Low-temperature monoclinic layer stacking in atomically thin CrI 3 crystals
Nicolas Ubrig, Zhe Wang, Jérémie Teyssier, Takashi Taniguchi, Kenji Watanabe, Enrico Giannini, Alberto F. Morpurgo, Marco Gibertini
LLow-temperature monoclinic layer stacking in atomically thin CrI crystals Nicolas Ubrig,
1, 2, ∗ Zhe Wang,
1, 2
J´er´emie Teyssier,
1, 2
Takashi Taniguchi, KenjiWatanabe, Enrico Giannini, Alberto F. Morpurgo,
1, 2 and Marco Gibertini
1, 4, † Department of Quantum Matter Physics, University of Geneva, 24 Quai Ernest Ansermet, CH-1211 Geneva, Switzerland Group of Applied Physics, University of Geneva, 24 Quai Ernest Ansermet, CH-1211 Geneva, Switzerland National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan National Centre for Computational Design and Discovery of Novel Materials (MARVEL),´Ecole Polytechnique F´ed´erale de Lausanne, CH-1015 Lausanne, Switzerland (Dated: August 27, 2019)Chromium triiodide, CrI , is emerging as a promising magnetic two-dimensional semiconductorwhere spins are ferromagnetically aligned within a single layer. Potential applications in spintronicsarise from an antiferromagnetic ordering between adjacent layers that gives rise to spin filteringand a large magnetoresistance in tunnelling devices. This key feature appears only in thin multi-layers and it is not inherited from bulk crystals, where instead neighbouring layers share the sameferromagnetic spin orientation. This discrepancy between bulk and thin samples is unexpected, asmagnetic ordering between layers arises from exchange interactions that are local in nature andshould not depend strongly on thickness. Here we solve this controversy and show through po-larization resolved Raman spectroscopy that thin multilayers do not undergo a structural phasetransition typical of bulk crystals. As a consequence, a different stacking pattern is present in thinand bulk samples at the temperatures at which magnetism sets in and, according to previous first-principles simulations, this results in a different interlayer magnetic ordering. Our experimentalfindings provide evidence for the strong interplay between stacking order and magnetism in CrI ,opening interesting perspectives to design the magnetic state of van der Waals multilayers. The discovery of magnetic order has disclosed novelopportunities in the field of two dimensional (2D) vander Waals crystals and heterostructures . In manycases , the magnetic configuration of thin layers is thesame as in the 3D parent compounds, although possiblywith a reduced critical temperature owing to the largersensitivity of 2D magnets to thermal fluctuations. Thisis expected as the intra- and inter-layer exchange interac-tions that determine the ground-state magnetic configu-ration are typically local and do not change significantlywhen thinning down the material.A surprising exception is represented by chromiumtriiodide, CrI , a van der Waals material that in itsbulk form shows ferromagnetic (FM) ordering bothwithin and between layers below a critical tempera-ture T c (cid:39)
61 K . Recently, a multitude of ex-periments, ranging from magneto-optical Kerr effectmeasurements to tunnelling magnetotransport and scanning magnetometry , have shown unarguablythat instead thin samples up to at least ∼
10 layersdisplay an antiferromagnetic (AFM) interlayer exchangecoupling between the ferromagnetic layers. The AFMordering can be manipulated through external electricfields or doping and it is responsible for a spin-filtering effect on electrons tunnelling through CrI bar-riers, giving rise to a record-high magnetoresistance with potential application in spin transistors .In an attempt to clarify this unexpected change inmagnetic ordering from bulk to few layers, most theo- ∗ [email protected] † [email protected] retical investigations have focused on the presence of astructural phase transition in bulk CrI at about 200-220 K . Across this transition, the structure evolvesfrom a high-temperature monoclinic phase (Fig. 1a, spacegroup C /m ) to a rhombohedral structure (Fig. 1b, spacegroup R
3) at low temperature, with the main distinctionbetween the two phases being a different stacking order ofthe layers. First-principles simulations in Ref. 12, corrob-orated by additional theoretical investigations , haveshown that the interlayer exchange coupling is FM in therhombohedral phase (in agreement with experimental ob-servations for bulk CrI ), while it is AFM in the mono-clinic structure. The strong interplay between stackingorder and magnetic configuration suggests a possible sce-nario to solve the conundrum: if thin samples exfoliatedat room temperature from bulk monoclinic crystals arenot able to undergo a structural phase transition, theyremain in the metastable monoclinic phase and are thusexpected to display AFM ordering at low temperature.This picture is in agreement with recent measurementson few-layer CrI where either an accidental puncture or an external pressure provided the energy to un-dergo a structural transformation with a correspondingtransition to FM ordering. Additional validations sup-porting the connection between crystal structure andmagnetism have been achieved in a related material,CrBr , by observing different magnetic ordering associ-ated with novel stacking patterns (not corresponding tothe bulk phases) in bilayers grown by molecular beamepitaxy . The ultimate confirmation of the proposedscenario requires a technique sensitive to the stacking or-der of few layer structures in order to verify the absence ofstructural phase transition in few layers. In this regard, a r X i v : . [ c ond - m a t . m e s - h a ll ] A ug second-harmonic generation is an effect which is sensitiveto the different crystal symmetry in the two phases andthat has been recently adopted to show that bilayerCrI remains monoclinic down to very low temperature.Alternatively, another practical approach that has beensuccessfully employed in a similar material, CrCl , re-lies on polarization resolved Raman spectroscopy.In this work, we show the absence of structural phasetransitions in thin CrI through polarization resolved Ra-man spectroscopy. Based on general symmetry argu-ments, we develop a strategy to distinguish the mono-clinic and rhombohedral phases by looking at the angu-lar dependence of the Raman response to linearly polar-ized light. We validate this approach for bulk crystals byevidencing the existence of a monoclinic phase at hightemperature and a rhombohedral one at low tempera-ture, in agreement with the general understanding. Ra-man measurements on encapsulated CrI multilayers onthe contrary show that thin crystals remain in the mon-oclinic phase even when the sample is cooled down tobase temperature. This has crucial implications on themagnetic ground state of atomically thin samples, whichis very sensitive to the stacking order of the layers, andfinally explains the controversial AFM ordering observedin experiments. METHODS
CrI crystals are grown by the chemical vapor trans-port method and, owing to the enormous sensitivity ofthis material to atmosphere, stored in a nitrogen-gas-filled glove box with sub-ppm concentration of O andH O. The investigated bulk crystals are freshly cleaved,mounted on a He-flow cryostat (cryovac KONTI cryo-stat) in the glove box, and sealed in the vacuum chamberwith optical access before being transferred to the opti-cal setup. The nm-thick multilayers of CrI are obtainedby mechanical exfoliation with scotch tape. The flakesare then picked up with standard dry transfer techniquesand fully encapsulated in 10-30 nm thick exfoliated hBN.The samples are removed from the glovebox and placedinto the cryostat for optical investigations.All Raman spectroscopy measurements in this work areperformed using a Horiba scientific (LabRAM HR Evo-lution) confocal microscope in backscattering geometry.The nominal laser power before the microscope objectiveand the window of the cryostat is 60 µ W and the ex-citation wavelength 532 nm. After laser excitation thedispersed light is sent to a Czerni-Turner spectrometerequipped with a 1800 groves/mm grating, which resolvesthe optical spectra with a precision of 0.3 cm − . The lightis detected with the help of a N -cooled CCD-array. Theincident linear polarization of the laser is varied usinga λ /2-plate while the analyzer, placed on the detectinglight path, is kept fix.First-principles simulations have been performedwithin density functional theory using the Quantum a bc Rhombohedrallow- T phaseMonoclinichigh- T phase a b a bc a A g + B g c a FIG. 1. Lateral and top views of the crystal structure of CrI in the monoclinic (high temperature) phase ( a ) and in therhombohedral (low temperature) phase ( b ). Both the primi-tive (thin dashed line) and the conventional (thick solid line)unit cells are reported. c . Typical Raman spectrum of bulkCrI at room temperature without resolving the polarization.The black arrows indicate the pairs of A g and B g vibrationalmodes sensitive to the structural phase transition. The bluedashed rectangle highlights the Raman active modes on whichwe focus our attention in the following. ESPRESSO suite of codes . In order to treat mag-netism and van der Waals interactions on an equal foot-ing we have adopted the spin-polarized extension of thevan der Waals density functional (vdw-DF) method .The unit cell is kept fixed to the experimentally reportedstructure for both the rhombohedral and monoclinicphase, while atomic positions have been relaxed so thatany component of the force on any atom does not exceed2 . × − eV/˚A. Phonon frequencies at vanishing wavevector have been then computed by finite differences us-ing the phonopy software . From the computed phonondisplacement patterns, the Raman tensors have been cal-culated within the Placzec approximation as derivativesof the electronic contribution to the dielectric tensor withrespect to the phonon amplitude, again using finite dif-ferences. In all calculations, we adopt pseudopotentialsfrom the Standard Solid State Pseudopotential Library(SSSP) , with a cutoff of 60 Ry for wavefunctions and480 Ry for the charge density. The Brillouin zone cor-responding to the primitive unit cell is sampled using aregular Monkhorst-Pack grid centered at Γ with 8 × × × × RESULTS AND DISCUSSION
Fig. 1c shows a typical Raman spectrum of bulkCrI at room temperature, in agreement with previousliterature . The visible modes belong to either one oftwo possible irreducible representations, A g or B g , of the2 /m (or C h ) point group corresponding to the high-temperature phase. When the structure undergoes atransition to the rhombohedral phase, some pairs of A g and B g modes (highlighted in Fig. 1) become degenerateand transform according to the two-dimensional E g irre-ducible representation of the low-temperature ¯3 (or C i )point group. The presence of degenerate or split modesthus represents a potential signature to distinguish be-tween the two structural phases and to track the phasetransition. Still, the frequency separation between thesplit modes is typically very small (few cm − ) and thusexpected to get harder to be visible in unpolarized Ra-man spectra when the thickness of the sample is narroweddown and the signal gets weaker.Such difficulty can be overcome in polarization resolvedRaman spectroscopy by exploiting the different Ramanresponse of A g , B g , and E g modes to polarized light. In-deed, as we shall see, the dependence on the polarizationangle cancels out when the contribution from the twodegenerate modes forming a E g peak is summed over inthe rhombohedral phase, resulting in a constant spec-trum insensitive to the polarization configuration. Onthe contrary, in the monoclinic structure the A g and B g modes that result from the splitting of the degenerate E g peak have opposite response, giving rise to two peakswith an intensity that oscillates out of phase with thepolarization angle, so that the close A g and B g peaks aremuch easier to resolve .To provide a rigorous foundation of this procedure, wefirst recall that in non-resonant Stokes conditions, theRaman spectrum can be expressed as I ( ω ) = I (cid:88) ν ω I ω S ω ν | (cid:15) S · R (cid:126)(cid:126) ν · (cid:15) I | [ n ν + 1] δ ( ω − ω ν ) , (1)where the line-shape has been simplified to a δ -function, ω is the Raman shift, ω ν is the frequency of the ν -th long-wavelength phonon mode, (cid:15) I and (cid:15) S the polarization vec-tors of the incident and scattered light with frequency ω I and ω S = ω I − ω , and n ν = [exp( (cid:126) ω ν / ( k B T )) − − is the Bose-Einstein occupation of the ν -th mode. Basedon symmetry arguments, the Raman tensors R (cid:126)(cid:126) ν enteringEq. (1) have the following general expressions for modesbelonging to the A g or B g representations of the high-temperature point group R (cid:126)(cid:126) A g = a d c d b R (cid:126)(cid:126) B g = e fe f (2)and R (cid:126)(cid:126) E g = m n pn − m qp q R (cid:126)(cid:126) E g = n − m − q − m − n p − q p (3)for pairs of degenerate modes belonging to the E g repre-sentation of the low-temperature point group.To identify a strategy to distinguish the two phases,we focus on the most common back-scattering geometrywith linearly polarized light, whose polarization vectorscan thus be written as (cid:15) I/S = (cos θ I/S , sin θ I/S , E g modes split into a A g and a B g mode, we expect a ≈ − c (and | a | ≈ | e | ), so that R νyy ≈ − R νxx for all themodes considered here. As a consequence, we find (cid:15) S · R (cid:126)(cid:126) ν · (cid:15) I = cos θ S cos θ I R νxx + sin θ S sin θ I R νyy + sin( θ S + θ I ) R νxy (4)= cos θR νxx + sin θR νxy , yielding an intensity in Eq. (1) that can be written interms of the cumulative angle θ = θ S + θ I . From thegeneral expressions for the Raman tensors, we find thatthe Raman spectrum is completely independent of thepolarization angles close to a degenerate E g peak in thelow-temperature phase, I E g ( ω ) = I ω I ( ω I − ω ) ω E g [ n E g + 1]( m + n ) δ ( ω − ω E g )(5)while the intensity of the split A g and B g modes of themonoclinic structure oscillates out of phase as a functionof the angle θ : I A g + B g ( ω ) = I ω I ( ω I − ω ) a × (6) (cid:20) n A g + 1 ω A g cos θδ ( ω − ω A g ) + n B g + 1 ω B g sin θδ ( ω − ω B g ) (cid:21) . This provides us with a strategy to distinguish the twostructural phases by looking at the evolution of the Ra-man spectrum as the cumulative polarization angle θ isvaried, e.g. by keeping fixed θ S while sweeping θ I . Inthe rhombohedral phase we expect degenerate E g peakswhose intensity and frequency position do not changewith the polarization angle, while the monoclinic struc-ture is characterized by pairs of close peaks associated abc FIG. 2. Phonon displacement pattern according to first-principles simulations of the modes visible in the Ramanspectrum close to 100 cm − either in the rhombohedral ( a )or monoclinic ( b ) phase. The modes appear in order of in-creasing frequency. c : Colour plot of the normalized Ramanspectrum as a function of the polarization angle and Ramanshift. Results for both the rhombohedral (left) and monoclinic(right) phase of bulk CrI are reported. Here we assume thatthe polarization angle of the incident light θ I is varied, whilekeeping the detector for the scattered light fixed at θ S = 0.Intensities and vibrational frequencies are computed from firstprinciples as detailed in the Methods, although the positionof the brightest A g and B g modes of the monoclinic structure(as well as the corresponding E g mode in the rhombohedralphase) have been displaced by 4 cm − to obtain a better qual-itative agreement with experiments (see below). The upperinsets show the Raman spectra in parallel (blue) or cross (red)polarization, corresponding to the horizontal dashed lines inthe colour plots. with A g and B g modes whose intensity alternates outof phase as a function of θ , enhancing the visibility ofthe split modes even when the frequency separation isvery small. In the following we focus on the spectralrange around 100 cm − , where this strategy is particu-larly suitable owing to the presence of two nearby E g modes in the rhombohedral phase split into two pairs of A g + B g modes in the monoclinic phase.The procedure is exemplified in Fig. 2 in a model calcu-lation, where the Raman intensities and vibrational fre-quencies have been computed for the rhombohedral andmonoclinic structures from first principles (see Methods),although the position of the strongest A g + B g peaks ofthe monoclinic crystal (and for consistency also the cor-responding E g peak in the rhombohedral phase) havebeen shifted by 4 cm − to result in a better qualitativeagreement with experiments. The angular dependence ofthe two spectra are clearly different, supporting the effec-tiveness of our strategy to distinguish the two structuralphases. Indeed, as expected from the above discussion,for the rhombohedral structure, the Raman spectrum isinsensitive to the polarization angle θ I (here we assume θ S = 0), while in the monoclinic phase we have a trans-fer of spectral intensity as a function of θ I between twopeaks of a split A g + B g pair. In particular, this re-sults into very different spectra in parallel configuration( θ I = θ S = 0, or Z ( XX ) ¯Z in Porto notation), where only A g modes are visible, or cross configuration ( θ I = π/ Z ( YX ) ¯Z ), where only B g modes are present, allowingto clearly resolve their frequency separation.We first validate our approach by considering bulksamples, for which a structural phase transition is ex-pected to occur at 200-220 K and should manifest itselfin a change of the angular dependence of the Raman spec-trum. Fig. 3 shows the Raman response measured at twodifferent temperatures, above and below the structuralphase transition, as a function of the polarization angle θ I of the incident light, while the detecting polarizer iskept fixed (see Methods). At 5 K a weak and a strongpeak are present at 103 and 107 cm − respectively, andtheir intensity does not evolve with θ I , clearly showingthat these are E g modes of the rhombohedral structure.In particular, the relative intensity of the two modes isin very good agreement with the first-principles results inFig. 2 and allows us to make a more definite assignmentof the corresponding phonon patterns. At high temper-ature (280 K), each peak splits into two with intensitiesthat oscillate out of phase as a function of θ I , so thatfor parallel and cross polarization (upper panel) only oneof the two split modes is visible. This is exactly whatis predicted for a monoclinic structure in Fig. 2 and wecan thus unambiguously identify the peaks as pairs of A g + B g modes, indicating that the structure is mono-clinic at high temperature. Our approach thus confirmsthat bulk crystals undergo a structural transition from amonoclinic phase at high temperature to a rhombohedralphase at low temperature.We are now in a position to consider thin samples ob-tained by mechanical exfoliation (see Methods). Fig. 3shows the Raman spectra obtained at 5 and 280 K fora 4 nm thick CrI crystal (see inset, approximately 6layers) as a function of the polarization angle. For defi-niteness, we focus on the same spectral range consideredfor bulk samples. In this case, apart from a clear reduc-tion of the peak width upon decreasing temperature, the Z(XX)ZZ(YX)Z
Z(XX)ZZ(YX)Z a b c d
FIG. 3. Color plots of the normalized intensity as a function of the Raman shift (in cm − ) in the investigated frequency regionand of the angle of the incoming linearly polarized light. The white dashed lines indicate co- and cross-polarized configurations( Z ( XX ) ¯Z and Z ( YX ) ¯Z , respectively). The top panels show individual line cuts for Z ( XX ) ¯Z and Z ( YX ) ¯Z . Bulk CrI at T = 5 K( a ) and T = 280 K ( b ) show excellent agreement with the theoretical predictions showing that the structural phase transitionfrom monoclinic, at high temperatures, to rhombohedral, at low temperatures, takes place. The experimental data for a 4 nmthick crystal of CrI is shown in c and d for T = 5 K and T = 280 K, respectively. The area probed here and an opticalmicrograph of the flake is depicted in the inset of panel c . The scale bar corresponds to 10 µ m. Except for a slight stiffeningof the modes due to the decreased temperature we do not observe significant differences between the experimental data at lowand high temperatures. In particular, the polarization pattern is virtually identical, indicating that no structural transitionoccurs so that the system remains in the monoclinic phase down to low temperature. two spectra are virtually identical. In particular, both athigh and low temperature we find two pairs of close bypeaks whose intensity varies with the polarization anglein phase opposition. Such transfer of spectral intensityas a function of θ I between nearby peaks is the clear sig-nature of the monoclinic phase introduced before, rulingout the emergence of the rhombohedral phase.As temperature plays a crucial role in rhombohedral-monoclinic transition, sound conclusions on the presenceor absence of structural changes require an independentcross check of the effective temperature of the samplefor every experiment. Indeed, in a measurement of theRaman spectrum of insulators –which usually have lowthermal conductivity– the laser can heat up the illumi-nated sample area. For instance the temperature can belifted locally above a phase transition temperature, po-tentially leading to spectra that artificially look similareven at very different nominal temperatures . Throughthe analysis of the intensity ratio between the Stokes andthe anti-Stokes peaks in the entire spectral range we en-sure that the sample area which is probed remains belowthe temperatures of the phase transitions.We can thus safely state that thin samples remain in the monoclinic structure down to very low temperature,even below the critical temperature T c at which mag-netism sets in. In this respect, the persistence of themonoclinic phase explains the observation of layerantiferromagnetism in thin crystals, as opposed to thebulk FM order. Indeed, the monoclinic stacking or-der has been predicted to favour an AFM interlayer ex-change coupling according to density-functional-theorysimulations . The different magnetic state also re-sults in a change in critical temperature, from 61 K inthe bulk to 51 K (Ref. 12) in thin crystals.Remarkably, this reduced T c matches exactly the tem-perature at which an anomaly is observed in the mag-netization curves of bulk CrI . This could indicate thatalso the outermost layers of bulk samples do not undergoa structural transition, in the same way as thin crystals.Indeed, by remaining in the monoclinic phase, such layerswould display AFM order, giving rise to an anomaly atthe onset of antiferromagnetism in monoclinic CrI (51 Kinstead of 61 K), which corresponds to the temperatureof the anomaly observed in experiments.The common behaviour of thin crystals and the outer-most layers of bulk CrI would then suggest the impor-tance of free surfaces in the suppression of the structuraltransition. Indeed, the absence of neighbouring layers atthe surface could affect both the thermodynamics andthe kinetics of the phase transition, e.g. by changing thevibrational free energy or the barrier height. Such effectscould extend quite deeply inside the material or for rela-tively large thicknesses. Although this seems promising,further studies will be needed to clarify the precise na-ture and the spatial extension of the surface effects onthe structural transition. CONCLUSION
In conclusion, we have identified a strategy to distin-guish between the two structural phases of CrI throughpolarization resolved Raman spectroscopy. We have val-idated our approach in the case of bulk crystals, confirm-ing the existence of a structural transition from a mono-clinic phase at high temperature to a rhombohedral phaseat low temperature. When considering thin samples, ourRaman spectroscopy analysis shows that the monoclinicstructure persists down to very low temperature, clearly indicating the absence of any structural change when thethickness of the material is narrowed to few atomic lay-ers. These results provide fundamental insight to confirma plausible scenario that explains the full set of experi-mental data on CrI , possibly including the presence ofanomalies in the magnetization curves of bulk crystals. Note : during the preparation of this manuscript we be-came aware that Raman results similar to the ones re-ported here have very recently appeared in Ref. 26.
ACKNOWLEDGEMENTS
We sincerely acknowledge Alexandre Ferreira for tech-nical support. A.F.M. gratefully acknowledges financialsupport from the Swiss National Science Foundation (Di-vision II) and from the EU Graphene Flagship project.M.G. acknowledges support from the Swiss National Sci-ence Foundation through the Ambizione program. Simu-lation time was provided by CSCS on Piz Daint (projectIDs s825 and s917). K.W. and T.T. acknowledge supportfrom the Elemental Strategy Initiative conducted by theMEXT, Japan, A3 Foresight by JSPS and the CREST(JPMJCR15F3), JST. B. Huang, G. Clark, E. Navarro-Moratalla, D. R. Klein,R. Cheng, K. L. Seyler, D. Zhong, E. Schmidgall, M. A.McGuire, D. H. Cobden, W. Yao, D. Xiao, P. Jarillo-Herrero, and X. Xu,
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