxation rate 121(R1) in YPtSb. The solid line is the least-square ﬁt to 121(R1) ¼ aT2 b described in the text.
In the present study, the half Heusler phases YPdSb, YPtSb and LuPtSb were found to be diamagnetic small-band gap semiconductors. The energy gaps derived within the two-channel electrical conductivity model compare favourably well with the band structure calculations presented in Ref.  and the experimental value reported for YPtSb in Ref. . However, the ﬁnding of ﬁnite gaps in all three compounds differs from the scenario of gapless conductivity postulated in Refs. [20e22]. This disagreement may originate from dissimilar level of structural disorder and/or impurity content in the samples examined in the independent investigations. Band structure calculations show that the size of the band gap decreases with increasing amount of atomic disorder, and eventually closes completely as shown for TiNiSn in Fig. 12 of Ref. . In the current case, the observation of Solomon echoes of halfinteger quadrupolar nuclei 121Sb with spin I ¼ 5/2 and 123Sb with
B. Nowak, D. Kaczorowski / Intermetallics 40 (2013) 28e35
spin I ¼ 7/2 clearly indicated the presence of some static EFG and weak deviation from perfect tetrahedral symmetry in the samples investigated. Further comprehensive investigations of the YPdSb, YPtSb and LuPtSb phases are indispensable to clarify the source of the observed discrepancies in the experimental ﬁndings communicated in the literature by different research groups. For YPdSb and YPtSb, respectively, the isotope ratio of the spinlattice relaxation rates 121(R1)/123(R1) ¼ 1.24(7) and 1.28(7), and temperature dependence of the relaxation in YPtSb of the form 121 (R1) f T2 indicate that 121(R1) is entirely quadrupolar in the origin and is due to the dominant two-phonon Raman process based on the Debye model for the lattice vibrations. The line width of 195Pt NMR in YPtSb and LuPtSb is about one order of magnitude larger than calculated dipolar one and suggests a presence of pseudodipolar and/or scalar interactions 195Pte121,123Sb which are unresolved in the static NMR. Acknowledgement This work was supported by the National Science Centre (Poland) under research grant 2011/01/B/ST3/04466. References  Casper F, Graf T, Chadov S, Balke B, Felser C. Semicond Sci Technol 2012;27: 063001.  Graf T, Parkin SSP, Felser C. Prog Solid State Chem 2011;39:1.  Kaczorowski D, Gofryk K, Plackowski T, Leithe-Jasper A, Grin Yu. J Magn Magn Mater 2005;290e291:573.  Gofryk K, Kaczorowski D, Plackowski T, Leithe-Jasper A, Grin Yu. Phys Rev B 2005;72:094409.  Gofryk K, Kaczorowski D, Plackowski T, Mucha J, Leithe-Jasper A, Schnelle W, et al. Phys Rev B 2007;75:224426.  Gofryk K, Kaczorowski D, Plackowski T, Leithe-Jasper A, Grin Yu. Phys Rev B 2011;84:035208.  Canﬁeld PC, Thompson JD, Beyermann WP, Lacerda A, Hundley MF, Peterson E, et al. J Appl Phys 1991;70:5800.  Hundley MF, Thompson JD, Canﬁeld PC, Fisk Z. Phys Rev B 1997;56:8098.  Jung MH, Yoshino T, Kawasaki S, Pietrus T, Bando Y, Suemitsu T, et al. J Appl Phys 2001;89:7631.  Goll G, Marz M, Hamann A, Tomanic T, Grube K, Yoshino T, et al. Physica B 2008;403:1065.
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