Magnetic Behavior and Spin-Lattice Coupling in Cleavable, van der Waals Layered CrCl3 Crystals
Michael A. McGuire, Genevieve Clark, Santosh KC, W. Michael Chance, Gerald E. Jellison Jr., Valentino R. Cooper, Xiaodong Xu, Brian C. Sales
aa r X i v : . [ c ond - m a t . o t h e r] J un Magnetic Behavior and Spin-Lattice Coupling in Cleavable, van der Waals Layered CrCl Crystals
Michael A. McGuire, ∗ Genevieve Clark, Santosh KC, W. Michael Chance,
1, 3
Gerald E. Jellison, Jr., Valentino R. Cooper, Xiaodong Xu,
2, 4 and Brian C. Sales Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 USA Department of Materials Science and Engineering, University of Washington, Seattle, Washington, 98195, USA Department of Materials Science and Engineering, The University of Tennessee, Knoxville, TN 37996, USA Department of Physics, University of Washington, Seattle Washington, 98195, USA
CrCl is a layered insulator that undergoes a crystallographic phase transition below room temperature andorders antiferromagnetically at low temperature. Weak van der Waals bonding between the layers and ferromag-netic in-plane magnetic order make it a promising material for obtaining atomically thin magnets and creatingvan der Waals heterostructures. In this work we have grown crystals of CrCl , revisited the structural andthermodynamic properties of the bulk material, and explored mechanical exfoliation of the crystals. We findtwo distinct anomalies in the heat capacity at 14 and 17 K confirming that the magnetic order develops in twostages on cooling, with ferromagnetic correlations forming before long range antiferromagnetic order developsbetween them. This scenario is supported by magnetization data. A magnetic phase diagram is constructedfrom the heat capacity and magnetization results. We also find an anomaly in the magnetic susceptibility at thecrystallographic phase transition, indicating some coupling between the magnetism and the lattice. First princi-ples calculations accounting for van der Waals interactions also indicate spin-lattice coupling, and find multiplenearly degenerate crystallographic and magnetic structures consistent with the experimental observations. Fi-nally, we demonstrate that monolayer and few-layer CrCl specimens can be produced from the bulk crystalsby exfoliation, providing a path for the study of heterostructures and magnetism in ultrathin crystals down tothe monolayer limit. I. INTRODUCTION
Recent interest in layered ferromagnetic materials is drivenby the desire to develop functional van der Waals heterostruc-tures [1, 2]. For this purpose materials must be cleavable downto very thin, ideally monolayer, specimens. This is possiblewhen the layers composing the crystal are held together byweak van der Waals bonds so they can be mechanically sepa-rated or exfoliated by chemical intercalation routes [3]. Thisled to the identification and study of CrSiTe and CrGeTe [4–7]. These are small band gap semiconductors with Curietemperatures of 33 K for CrSiTe [8] and 61 K for CrGeTe [9]. The cleavage energy of these materials is calculated to be0.35-0.38 J/m [5], similar to graphite (0.43 J/m ) and MoS (0.27 J/m ) [10]. Studies of nanosheets of CrSiTe suggestferromagnetism may persist in ultrathin specimens [11], andferromagnetic few-layer-thick crystals of CrGeTe have re-cently been reported [12]. The tin analogue CrSnTe is alsopredicted to be a ferromagnet [13]. Other recently discov-ered materials include Fe GeTe [14], a metal with itinerantferromagnetism below T C =220-230 K [14–16]. Chromiumtriiodide, and transition metal halides in general [17], havealso been put forth as candidates for cleavable magnetic ma-terials [18–21]. Experimentally, CrI is a ferromagnet with T C = 61 K [18, 22, 23], CrBr is a ferromagnet with T C =37 K [24], and CrCl is an antiferromagnet with an orderingtemperature near 17 K [25, 26]. Several theoretical studieshave been recently published on chromium trihalides address-ing bulk magnetic properties and behavior in monolayer form[18–21, 27, 28], and also on VCl and VI , which are pre-dicted to be ferromagnetic and Dirac half-metals [29]. All of ∗ [email protected] the calculations predict low cleavage energies for these com-pounds, similar to those noted above for graphite and MoS .Recently ferromagnetism has been experimentally confirmedin monolayer CrI with intriguing thickness dependent mag-netic phases [30], and heterostructures incorporating ultrathinCrI have enabled remarkable control of the spin and valleypseudospin properties in monolayer WSe through a large ex-change field effect [2].It is interesting to note that the magnetic ordering tempera-tures of the chromium trihalides increase as the halogen sizeincreases from Cl to Br to I. Since the Cr-Cr distances increasewith increasing halogen size, the direct exchange is expectedto be weakened along this series. This indicates that superex-change, which is expected to favor ferromagnetic alignment,is the more important magnetic interaction [28]. As the elec-tronegativity is decreased from Cl to Br to I, it is expected thatthe Cr-halogen bonding becomes more covalent, strengthen-ing superexchange interactions and raising ordering temper-atures. Indeed all three of these chromium trihalides exhibitferromagnetic ordering of Cr moments within the layers at lowtemperature [18, 24, 26, 31]. Moving from Cl to Br to I is alsoexpected to increase spin orbit coupling associated with thehalogen, which has been identified as a source of magneticanisotropy in these materials [28].The present work focuses on chromium trichloride. Initialstudies of magnetism in this material date back nearly 100years [32]. The antiferromagnetic ground state consists ofmoments lying in the plane defined by the Cr layers. Thosemoments are aligned ferromagnetically within a layer, and thelayers stack antiferromagnetically, as demonstrated by neu-tron diffraction [26]. The transition temperature of 17 K wasidentified by heat capacity measurements [25, 33]. Kuhlowperformed Faraday rotation measurements and concluded thatupon cooling the magnetic order appeared to develop by firstforming two-dimensional ferromagnetic order within the lay-ers and then, at slightly lower temperature, forming long rangethree-dimensional order through antiferromagnetic couplingbetween the layers [34]. Faraday rotation, magnetization, andneutron diffraction measurements show that the ordered statehas very little anisotropy, and fields of only a few kOe are re-quired to fully polarize the magnetization in or out of the plane[26, 34, 35]. Weak magnetic anisotropy and weakly antifer-romagnetic interlayer interactions are also reported from spinwave analysis [36]. In addition, CrCl is known to undergo acrystallographic phase transition near 240 K, similar to CrBr and CrI , corresponding to a change in the layer stacking ar-rangement and a transition from monoclinic ( C /m ) at hightemperature to rhombohedral ( R ) at low temperature withlittle change in the intralayer structure [18, 37].There have been several recent theoretical studies ofCrCl based on first principles electronic structure calcula-tions. Wang et al. employed all-electron calculations forbulk CrCl , and the experimentally observed rhombohedral-antiferromagnetic ground state was reproduced for one of themethods used for incorporating U, the on-site Coulomb repul-sion for Cr [27]. The authors noted that the energetics of thedifferent crystal and magnetic structures are sensitive enoughto the specific approach used that it is difficult to draw defini-tive conclusions about their relative stability, consistent withthe experimentally observed temperature induced crystallo-graphic phase transition and the weak magnetic anisotropyin the antiferromagnetic state. Other theoretical studies fo-cus mainly on CrCl monolayers. Liu et al. observed fer-romagnetic order below 66 K in Monte Carlo simulations ofmonolayers, and suggested that hole doping should increasethe Curie temperature [20]. The cleavage energy in the bulkcrystal was calculated using a van der Waals density func-tional (vdW-DF) method to account for the dispersion forcesin the bulk crystal. This gave a very low cleavage energy of0.10 − . Zhang et al. calculate a cleavage energy of0.3 J/m using a different vdW-DF [19]. Monte Carlo simula-tions using their first principles calculations results for mono-layer CrCl suggest a Curie temperature of 49 K, which is pre-dicted to increase with applied strain. The results of those twostudies indicate that CrCl monolayers should be mechani-cally stable.Here we report results from a thorough study of bulk CrCl crystals, including x-ray diffraction, magnetization, and heatcapacity data, along with van der Waals density functionalstudies of the structure and magnetism. In addition we includeoptical images and atomic force microscopy measurements onultrathin specimens cleaved from the bulk crystals. Our obser-vations for the bulk crystals are in agreement with previouslypublished literature, and in addition: (1) we note an anomalyin the magnetic susceptibility at the crystallographic phasetransition indicating some coupling of the magnetism to thecrystal lattice, (2) we find good structural agreement betweentheory and experiment only when magnetism is included inthe calculations, again indicating spin-lattice coupling, (3) weobtain an estimate of the in-plane spin-flop field from magne-tization measurements, (4) we observe two separate heat ca-pacity anomalies associated with magnetic ordering indicative of short-ranged or two-dimensional ferromagnetism evolvinginto long-range antiferromagnetism, (5) we present the evolu-tion of isothermal magnetization curves that is consistent withthis scenario and construct a temperature-field phase diagramfor CrCl , and (6) we demonstrate stable monolayer and few-layer specimens can be cleaved from bulk crystals. Overall,it is apparent that CrCl is a promising material for the studyof magnetism in ultrathin crystals and for incorporating mag-netism into van der Waals heterostructures. II. PROCEDURES
Crystal growth is described in the following Section. APANalytical X-Pert Pro MDP diffractometer equipped with anOxford PheniX cryostat was used for x-ray diffraction mea-surements (Cu-K α radiation). Heat capacity and ac mag-netization measurements were performed using a QuantumDesign PPMS, and dc magnetization was measured using aQuantum Design MPMS. Optical absorbance A was deter-mined from the measured optical transmittance T by A = − log ( T ) . Transmission measurements were made using ahome-built system specifically designed for small samples.The light source was an Energetiq LDLS 99, which was col-limated coming from the fiber. The detector was an OceanOptics USB4000 0.1 meter spectrometer attached to a 600 mi-cron multimode fiber. The sample was placed directly in frontof the 600 micron entrance of the fiber. The transmission wasdetermined by the ratio of the spectroscopic intensity with thesample in place and the intensity with the sample removed.Exfoliation of bulk CrCl was achieved using mechanical ex-foliation with scotch tape onto 90 nm SiO substrates. Opticalmicroscopy images were obtained using an Olympus BX51Mmicroscope, while atomic force microscopy (AFM) was car-ried out using a Bruker Edge Dimension atomic force micro-scope.DFT calculations were performed using the Vienna Ab-initio Simulation Package (VASP) [38] with the projector-augmented wave (PAW) [39] potentials in order to understandthe crystallographic and electronic properties of bulk CrCl .The exchange-correlation was approximated with generalizedgradient approximation (GGA) of Perdew-Burke-Ernzerhof(PBE) functionals [40] as well as van der Waals correctionusing vdW-DF-optB86b functional [41–44]. The pseudopo-tentials used explicitly treat p , s , d , and s , p elec-trons as valence electrons for Cr and for Cl, respectively.The Brillouin zone (BZ) integration was performed using theMonkhorst-Pack [45] sampling method with a 4 × × R )and 4 × × C /m ) k-meshes for structural optimization.Theenergy cutoff was 500 eV and the criteria for energy and forceconvergence were set to be × − eV and 0.01 eV/ ˚A, re-spectively. FIG. 1. (a) CrCl single crystals grown for this study. (b) The op-tical absorbance spectrum showing strong absorption of green andred resulting in the observed violet color. (c) Temperature depen-dence of the layer spacing in CrCl measured using x-ray diffractionduring the first cooling of the crystal. (d) Relative amount of themonoclinic phase present during the first cooling through the mon-oclinic to rhombohedral phase transition. The two crystal structuresare depicted on this panel as well. (e) Contour plot of the diffractedintensity from the monoclinic 0 0 5 and rhombohedral 0 0 15 reflec-tions on the second cooling and warming cycles. III. RESULTS AND DISCUSSIONA. Crystal growth, structure, and spin-lattice coupling
Thin, plate-like single crystals of CrCl with lateral dimen-sions up to several millimeters are easily grown by recrystal-lizing commercial CrCl using chemical vapor transport [33]. Here CrCl from Alpha Aesar with a metals-basis purity of99.9 % was used. The as-received material, in the form ofsmall platelets, was sealed inside evacuated silica tubes. Atypical growth used about 1 g of CrCl in a 15 cm long tubewith 16 mm inner diameter and 1.5 mm wall thickness. Thetubes were placed in a horizontal tube furnace so that the start-ing material was at the end of the tube near the center of thefurnace and the other end of tube was near the opening at theend of the furnace. The temperature at the center of the fur-nace was set to 700 ◦ C, and the temperature at the cooler endof the tube was measured to be 550 ◦ C. The growth beginsrapidly and slows as the starting material is consumed. Large,violet-colored, transparent platelets like those shown in Fig.1a are present after 48 h at temperature, while it may take upto a week for all of the CrCl to be transported. After therecrystallizations are complete a green powder, presumablyCr O , is left at the hot end of the tubes. This is attributed tooxide impurity in the starting material.The optical absorbance of a CrCl crystal grown for thepresent study is shown in Fig. 1b. A color scale showingthe approximate color of the visible light for photon energiesbetween 1.7 and 3.3 eV is included on the plot. The resultsare consistent with the data reported in the thorough study ofthe optical properties of this material by Pollini and Spinolo[46]. A band gap of 3.1 eV is approximated by the onset ofstrong absorption at higher energies. Below the band edge,there are two broad absorptions in the red and green centerednear 1.7 and 2.3 eV, to which the violet color of the crystalcan be attributed. These bands, which have fine structure notresolved here, arise from Cr d - d transitions as described indetail in Ref. [46].As noted above, CrCl is known to undergo a crystal-lographic phase transition below room temperature. Usingsingle crystal diffraction, Morosin and Narath [37] demon-strated that CrCl adopts the monoclinic space group C /m at room temperature and the rhombohedral space group R at 225 K. They used nuclear quadrupole resonance to identifythe phase transformation temperature as 240 K. The crystal-lographic phase transitions involves mainly a change in thelayer-to-layer shift in the stacking sequence. The intralayerstructure remains nearly the same, with an ideal honeycombnet of Cr in the rhombohedral structure and a slightly distortedhoneycomb net in the monoclinic structure [18, 37]. For ex-ample, in CrCl the in-plane Cr-Cr distances are 3.431 ˚A at225 K (rhombohedral) and 3.440 and 3.441 ˚A at 298 K (mon-oclinic) [37].Results of x-ray diffraction measurements through thisphase transition are shown in Figure 1c-e. During the firstcooling the high and low temperature phases coexist over arelatively wide temperature range (Fig. 1c). The fraction ofthe monoclinic phase present during this initial cool down, de-termined by the ratio of the peak intensities, is shown in Fig-ure 1d. More than 85% of the crystal transforms between 240and 230 K, and the remaining small fraction of the high tem-perature phase essentially vanishes between 140 and 130 K.The two crystal structures are shown on this figure.During subsequent cooling and heating cycles the phasetransformation is much sharper (Fig. 1e), as was found to thecase in CrI crystals [18]. This suggests that the retained hightemperature phase present in the first cool down is likely as-sociated with defects or strain frozen into the crystals duringthe growth at elevated temperature and subsequent cooling toroom temperature. There is still significant thermal hysteresisafter the first thermal cycling, consistent with the first ordernature of the phase transition.Results of our DFT calculations for CrCl in both the mon-oclinic and rhombohedral structures are summarized in TableI. We investigated non-magnetic (NM), ferromagnetic (FM),and antiferromagnetic (AFM) configurations for both crystalstructures. The AFM configuration refers to the experimen-tal magnetic structure, with ferromagnetic planes stacked an-tiferromagnetically. Results are presented for both PBE andvdW-DF-optB86b functionals. For one of these cases, theFM rhombohedral structure, results have been previously re-ported by Zhang et al. using PBE and the van der Waals den-sity functional optB88 [19].The results shown in Table I forthis configuration are within 1% of the values reported there.Our calculations indicate the monoclinic structure to be fa-vored by 0.05 eV/atom in the non-magnetic calculations, andessentially degenerate monoclinic and rhombohedral struc-tures for the magnetically ordered cases, with a very small0.001 eV/atom preference for the experimentally observedrhombohedral structure. The presence of nearly degeneratecrystallographic ground states is consistent with the observedtemperature induced structural phase transition.The cleavage energy calculated in the rhombohedral struc-ture with vdW-DF-optB86B is 0.3 J/m , in agreement with thecalculated value for CrCl given in Ref. 19. This is similarto values determined using similar approaches for the otherchromium trihalides [18, 19], as well as other related, easily-cleaved materials noted in the Introduction. The low cleav-age energy enables monolayer and few-layer specimens to becleaved from the CrCl crystals, as demonstrated below.The optimized lattice parameters for the FM and AFM unitcells are similar to one another, and those determined fromvdW-DF-optb86b calculations agree well with the experimen-tal structure (Table I). As expected the PBE results show anelongation along the stacking directions, the c axes. It isparticularly interesting to note the significant difference be-tween the optimized lattice parameters for the NM structureand those determined for the magnetically ordered structures.In each case the NM unit cell is significantly smaller. Thisis true for both the monoclinic and rhombohedral structures.For the vdW-DF-optb86b results in the AFM and FM struc-tures, the optimized unit cell volumes are within 2% of theexperimental values. For the NM case they are smaller bymore than 10% (Table I). The reason for this is not com-pletely clear, but it does suggest a strong coupling betweenthe spins and the crystal lattice in CrCl . The differencein unit cell volume arises primarily from variation in the in-plane lattice constants, where magnetic exchange is expectedto be the strongest; however, it is important to note that themethod used here includes spin only in the local part of theexchange-correlation functional, and not in the non-local part[44], which may be more important in the interplanar interac-tions. Crystallographic studies through the magnetic ordering temperature would be helpful in probing the spin-lattice cou-pling identified in these calculations. Although our diffrac-tion measurements do not extend to low enough temperatureto examine this in CrCl , a structural response at the magneticordering temperature was noted in isostructural CrI [18].Additional evidence of spin-lattice coupling is seen in themagnetization data near the structural phase transition plot-ted in Fig. 2a. Temperature dependent magnetic suscepti-bility data, plotted as inverse susceptibility H/M , reveal asmall discontinuity at 256 K. The data was collected on warm-ing, and the temperature of the discontinuity agrees well withthe transition temperature determined by x-ray diffraction onwarming (Fig. 1e). Similar evidence of coupling between themagnetism and crystal lattice was previously noted for CrI [18]. Above and below this temperature Curie-Weiss behavioris observed, down to about 100 K and up to 380 K, the high-est temperature investigated here. The results are in agree-ment with other analyses of high temperature data [33, 47],although the anomaly at the structural phase transition wasnot noted in previous measurements due to relatively sparsedata. Both the high and low temperature fits in Fig. 2a give aneffective moment that is close to the expected value for spin-only Cr (3.87 µ B ).The primary difference between the paramagnetic behaviorabove and below the structural transition is in the Weiss tem-perature θ , which is smaller in the high temperature mono-clinic phase than in the low temperature rhombohedral phase.The Weiss temperatures are positive, indicating that the intra-planar ferromagnetic interactions dominate the magnetic be-havior in the paramagnetic state. The strength of the mag-netic interactions, primarily superexchange, are expected to besensitive to the details of the chemical coordination, allowingcoupling of the magnetic behavior to the crystal structure de-tails. In particular, the antiferromagnetic interplanar superex-change interactions will depend upon how the CrCl layersstack. Since the crystallographic phase transition amounts es-sentially to a change in the layer stacking, this is identified asa likely source of the coupling between the magnetism and thelattice that produces the magnetic anomaly near 250 K.While both CrCl and CrI [18] show evidence of spin-lattice coupling, key differences can be noted in their behav-iors and magnetic structures. The most obvious difference isthe orientation of the ordered moments in the two phases, in-plane for the chloride and out of plane for the iodide (and bro-mide). In addition, the response of the magnetic susceptibilityto the structural phase transition, as quantified by fits using aCurie-Weiss model, differ in the two materials. In CrCl , theWeiss temperature changes by nearly a factor of three, whilein CrI this parameter changes little and a response is seenmainly in the effective moment. As noted above, the crys-tallographic layer spacing was seen to decrease upon coolinginto the magnetically ordered state CrI [18]. A similar typeof coupling between the crystal structure and magnetic ordermay be expected in CrCl , though the present diffraction mea-surements do not extend to low enough temperature to test thishypothesis. A detailed crystallographic study of chromiumtrihalides through the magnetic ordering temperatures as wellas a comparative theoretical study incorporating non-collinear TABLE I. Structural parameters from DFT calculations using PBE/GGA and vdW-DF-optB86b for bulk CrCl in the monoclinic and rhom-bohedral crystal structures, with corresponding experimental values from Ref. 37. Energies given in eV/atom can be converted to eV/Cr bymultiplying by four. Monoclinic, C /m non-magnetic ferromagnetic antiferromagnetic exp. [37]PBE vdW-DF PBE vdW-DF PBE vdW-DF T = 298 Ka ( ˚A) 5.992 5.825 6.060 5.944 6.039 5.945 5.959b ( ˚A) 10.372 9.404 10.490 10.288 10.457 10.290 10.321c ( ˚A) 6.517 6.086 6.656 6.043 6.571 6.036 6.114 β (deg.) 107.3 107.5 107.1 108.6 107.3 108.7 108.5vdW gap ( ˚A) 3.775 3.100 3.869 3.245 3.772 3.205 3.299Energy (eV/atom) – -3.503 – -3.785 – -3.785 –Rhombohedral, R non-magnetic ferromagnetic antiferromagnetic exp. [37]PBE vdW-DF PBE vdW-DF PBE vdW-DF T = 225 Ka ( ˚A) 5.652 5.563 6.054 5.942 6.053 5.930 5.942c ( ˚A) 19.641 17.288 19.239 17.088 19.027 17.184 17.333vdW gap ( ˚A) 3.816 3.035 3.746 3.037 3.676 3.070 3.093Energy (eV/atom) – -3.454 – -3.786 – -3.786 – K20
K14
K17
K 10
K20
K14
K17 K CrCl FIG. 2. Measured magnetic behavior of CrCl crystals. (a) Temperature dependence of the inverse susceptibility (H/M) measured with a10 kOe field applied in the plane showing the small anomaly at the structural phase transition (inset) and Curie-Weiss fits to data above andbelow the transition. (b) Moment per Cr atom vs temperature near the magnetic ordering measured upon cooling in the indicated appliedmagnetic fields both in and out of the plane. (c) Isothermal magnetization curves near the magnetic ordering temperatures. Curves weremeasured at temperature intervals of 1 K and data sets at 10, 14, 17, and 20 K are labeled. (d) Moment per Cr atom measured at 2 K. Due tothe thin plate-like shape of the crystals, a demagnetization factor of 4 π (cgs units) was used to determine the internal field for the field out ofthe plane measurements. The inset shows both uncorrected (open circles) and corrected data (solid circles). magnetic structures and spin-orbit coupling would be desir-able to help quantify and better understand the coupling be-tween the magnetism and the lattice in these compounds. B. Magnetic behavior and phase transitions
Magnetization data from our crystals near the magnetic or-dering transitions are summarized in Figure 2b-c. The tem-perature dependent data were collected upon cooling, and theisothermal magnetization curves were collected upon decreas-ing the applied field. The results are in general agreement withprevious studies employing a variety of techniques, whichfind below about 14 K moments in each layer ferromagneti-cally aligned and lying in the ab -plane with antiferromagneticstacking between planes along the c -axis and weak magneticanisotropy [26, 34–36]. The temperature dependence of themagnetic moment per Cr atom measured near the Curie tem-perature is shown in Figure 2b. At 4 K and 2 T a moment of3.0 µ B per Cr is measured, as expected for S = trivalent Cr.Data are shown for multiple applied magnetic fields (no cor-rection for demagnetization) with the field both in the planeof the CrCl layers and out of the plane. The curves are verysimilar to those reported in Ref. 35. Kuhlow reported sim-ilar behavior in Faraday-rotation measurements [34]. In thatstudy, the magneto-optical measurements indicated that themagnetic order developed in two steps upon cooling, corre-sponding to the upturn in the measured magnetization (Fig.2b) below about 20 K and the sharp cusp apparent in low fieldmeasurements near 14 K. This was interpreted as 2D ferro-magnetic order within the layers developing first, with inter-layer long-range antiferromagnetic order setting in at lowertemperature.This two-step development of magnetic order can also beinferred from the isothermal magnetization curves of Bizette et al . [35], as pointed out by Kuhlow, who saw similar behav-ior in isothermal Faraday rotation curves [34]. This behavioris demonstrated for the crystals used in the present study inFigure 2c. Magnetization is shown as a function of field fortemperatures between 10 and 20 K, with the field applied outof the plane defined by the CrCl layers and with the fieldapplied out of this plane. Data collected with the field nor-mal to the thin platelet crystals was corrected for demagne-tization effects by assuming a demagnetization factor of 4 π (cgs units). The curves in Figure 2c can be divided into threefamilies based on their curvature, and are delineated by dif-ferent colors and symbols in the figure. The distinctions aremost apparent in the out of plane data. Between 20 and 18 Kthe curves are linear. At 17 K a negative curvature develops,indicating a ferromagnetic-like response. This behavior is en-hanced upon cooling to 14 K. At 13 K the response changesto nearly linear at low fields, characteristic of the behavior ex-pected for polarizing an antiferromagnet with low anisotropy.Thus, the data suggests the onset of ferromagnetic correla-tions at 17 K and antiferromagnetic order at 13 K, in generalagreement with Kuhlow’s observations [34].Results of heat capacity measurements on our CrCl crys-tals are summarized in Figure 3. The data clearly show two thermal anomalies, a broad feature centered at 17.2 K and asharp lambda-like peak centered at 14.1 K. Data from twosamples are shown in Figure 3a and they are nearly identi-cal. These well-resolved anomalies are not reported in pre-vious heat capacity studies, which only observe a broad peaknear 17 K [25, 48]. The presence of two well-separated ther-mal signatures in the heat capacity data at low magnetic fieldsshown in Figure 3a strongly supports the interpretation of themagnetic data in terms of the evolution of magnetic order pro-posed by Kuhlow [34] and described above.The magnetic heat capacity c mag was estimated by sub-tracting a smooth curve fitted to the zero field data at tem-peratures between 2 and 50 K excluding the 7.5 −
33 K range.Figure 3c shows results for data collected in applied magneticfields of 0 and 5 kOe. Integrating c mag /T to extract the mag-netic entropy released up to 30 K gives about 2 J K − mol-Cr − at both fields. This is a small fraction of the expectedvalue of R ln(2S+1) = 11.5 J K − mol-Cr − , and suggests thatmost of the magnetic entropy is released as magnetic correla-tions develop well above the onset of long range order. This isconsistent with previous observations for isostructural CrBr and CrI [18, 49].Similarly small lambda anomalies have been reported at thelong range ordering temperatures in honeycomb layered com-pounds, for example MnPS [50, 51] and BaCo (AsO ) [52],in which magnetic fluctuations are expected to be responsiblefor the “missing” entropy. Development of these fluctuationsproduces a very broad contribution to the temperature depen-dence of the heat capacity extending to well above the order-ing temperature. Thus, while significant magnetic fluctuationsare expected to be present in CrCl , they are likely not the ori-gin of the ferromagnetic-like response seen just above 14 K,since a relatively sharp thermal anomaly is seen at the onsetof that behavior.To further probe the nature of the magnetic phase transi-tions, heat capacity data were collected in applied magneticfields (normal to the CrCl layers) and the data are presentedin Figure 3b. For small applied magnetic fields, up to 2 kOe,the feature near 17 K is nearly unchanged while the featureat 14 K is suppressed in magnitude and temperature. At ap-plied fields of 5 kOe and higher the low temperature feature iscompletely suppressed and the 17 K feature begins to broadenand move to higher temperature. The latter behavior is typi-cal of heat capacity anomalies associated with ferromagneticorder, which is reinforced by an applied magnetic field. Theheat capacity anomaly at 14 K is suppressed with field muchmore rapidly than is seen in typical antiferromagnets. In thiscase, such behavior can be attributed to the competing ferro-magnetic order at low applied fields in this weakly anisotropicmagnetic system.Two heat capacity anomalies have been observed in datafrom the closely related compound RuCl , and have been as-sociated with different types of magnetic order occurring indifferent parts of the sample that have different crystal struc-tures or stacking fault densities [53, 54]. Several observationssuggest that this is not the case for the CrCl data shown inFig. 3. First, identical behavior is observed in two samplesselected from separate growths (Fig. 3a). Second, the evo-
10 15 20 25 301.01.52.02.53.03.5 10 15 20 25 3010 15 20 25 301.01.52.02.53.0 5 10 15 20 25 300.00.10.20.3 (b) T (K) H = 0500 Oe1 kOe2 kOe c P ( J K - m o l - a t. - ) T (K) H = 05 kOe10 kOe20 kOe (a) CrCl , H = 0 sample 1 sample 2 c P ( J K - m o l - a t. - ) c P ( J K - m o l - a t. - ) T (K) H = 0 5 kOe c m ag / T ( J K - m o l - C r - ) T (K) 012 (c) S m ag ( J K - m o l - C r - ) FIG. 3. Heat capacity of CrCl crystals. (a) Data collected on twodifferent samples near the magnetic ordering, with position of thetwo observed peaks noted. Data from 2 to 300 K are shown in theinset. (b) Magnetic field dependence of the heat capacity at low fields(left) and higher fields (right). The field was applied out of the plane.(c) Estimated magnetic heat capacity plotted as c mag /T (symbols)determined for data collected in zero field and at 20 kOe, and theassociated magnetic entropies (lines). lution of the two heat capacity anomalies with applied fieldare coupled as described above. Third, the magnetization data(Fig. 2c) show that the FM-like behavior onsetting at 17 Kvanishes at the 14 K transition indicating that the magneticbehavior of the entire sample is affected. Fourth, the ferro-magnetic in-plane magnetic structure of CrCl should resultin less sensitivity to stacking faults than the more complexzig-zag antiferromagnetic order in RuCl .Using heat capacity data like that shown in Figure 3b, H ≥ 3 kOe H = 0 H ≥ 6 kOe (b)(a) FIG. 4. (a) Magnetic phase diagram of CrCl crystals. H is the ap-plied external field, directed out of the plane of the Cr layers. Thepoints were determined from heat capacity measurements like thoseshown in Figure 3b. PM = paramagnetic, AFM = antiferromagnetic,“FM” = ferromagnetic-like. (b) Magnetic structures of CrCl acces-sible with relatively small applied magnetic fields. where the local maxima can be easily identified and tracked asthe applied magnetic field is changed, the magnetic phase di-agram for CrCl shown in Figure 4 can be constructed. Threeregions are delineated: (1) the paramagnetic (PM) phase athigh temperatures and low fields, (2) the antiferromagnetic(AFM) region where the magnetic moments are aligned fer-romagnetically within layers and the layers are stacked anti-ferromagnetically, and (3) a ferromagnetic-like phase (“FM”),which is either field polarized in the case of the high field re-gion or short ranged or low dimensional in the case of the lowfield region between the PM and AFM phases. Note that theboundaries are not as well defined as this depiction might sug-gest, especially at higher magnetic fields. C. Magnetic anisotropy and potential for monolayer andheterostructure studies
As noted above, the observed magnetic anisotropy in theordered state is small. Figure 2d shows the magnetic momentas a function of magnetic field measured at 2 K with the fieldin the plane and out of the plane. The out of plane data isshown both as a function of internal field (demag. corr.) andapplied field (no demag. corr.) and is consistent with the dataof Narath and Davis [36]. Demagnetization effects are sig-nificant as expected. An applied field of 6 kOe is required toessentially fully polarize the magnetization out of the plane,consistent with neutron diffraction results [26]. This corre-sponds to an internal field of only 2.5 kOe. Interestingly, thisis the same field required to polarize the magnetization in theplane. Since within each plane the moments are ferromagnet-ically aligned and lie in the plane, it is expected that polariza-tion out of the plane is realized through a coherent rotation ofmoments within each layer [34]. When the field is applied inthe plane, different field induced behaviors are expected de-pending on whether the field is parallel or perpendicular tothe moment direction. In the latter case, a coherent rotationoccurs, while in the former case a spin flop can be expectedto occur first. The sample used for the in plane measurementcomprised several thin crystals that were not co-aligned withrespect to the ab -plane, so the direction of the applied field rel-ative to the moment direction in the zero field magnetic struc-ture is not well defined. As a result the signature of the spinflop on the magnetization data is somewhat diluted, but it isstill observable in Figure 2d. The spin flop is seen to occurat a field between 100 and 200 Oe at T = 2 K, consistent withthe value of 163 Oe estimated from magneto-optical measure-ments at 7 K from which an in-plane anisotropy field of about10 Oe is determined [34]. This is small relative to the fieldrequired to rotate the moments out of the plane, suggesting anXY-Heisenberg description for the moments in CrCl .Note that the energies of the FM and AFM configurationsin Table I are the same within the precision of the calculations;the magnetically ordered structures are about 0.3 eV/atomlower in energy than the NM states in both the monoclinicand rhombohedral crystal structures in the vdW-DF-optb86bcalculations. This is similar to the 0.4 eV/atom stability foundin the calculations of Ref. 27. This appears consistent with theobservation that the moments can be fully polarized with rel-atively small applied fields. Note that spin-orbit coupling, akey source of magnetocrystalline anisotropy, is not includedin the calculations. However, this effect is expected to beweak in trivalent chromium with electronic configuration d and nearly octahedral coordination due to quenching of theorbital moment. Thus single ion anisotropy should be weakfor Cr, as was demonstrated recently for CrI by Lado andFern´andez-Rossier [28]. In that study, spin-orbit coupling onthe heavy iodine ions was found to contribute the majority ofthe anisotropy through Cr-I-Cr superexchange. In CrCl thiseffect is expected to be much weaker, since the spin-orbit cou-pling strength varies as the fourth power of the atomic number.Thus, spin-orbit coupling is expected to be negligible for bothelements in CrCl , and this is likely the reason for the muchsmaller anisotropy field observed in CrCl than CrI .The low magnetic anisotropy and ferromagnetic in-planeorder make CrCl potentially very attractive for van der Waalsheterostructure studies. Figure 4b shows the magnetic struc-ture of two adjacent layers of CrCl in zero field, a rela-tively small out-of-plane field, and a relatively small in-planefield. These distinct magnetic orderings would produce dis-tinct magnetic proximity effects on neighboring materials.Importantly, tuning among these and any intermediate mag-netic states should be possible, which would enable exquisitecontrol over interactions and associated functionalities whencoupled to appropriate electronic or optical materials within aheterostructured device. FIG. 5. (a) AFM micrograph showing several step edges on a cleavedsurface of a CrCl crystal. (b) Height profile across the step edge in-dicated by the red line in (a), with the CrCl layer spacing of 0.58 nmdetermined from the bulk crystal structure [37] indicated on the plot.(c) Optical micrograph of an ultrathin specimen cleaved from a bulkCrCl crystal. Regions of varying optical contrast are labeled bythe corresponding thickness in number of CrCl layers. A separatemonolayer specimen is shown in the inset. Finally, we show here that monolayer CrCl can indeed berealized by exfoliation of bulk crystals. Figure 5a shows anAFM image of a flake of CrCl on a SiO substrate. Sev-eral step edges are observed across the flake. Figure 5b showsthe height profile across an edge measured along the path in-dicated by the red line in Figure 5a. The single layer spac-ing in CrCl determined from the bulk crystal structure is c sin β = 0 . nm, indicated on the figure. The measured stepheight of ≈ . nm indicates that this step is one monolayerhigh. By correlating changes in optical contrast with the stepheight measured using AFM, optical contrast can be used toqualitatively assign layer number. An optical micrograph ofan ultrathin specimen cleaved from a bulk crystal is shown inFigure 5c on a 90 nm SiO substrate. Measured optical con-trast is used to identify the thicknesses of different regions,which is shown on the image in units of CrCl layers. Theinset shows a separate specimen determined to be one mono-layer thick. It is expected that the single-layer CrCl may dis-play ferromagnetism at low temperature, as observed in CrI [30] and as predicted by first principles calculations for all ofthe chromium trihalides [19, 20]. IV. SUMMARY AND CONCLUSIONS
We have presented a thorough investigation of the bulkproperties of the layered antiferromagnet CrCl . The mag-netic behavior of our crystals is in general agreement with lit-erature reports, indicating ferromagnetic correlations emerg-ing upon cooling before entering the long range antiferromag-netically ordered ground state. Low magnetic anisotropy isobserved in the ordered state. A spin flop is seen near 150 Oewhen the field is applied in plane, and fields of several kOeare sufficient to polarize the moments in any direction. Inaddition, we find that the magnetic susceptibility shows asmall anomaly at the crystallographic transition temperature,indicating some coupling of the magnetism to the lattice inthe paramagnetic state. Spin-lattice coupling is also appar-ent in our first principles calculations, in which the experi-mental structure is matched only when magnetism is includedin the calculations. Our heat capacity measurements confirmthe two-step nature of the magnetic ordering transition. Abroad feature appears near 17 K indicating the developmentof ferromagnetism and a sharp, lambda-like anomaly is seenat 14 K as the antiferromagnetic long range order forms. Theobserved evolution of the heat capacity with applied magneticfield supports this scenario, and allows the construction of themagnetic phase diagram for CrCl shown in Figure 4. Neu-tron scattering experiments would be highly desirable to gainfurther insight into the development of the magnetic order,specifically to elucidate the potential roles of magnetic fluc-tuations, short range order, or 2 dimensional order. We havedemonstrated that cleaving of CrCl crystals into stable mono- layer specimens is possible, and note several properties thatmake CrCl a promising material for incorporating magnetisminto van der Waals heterostructures at low temperatures: bulkcrystals are easily grown, stable in air, electrically insulating,and have magnetic order that can be manipulated with rela-tively low external fields. ACKNOWLEDGEMENTS
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