Effects of Cd vacancies and unconventional spin dynamics in the Dirac semimetalCd3As2Dimitrios Koumoulis, Robert E. Taylor, Jeffrey McCormick, Yavuz N. Ertas, Lei Pan, Xiaoyu Che, Kang L.Wang, and Louis-S. Bouchard

Citation: The Journal of Chemical Physics 147, 084706 (2017); doi: 10.1063/1.4999467View online: http://dx.doi.org/10.1063/1.4999467View Table of Contents: http://aip.scitation.org/toc/jcp/147/8Published by the American Institute of Physics

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THE JOURNAL OF CHEMICAL PHYSICS 147, 084706 (2017)

Effects of Cd vacancies and unconventional spin dynamicsin the Dirac semimetal Cd3As2

Dimitrios Koumoulis,1,a),b) Robert E. Taylor,1 Jeffrey McCormick,1 Yavuz N. Ertas,2 Lei Pan,3Xiaoyu Che,3 Kang L. Wang,3 and Louis-S. Bouchard1,4,b)1Department of Chemistry and Biochemistry, University of California, Los Angeles, 607 Charles E. Young DriveEast, Los Angeles, California 90095, USA2Department of Bioengineering, University of California, Los Angeles, 420 Westwood Plaza, Los Angeles,California 90095, USA3Department of Electrical Engineering, University of California, Los Angeles, California 90095, USA4California NanoSystems Institute, University of California, Los Angeles, 570 Westwood Plaza, Los Angeles,California 90095, USA

(Received 2 May 2017; accepted 19 July 2017; published online 28 August 2017)

Cd3As2 is a Dirac semimetal that is a 3D analog of graphene. We investigated the local structure andnuclear-spin dynamics in Cd3As2 via 113Cd NMR. The wideline spectrum of the static sample at 295 Kis asymmetric and its features are well described by a two-site model with the shielding parametersextracted via Herzfeld-Berger analysis of the magic-angle spinning spectrum. Surprisingly, the 113Cdspin-lattice relaxation time (T1) is extremely long (T1 = 95 s at 295 K), in stark contrast to conductorsand the effects of native defects upon semiconductors; but it is similar to that of 13C in graphene (T1= 110 s). The temperature dependence of 1/T1 revealed a complex bipartite mechanism that includeda T2 power-law behavior below 330 K and a thermally activated process above 330 K. In the high-temperature regime, the Arrhenius behavior is consistent with a field-dependent Cd atomic hoppingrelaxation process. At low temperatures, a T2 behavior consistent with a spin-1/2 Raman-like processprovides evidence of a time-dependent spin-rotation magnetic field caused by angular oscillationsof internuclear vectors due to lattice vibrations. The observed mechanism does not conform to theconventional two-band model of semimetals, but is instead closer to a mechanism observed in high-Zelement ionic solids with large magnetorotation constant [A. J. Vega et al., Phys. Rev. B 74, 214420(2006)]. Published by AIP Publishing. [http://dx.doi.org/10.1063/1.4999467]

I. INTRODUCTION

Cadmium arsenide (Cd3As2) is a AII3 BV2 chemically sta-

ble n-type semiconductor with high carrier mobility, whichmakes it a candidate for device applications.1–8 Cd3As2was predicted theoretically by Wang et al.2 to be a Diracsemimetal (DSM). It has an inverted band symmetry mainlydue to a strong spin-orbit coupling (SOC). Its 3D Diraccones were recently observed experimentally.3 Two dimen-sional (2D) or three dimensional (3D) Dirac semimetalsinclude graphene and the 2D surface states of 3D topolog-ical insulators (TI) with the Fermi level at the Dirac pointinside the bulk band gap (Cd3As2, Na3Bi etc.).4 Unconven-tional phenomena and physical properties including exoticelectrical and thermal conductivity, high-temperature linearquantum magnetoresistance, and oscillating quantum spinHall effects have been detected by angle resolved pho-toemission spectroscopy (ARPES) and magneto-transporttechniques.2–11

a)Present address: School of Physical Science and Technology, ShanghaiTechUniversity, Pudong, Shanghai 201210, China.

b)Authors to whom correspondence should be addressed: louis.bouchard@gmail.com and dkoumoulis@shanghaitech.edu.cn

Here, we have performed 113Cd NMR measurements onCd3As2. Due to its ability to probe structural and band struc-ture characteristics at specific atomic sites, nuclear magneticresonance (NMR) spectroscopy can provide information thatis hidden to other techniques (transport, ARPES etc.). In thisstudy, NMR data in Cd3As2, accompanied by calorimetricand X-ray diffraction studies, are analyzed as functions oftemperature and magnetic field to shed light on the struc-tural and electronic characteristics at a local level. A siteinequivalence between the Cd atoms within the lattice wasdetermined by static and magic angle spinning (MAS) spec-tral analysis. A two-site model with the shielding parametersextracted from the Herzfeld-Berger analysis of the MAS spec-trum describes the observed spectra. Interestingly, a bipartitespin-lattice relaxation mechanism was found to describe theentire relaxation process across the temperature (T ) range. Thepower-law (T2) dependence that occurs at the low-T regime isconsistent with a nuclear spin-rotation relaxation mechanism,strongly effective in heavy Z-elements followed by a Cd hop-ping mechanism in the high-T regime, due to the large numberof Cd vacancies that permit migration of Cd atoms within thelattice. The aforementioned complex relaxation process as afunction of temperature and magnetic field bears resemblanceto both the spin dynamics of ionic solids and graphene but isdissimilar to the one expected for conventional semimetals.41

0021-9606/2017/147(8)/084706/6/$30.00 147, 084706-1 Published by AIP Publishing.

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084706-2 Koumoulis et al. J. Chem. Phys. 147, 084706 (2017)

II. EXPERIMENTAL

The crystal structure of Cd3As2 was characterized atambient temperature from powder samples using an X-raydiffractometer (XRD, Bruker D8 Discover powder X-raydiffractometer). Crystal structure analysis was performedusing Θ–2Θ scans, where the shape and width of the XRDspectra peaks were determined with the Rietveld refinementtechnique. Figure 1(a) shows the XRD patterns for the bareand annealed samples, which both reveal a polycrystallinesample. A diffraction peak analysis reveals the presence oftetragonal Cd3As2 (JCPDS: 21-0107) for both samples. TheRietveld refinement on the XRD pattern yields lattice constantsof a = 12.6515 Å and c = 25.4432 Å. A second, hexagonal-close packed (hcp), Cd2 phase (JCPDS: 00-8491) was alsoobserved for both samples. The samples had hcp Cd2 peaksfor 2Θ = 31.78 and 38.45, which correspond to (002) and(011) crystal directions. Cd3As2 shows a tetragonal unit cellwith the Cd atoms occupying tetrahedrally coordinated sitesand As having cubic coordination. The crystal structure ofCd3As2 has been reexamined in consideration of the topo-logical properties predicted for three-dimensional crystals.12

The authors describe the crystal structure in terms of that ofCaF2, showing that the Cd is distributed in the cube-shapedarray occupied by F in CaF2, while the As is in the FCCpositions occupied by Ca.12 The crystal structure of Cd3As2can be described relative to an anti-fluorite structure pos-sessing 25% Cd site vacancy. The ordering or disorderingof the vacancies affects the space group to which the crystalbelongs.12

Differential scanning calorimetry measurements onCd3As2 were performed using a PerkinElmer DSC 8000scanner across the temperature range T = 303–523 K at arate of 5 °C/min during upwards and downwards ramping.Figure 1(b) presents a series of small features from 334 to355 K, including a sharp peak at 353 K (lower curve). Thesefeatures are not observed upon temperature ramp-down (uppercurve). This suggests that the sample undergoes an irreversiblesolid phase transition in this temperature regime. Around225 °C (498 K) the system undergoes a phase transitionfrom a primitive centrosymmetric tetragonal cell (space groupP42/nmc) to a body centered tetragonal non-centrosymmetricunit cell (space group I41cd).8,13,14 Our temperature rangeof interest is below 400 K. The aforementioned structuralphase transition is not probed by our NMR experiments.Additionally, a comprehensive chemical composition analysiswas performed via scanning electron microscopy and energydispersive X-ray spectroscopy (SEM-EDS) in our sample[Fig. 1(c)]. The elemental mapping of the sample was per-formed using ZEISS Supra 40VP SEM at 25 kV. The Kα bandsfor Cd and As were outside the detectable range of the energyspectrum, where Lα bands were sufficient for detection andanalysis. Cd and As peaks are clearly seen in the EDS spectrawith weight percentages of 63% and 37%, respectively. Theremaining small peaks that are mainly O (ambient oxygen)were not labeled for the sake of simplicity and purpose of thiswork. The percentage error in determining the weight contentwas less than 1%. These elemental mapping results indicatethat the sample is composed of Cd and As. Lastly, our Cd3As2sample is an n-type material. The carrier type of our sample

FIG. 1. The X-ray diffraction patternsfor the bare (red) and annealed (black)Cd3As2, which both reveal a polycrys-talline nature (a) Differential scanningcalorimetry measurements on Cd3As2,measuring from 303 to 523 K at5 °C/min during temperature ramp-ing upwards and downwards (b) andthe Hall coefficient measurement at300 K in a magnetic field of ±3 T(inset). Chemical composition analysisvia Scanning Electron Microscopy andEnergy Dispersive X-ray spectroscopy(c).

084706-3 Koumoulis et al. J. Chem. Phys. 147, 084706 (2017)

was checked by a Hall coefficient measurement in a magneticfield of ±3 T at room temperature (Fig. 1, inset).

The 113Cd NMR data were acquired on a Bruker AV-600spectrometer using both MAS and wideline techniques at afrequency of 133.20 MHz. Additional 113Cd MAS and wide-line data were acquired on a Bruker DSX-300 spectrometerat 66.61 MHz. The 113Cd chemical shift scale was calibratedusing the unified Ξ scale,15 relative to the 113Cd resonance ofan aqueous solution of cadmium nitrate tetrahydrate. In par-ticular, we have measured 113Cd NMR spectra and spin-latticerelaxation rates (1/T1) vs T.

III. RESULTS AND DISCUSSION

The ambient-temperature 113Cd MAS spectrum ofCd3As2 spinning at 10 kHz is shown in Fig. 2. The spectrumconsists of two isotropic peaks at �107 ppm and �356 ppm.The remaining peaks are spinning sidebands. A two-siteHerzfeld-Berger16 model describes the spectral features. Theshielding parameters of the model for the two sites extractedfrom the data are given in Table I. There are six differentCd sites in the structure12 with the “low temperature (LT)centrosymmetic I41/acd structure,” which corresponds to thetemperature range for our NMR studies, having three uniqueCd atoms.12 Our MAS results resolve two main groups ofresonance in a 2:1 ratio (4:2 site configuration). This sug-gests that two of the sites have virtually identical bondingenvironments.

It is interesting to note that the anisotropic shieldingparameters obtained from the two-site model with the shieldingparameters extracted from the Herzfeld-Berger16 analysis ofthe MAS spectrum reproduce the major features of the 113Cdwideline spectrum of the static sample at 295 K, as shownin Fig. 3. The only spectral feature not reproduced is somespectral intensity around �238 ppm. This discrepancy in spec-tral intensity likely arises from the issue of exchange betweenthe two sites. The explanation for the missing intensity ofthis peak in the simulation arises from the 113Cd exchangebetween the two sites, which yields a new resonance at the

FIG. 2. 113Cd MAS spectrum at 295 K. The experimental spectrum is in bluewith a two-site simulation along with the summation (shown by the red dottedcurve).

TABLE I. 113Cd shielding tensor parameters of Cd3As2.

Experiment δ11 δ22 δ33 δiso ζcsaa ηb Ωc κd

Site 1 +110 �116 �325 �105 �220 0.97 437 +0.0310 kHzMASe,f

Site 2 �208 �412 �480 �355 +159 0.43 272 −0.510 kHzMASe,f

aζcsa = δ33 � δiso.bη = (δ22 � δ11)/ζcsa.cΩ = |δ33 � δ11 |.dκ = 3(δ22 � δiso)/Ω.eChemical shifts referenced to neat dimethylcadmium by use of 0.5M Cd(NO3)2 in H2Oas a secondary reference assigned as �49 ppm.17fEstimated uncertainties in the principal components of the shielding tensor as measuredby MAS are ±15 ppm.

average of the two isotropic shifts (ca. �238 ppm) in the man-ner of a classic two-site exchange problem.18 It should benoted that any additional resonance around �238 ppm in theMAS spectrum in Fig. 2 is obscured by the MAS spinningsidebands due to the residual width of the spinning sidebandresonances, the proximity of the two isotropic resonances, andtheir respective anisotropies. Varying the spinning speed didnot readily reveal the existence of such a peak. The presenceof such an additional resonance may be responsible for someof the uncertainty in the extracted shielding parameters fromthe MAS experiments. Rather than characterizing the dynam-ics of the exchange through spectral simulation, the natureof this exchange mechanism was analyzed with the nuclearspin-lattice relaxation data (vide infra).

All the resonances were temperature independent (220–380 K). Interestingly, the 113Cd NMR results for the Diracsemimetal Cd3As2 stand in clear contrast to those usuallyfound for conductors (metals) and also for nominally puresemiconductors in which native defects can produce signifi-cant charge carrier concentrations. This holds for both spectralshifts and spin-lattice relaxation behavior. For example, the113Cd shifts in Cd3As2 are over 4000 ppm away from the

FIG. 3. 113Cd wideline spectrum at 295 K. The experimental spectrum is inblue. The simulated spectrum (red curve) consists of a two-site model. Theshielding parameters are listed in Table I.

084706-4 Koumoulis et al. J. Chem. Phys. 147, 084706 (2017)

reported Knight shift of Cd metal,19 given as 4324 ppm rela-tive to an aqueous solution of cadmium nitrate.17 The observed113Cd shift is in the range of diamagnetic materials. Thedifferences in relaxation behavior are described below.

NMR relaxation measurements interrogate timescalesassociated with certain phonon or electron modes as well as arange of thermally activated processes. The 113Cd spin-latticerelaxation times (T1) at different temperatures were measuredin saturation-recovery experiments. The recovery curves werefitted by a single exponential function, M0−M(t)M0 = exp(−

tT1

),where M(t) represents the nuclear magnetization and M0 is itsvalue at thermal equilibrium. The extracted T1 was extremelylong, T1 = 95 s, at ambient temperature (295 K). The 113Cdspin-lattice relaxation rate for cadmium arsenide was also mea-sured under MAS at ambient temperature. The two isotropicresonances under MAS at a spinning rate of 10 kHz werefound to have the same 113Cd T1 value of 46 ± 2 s withinexperimental error at 295 K, in accordance with the obser-vation of a single exponential saturation-recovery behaviorfrom the static sample. Interestingly, these T1 values are notdescriptive of a metal or a semimetal.20 However, similarlylong T1 times have been measured for graphene (110 s).21

Hence, in addition to the aforementioned observed 113Cd shift,another remarkable difference with regard to the expectedsemimetallic nature is the very long spin-lattice relaxationtimes.

Band structure calculations of Cd3As2 have determinedthat the electronic properties are mostly determined by theCd-5s states (conduction band) and the As-4p states (valenceband).2 From an NMR point of view, the interaction of s-statecharge carriers in conductors and semiconductors results in aT1 on the order of milliseconds or tens of milliseconds. Asa specific example, the 207Pb spin-lattice relaxation time inPbTe is 12 ms.20 Therefore, based on the conventional Fermiliquid picture, the three orders of magnitude longer 113Cd T1that was found here suggests little interaction with the chargecarriers in spite of Cd3As2 being a semimetal. Moreover, thestatic sample has a T1 of 59 s at 294 K at 7 T (and 95 s measuredat 14 T). In short, the T1 was also found to be magnetic-fielddependent. At this point, it is worth making a further compar-ison between the narrow-gap semiconductors like PbTe20 orPbSe22 and Cd3As2. In PbTe or PbSe, the native defects yieldconduction electrons that shift the 207Pb resonance from that ofan insulator around 0 ppm to that of a semiconductor (mainlyarising from native defects) with a resonance shift of around1000 ppm, to finally obtain a Knight shift of metallic Pb at1.47%.20,22 In our case (113Cd, Cd3As2), even with the high(25%) vacancy of Cd sites within the lattice (although these arenot the native defects that give rise to conduction charge carri-ers), there is no indication of any nuclear shift resulting frominteraction with the electrons at the Fermi surface. Nor is thereany significant reduction in the relaxation rate, as was observedwith Pb(Se,Te),20,22 whose shift and number of carriers varydue to electronic inhomogeneity. Yet, the origin of the asym-metric resonances for Pb(Se,Te)20,22 that were not narrowedunder MAS due to the electronic inhomogeneity clearly dif-fers from the asymmetic line in the static sample of 113Cd ofCd3As2, which is easily narrowed by MAS, since it mainlyresults from shielding anisotropy effects.

FIG. 4. The nuclear spin-lattice relaxation rate (1/T1) in Cd3As2 as a functionof temperature. The low-T data are consistent with a spin-1/2 Raman mecha-nism (A ·T2) via nuclear spin-rotation interaction (upper left inset). Above 330K, the data follow a thermally activated mechanism [B · exp(− EkT )] with anenergy scale (0.17 eV) associated with the cadmium-hopping process (lowerright inset).

A plot of 113Cd 1/T1 vs T is shown in Fig. 4. The tempera-ture dependence of 1/T1 of Cd3As2 in the low-T range followsa power-law,22 1T1 = A · T

2 (as a red straight line in Fig. 4),

where A = (1.18 ± 0.05) × 10�7 s�1 K�2. This is evidencethat low energy spin excitations at the 113Cd NMR frequencyare governed mainly by non-s character conduction electrons,counter to what is expected in conventional metals (Korringalaw) and semi-metallic (two-band model) materials.23,41 Pre-viously, NMR studies from Young et al.,24 Koumoulis et al.,25

and Kölbl et al.26 have also observed a power-law behavior of1/T1T vs T in bulk topological insulators and GaAs epilayers.They have attributed it to the presence of native defects, dis-order or a high amount of vacancies within the lattice that cangenerate charge carriers and electronic inhomogeneity.42 In thecase of Cd3As2, the obtained T1 (95 s) values are undoubtedlynot representative of a metal or a semimetal. Thus, any inter-action between the nuclear spins and the conduction carriers(hyperfine interaction) is most likely negligible and the Fermi-contact interaction does not provide a significant pathway forrelaxation. As mentioned earlier, this is an unexpected result,considering that the band dispersion curves of Cd3As21,2 aremostly determined by the Cd-5s states (conduction bands).However, the present NMR results show that the Fermi-contactmechanism is not pertinent here. On the other hand, scalarrelativistic effects and spin-orbit effects in high-Z-elementsalso have a strong impact on the electron-nucleus interactionsand an effect on the NMR properties, since any change inthe symmetry of the conduction bands (band inversion effect)also influences both the Cd nuclear magnetic shielding andthe Cd spin dynamics and as a result the Fermi-contact termvanishes.

Recently, Okvátovity et al.27 investigated the NMRdynamics in Weyl semimetals (WSM) theoretically. The WSMshare parallel phenomenology to the Dirac semimetals. Inparticular, they have investigated the hyperfine interactionbetween the Weyl fermions and the nuclear spins around theWeyl point.27 In contrast to magnetic excitations around a

084706-5 Koumoulis et al. J. Chem. Phys. 147, 084706 (2017)

parabolic (E ∝ k2) band dispersion (as expected in a con-ventional metallic material), the linear dispersion (E ∝ k)leads to a strengthening of the orbital hyperfine contribu-tion and the temperature-independent Korringa mechanismbecomes a temperature-dependent process similar to the caseof nodal superconductors (power-law temperature depen-dence).39 Specifically, in WSM the nuclear spin-lattice relax-ation time closely behaves as in graphene (T1 ∼ T�3).27,40 Thisnonlinear behavior is closer to the 113Cd relaxation behav-ior but fundamentally different from that of a conventionalmetal or semimetal. Similarly, specific heat measurements inCd3As2 revealed that the contribution of electrons even atlow temperatures is negligible.28 In addition, a recent studyby Zhang et al.11 reported an unexpectedly low thermal con-ductivity of Cd3As2, smaller than that of a semiconductor orconventional (semi-) metal. Thus, the physical properties ofCd3As2 such as the electrical and thermal conductivity aredifferent from those expected of semimetals, in line with ourresults.

In order to discuss more quantitatively the spin dynamicsof Cd3As2 we take a closer look at the power-law temperaturedependence of 1/T1 and compare it with other heavy-Z ele-ment materials. In particular, the T -dependence of 1/T1 revealsthe observed power-law relaxation mechanism ( 1T1 = A · T

2)and the relaxation coefficient (A) is very close to that of α-SnF229 [A = (2.21 ± 0.02) × 10�7 s�1 K�2], as well as of thesame order of magnitude as Pb-containing compounds30 e.g.,PbTiO3 [A = 9.00 × 10�7 s�1 K�2]. The A coefficient (alsoknown as the Raman constant) of Cd3As2 is almost identi-cal to the one measured for α-SnF2.29 A is a measure of thespin-rotation coupling strength. Dividing A by the square ofthe gyromagnetic ratio (A/γ2) gives an estimate of the role ofthe magnetic contributions ( 1T1 ∝ γ

2) to the lattice vibrations

(phonons).29,31 In the case of Cd3As2, the calculated value(1022 · A

γ2), 0.37 s T2K�2, is close to the experimental result

0.22 s T2K�2 for 119Sn of α-SnF2, but one order of magni-tude smaller than the reported value for 207Pb in PbTiO3.29–32

This suggests that the low-T relaxation pathway is driven bya Raman-like nuclear spin-rotation relaxation mechanism32

of 113Cd nuclei in Cd3As2, akin to other heavy Z-elementsthat we have also previously reported, e.g., for 119Sn and 125Tenuclei as well as other lead-containing materials.29–32 We con-clude that the spin-rotation-mediated relaxation pathway in113Cd of Cd3As2 is similarly effective as the one for 119Sn(α-SnF2) but less effective than for 209Pb (PbTiO3). It shouldbe noted that this relaxation mechanism is unrelated to thevan Kranendonk33 mechanism that is applicable in the case ofquadrupolar nuclei (I > 1/2). The Raman nuclear spin-rotationmechanism32,34 encountered here is related to the modulationof the angular velocity29 (instead of the angular momentumof a molecule in the liquid phase) and its strength is propor-tional to the interatomic distance (nuclear spin-spin dipolarinteraction).29,32,34

At high temperatures (T > 330 K), the NMR data fol-low a thermally activated mechanism (Arrhenius law), 1T1= B · exp(− EkT ). We found an activation energy of E = 0.17 eV.The lower inset of Fig. 4 shows the Arrhenius plot of the hightemperature data, shown as a red straight line (Fig. 4, inset).

The calculated thermal activation energy obtained from the113Cd T1 experiments as a function of temperature is consis-tent with the reported “hopping” of Cd vacancies in similartypes of materials35,36 and supports the theoretical study byPlenkiewicz et al.37 As described by Conte et al.,38 the twoCd vacancies are diagonally opposite to each other in one faceof a small cube. This may explain the existence of the twoobserved sites in the 113Cd spectrum. The 113Cd lineshape ofCd3As2 does not shift or change noticeably over this tem-perature range. The observed migration of the Cd vacanciesprovides an explanation of the site exchange mechanism. Inaddition, the hopping mechanism is magnetic-field-dependentas the difference in Hz between the two resolved shifts dependslinearly on the magnetic field, as seen here. The validity of theaforementioned relaxation mechanism is further supported bythe observed magnetic field dependence of T1 as at 300 MHz(95 s at 295 K) and 600 MHz (59 s at 294 K). All the aboveresults confirm that Cd vacancies have a strong impact onthe physical properties and band structure characteristics ofCd3As2. Finally, the overall temperature dependence of thespin-lattice relaxation process (Fig. 4) can now be describedvia a bipartite mechanism as 1T1 = A · T

2 + B · exp(− EkT ), withA = (1.18 ± 0.05) × 10�7 s�1 K�2 and E = 0.17 eV as theactivation energy for the high temperature activation process.

IV. CONCLUSIONS

In summary, we have carried out 113Cd NMR experimentsin the Dirac semimetal Cd3As2. The 113Cd spectra are asym-metric due to a site inequivalence between the cadmium atomswithin the lattice. The MAS results resolve two main groupsof resonance in a 2:1 ratio. We observe a crossover from apower-law behavior (T2) of the spin-lattice relaxation rate(1/T1) at lower temperatures to Cd site hopping dynamics athigh temperatures. Surprisingly, the observed magnitude ofthe observed T1 values, the magnitude and sign of the 113Cdresonance shifts, and the magnetic field dependence of 1/T1of Cd3As2 are in direct contradiction to those typically foundfor conductors, semiconductors, and semimetals, in spite of itssemimetallic band structure. Its electronic properties are closerto graphene than a typical semimetal.

ACKNOWLEDGMENTS

We acknowledge the use of instruments at the MolecularInstrumentation (MIC) facility at UCLA, which included fund-ing from the MRI program of the National Science Foundationunder Grant No. 1532232. L.-S.B. acknowledges financialsupport from the Arnold and Mabel Beckman Foundation.

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