# Fileset [Cr2Ge2Te6_Manuscript_submit230607.pdf](https://mdr.nims.go.jp/filesets/effbcdfe-1d22-40cd-becb-b3811db14d58/download) ## Creator Han Wu, Jian-Xin Zhu, Lebing Chen, Matthew W. Butcher, Ziqin Yue, [Dongsheng Yuan](https://orcid.org/0000-0001-9650-2272), Yu He, Ji Seop Oh, Bin Gao, Jianwei Huang, Shan Wu, Cheng Gong, Yucheng Guo, Sung-Kwan Mo, Jonathan Denlinger, Donghui Lu, Makoto Hashimoto, Matthew B. Stone, Alexander I. Kolesnikov, Songxue Chi, Junichiro Kono, Andriy H. Nevidomskyy, Robert J. Birgeneau, Pengcheng Dai, Ming Yi ## Rights [In Copyright](http://rightsstatements.org/vocab/InC/1.0/) ## Other metadata [Two-step electronic response to magnetic ordering in a van der Waals ferromagnet](https://mdr.nims.go.jp/datasets/aee9ba7f-a703-40ec-8c1b-5034713d738a) ## Fulltext Two-Step Electronic Response to Magnetic Ordering in a van der Waals FerromagnetHan Wu,1 Jian-Xin Zhu,2, 3 Lebing Chen,4, 1 Matthew W Butcher,1 Ziqin Yue,1 Dongsheng Yuan,5, 6 Yu He,7 JiSeop Oh,1, 4 Jianwei Huang,1 Shan Wu,4 Cheng Gong,8 Sung-Kwan Mo,9 Jonathan Denlinger,9 DonghuiLu,10 Makoto Hashimoto,10 Matthew B. Stone,11 Alexander I. Kolesnikov,11 Songxue Chi,11 JunichiroKono,12, 13, 1, 14 Andriy H. Nevidomskyy,1 Robert J. Birgeneau,4, 5, 15 Pengcheng Dai,1 and Ming Yi1, ∗1Department of Physics and Astronomy and Rice Center for Quantum Materials, Rice University, Houston, TX, 77005 USA2Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA3Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA4Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA5Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA6National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan7Department of Applied Physics, Yale University, New Haven, CT 065118Department of Electrical and Computer Engineering and Quantum Technology Center,University of Maryland, College Park, Maryland 20742, USA9Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA10Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA11Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA12Department of Electrical and Computer Engineering, Rice University, Houston, Texas 77005, USA13Smalley-Curl Institute, Rice University, Houston, Texas, 77005, USA14Department of Material Science and NanoEngineering, Rice University, Houston, Texas 77005, USA15Department of Materials Science and Engineering, University of California, Berkeley, USA(Dated: June 8, 2023)The two-dimensional (2D) material Cr2Ge2Te6 is a member of the class of insulating van derWaals magnets. Here, using high resolution angle-resolved photoemission spectroscopy in a detailedtemperature dependence study, we identify a clear response of the electronic structure to a dimen-sional crossover in the form of two distinct temperature scales marking onsets of modifications inthe electronic structure. Specifically, we observe Te p-orbital-dominated bands to undergo changesat the Curie transition temperature TC while the Cr d-orbital-dominated bands begin evolving at ahigher temperature scale. Combined with neutron scattering, density functional theory calculations,and Monte Carlo simulations, we find that the electronic system can be consistently understood torespond sequentially to the distinct temperatures at which in-plane and out-of-plane spin correla-tions exceed a characteristic length scale. Our findings reveal the sensitivity of the orbital-selectiveelectronic structure for probing the dynamical evolution of local moment correlations in vdW insu-lating magnets.Exploring the magnetism in quasi-2D materials hasbeen a fascinating subject in quantum physics for morethan five decades. This field has received strong stimulifrom both the discovery of high temperature supercon-ductivity in the lamellar copper oxides in the late 1980sand, more recently, by studies of the ferromagnetism invan der Waals (vdW) materials [1–10]. The chromiumtellurides Cr2X2Te6 (X=Ge, Si and Sn) belong to a cate-gory of insulators with intrinsic long-range ferromagneticorder down to the 2D regime [6–17]. Cr2Ge2Te6, in par-ticular, exhibits ferromagnetism with a TC that rangesfrom 65 K in bulk to around 40 K when exfoliated downto bilayer flakes, with the easy axis along the c direc-tion [18–22]. The nature of the magnetism in two dimen-sions in the vdW magnets can be understood to origi-nate from the magnetic anisotropy that can counteractthe strong thermal fluctuations. A neutron scatteringstudy on Cr2Si2Te6 (TC= 35 K) has provided direct ev-idence on the development of the magnetic order, wherethe exchange interaction along the c direction is muchsmaller than that in the in-plane directions, and the dy-namic correlations can persist in the ab plane up to atleast 300 K [23]. Such an effective 3D to 2D dimensionalcrossover behavior of the magnetic order in Cr2Si2Te6has also been confirmed by spin correlation driven lat-tice distortions [24]. Electronically, these Cr-based vdWferromagnets are gapped at the Fermi level due to strongCoulomb repulsion [11, 15]. In contrast to the metal-lic FenGeTe2 (n=3-5) systems, Cr2Ge2Te6 as an insu-lating magnet with a simple magnetic order untangledwith other competing or intertwined electronic orders isan ideal platform to study the impact of low dimensionalmagnetism on the electronic degree of freedom.Here we report the observation of the electronic re-sponse to the development of the spin correlationsacross a wide range of temperatures in the vdW mag-net Cr2Ge2Te6 via angle-resolved photoemission spec-troscopy (ARPES). By mapping out the temperaturedependent band structure and the one-electron spectralevolution across TC , we observe two types of band evo-lutions. One group associated with Cr d orbitals thatexhibits a gradual shift with an onset temperature wellabove TC , and another associated with Te p orbitals thatrapidly shift near TC . From a combination of neutron2FIG. 1. Crystal structure, magnetization, and electronic structure of Cr2Ge2Te6. (a) Crystal structure. (b) Dilatometrymeasurement of the c-axis thermal coefficient α (upper) and magnetization (lower). (c) ARPES constant energy contoursmeasured in the FM phase at 40 K, with energy referenced to the valence band top (VBT). BZ centers and boundaries areshown, along with the polarization vector. (d) Spectral image along Γ-M-Γ-K-K as marked in (c). (e)-(f) DFT calculated bandstructures of the ferromagnetic Cr2Ge2Te6 projected onto the Cr-d (red) and Te-p (magenta) orbitals. (g) DFT calculationsfor the non-magnetic state without local moments.scattering, Monte Carlo simulations, and Density Func-tional Theory (DFT) calculations, we arrive at a holis-tic understanding of the sequential electronic responseas tracking the development of in-plane and out-of-planespin correlations. Due to the anisotropy in the in-planeand out-of-plane exchange couplings, the in-plane corre-lation length exceeds that of the lattice constant at atemperature roughly twice that of TC , while the out-of-plane spin correlation length reaches that of a lat-tice constant much closer to TC , affecting more signif-icantly the Te p orbitals through the Cr-Te-Cr superex-change interactions near TC . Our results provide a con-sistent understanding of the two-step evolution of theelectronic response to the interplay between local mo-ments in 2D magnets, and demonstrate the sensitivityof using orbital-dependent electronic structure to trackevolution of spin correlations in these vdW magnets.Cr2Ge2Te6 forms in the space group 148 (R̄3) in a lay-ered structure with weak vdW coupling between adjacentlayers (Fig. 1(a)). The lattice parameters at 15K deter-mined from neutron scattering are a = 6.832 Å and c =20.386 Å , consistent with previous reports [14, 15, 25].The magnetic anisotropy favors the easy axis to be alongthe c direction. As shown in Fig. 1(b), our field-cooledmagnetization measurements show a clear paramagnetic(PM) to ferromagnetic (FM) order transition at 65 K,in agreement with previous studies [14, 15]. In addition,the PM to FM transition can also be clearly observed inour dilatometry measurement of the c-axis thermal ex-pansion coefficient, α (Fig. 1b).Next, we present the ARPES measured electronicstructure in the FM phase. The electronic structure ofCr2Ge2Te6 mimics that of a semiconductor, with hole-like bands at the Γ points of the Brillouin zone (BZ)as the valence band top (VBT), consistent with previ-ous reports [14]. We reference the energy axis to theVBT. From the series of constant energy contours, theelectronic structure of the valence bands can be seen toevolve from point-like features at Γ to enlarged pockets atdeeper binding energy (Fig. 1(c)). This is corroboratedby dispersions measured along the Γ-M-Γ-K-K direction.Along this high symmetry direction, a series of highlydispersive valence bands are centered at the Γ point andmerge into relatively flat dispersions in the energy rangebetween -1.0 and -1.5 eV. From comparison to orbital-projected DFT calculations, the highly dispersive bandsnear the VBT in the FM state are dominated by theTe 5pz orbital (Fig. 1(f)), while the Cr 3d orbitals aremostly concentrated within the energy range between -1.0 eV to -1.5 eV. The overall electronic structure belowTC as shown in Fig. 1(d) is in qualitative agreement withthe DFT calculations (Fig. 1(e) and Fig. 1(f)).To pave the way for understanding the temperature-induced evolution of the electronic structure, we presenttemperature-dependent ARPES data in Fig. 2. Fromdispersions along the high-symmetry Γ-M-Γ direction3FIG. 2. Temperature evolution and analysis. (a) Raw spec-tral image and (b) its second energy derivative along Γ-M-Γmeasured at 45K (T < TC = 65 K). (c)-(d) Same as (a)-(b) but measured at 200K. (e)-(f) Fitted band position as afunction of temperature taken at energy/momentum pointsas labeled by unique markers in (a). The color of each fittedmarker represents the abruptness of change at TC , defined as∣∣∣∣ ∆ETc−Tlow∆ETc−Thigh∣∣∣∣ . All fitted points are shown in (a), while thosewith a temperature onset (T∗) well above TC are shown in (e)and those with changes at TC shown in (f). The inset in (e)shows the lattice a as a function of temperature adapted fromRef. [26]. The blue and red lines mark the two temperaturescales.measured at 45 K and 200 K, we observe that the in-sulating nature is persistent across TC (Fig. 2(a)-(d)),namely that an electronic gap remains. This is in dis-agreement with the non-magnetic DFT calculation (Fig.1(g)), which predicts a metallic state. As the Cr t2g statesare partially filled, this inconsistency suggests that localmoments likely survive well above TC into the param-agnetic phase, driving the system into a Mott insulatingstate, consistent with the previous report on its sistercompound Cr2Si2Te6 [23]. There are, nevertheless, ob-servable changes across the temperature range. The cur-vature of the α and β band tops, marked in pink andorange in Fig. 2(b), changes with temperature. Thelinear-like band, labeled as γ, disappears with temper-ature. Besides the overall changes of the α, β and γbands, all bands shift with temperature. To better un-derstand the evolution of the bands, we perform a de-tailed analysis of the energy distribution curves (EDCs)across the Γ-M-Γ cut by fitting and tracking the locationof the observable bands (see supplemental material (SM)at ARPES Measurements section and Fig. S1-3 for moredetails). All fitted bands and momentum points are la-beled by unique markers in Fig. 2(a). Interestingly, for allthe fittable bands, we can identify two temperature scaleswhere shifts in the band position onset, one at TC and theother (T∗) around 150 K. To better visualize each band’stendency to shift at the two onset temperatures, we takethe ratio of the band shift between TC and 200 K andbetween 50 K and TC ,∣∣∣ ∆ETc−Tlow∆ETc−Thigh∣∣∣ as the color scalefor each marker on each point. A larger value indicates agreater change of the band position at TC while a valuesmaller than 1 indicates a larger change at the highertemperature scale T∗. As a result, the changes that arestrongly correlated with TC have a cold color on thisscale reflecting a value above 2, and changes correlatedwith the higher temperature scale will have a warm colorreflecting a value below 1. Interestingly, most bands shiftgradually across TC except those near the VBT, wherethe changes occur primarily near TC . This is stronglycorrelated with the orbital character of the bands, withthose primarily associated with Cr 3d smoothly evolvingacross TC and those with Te 5p shifting abruptly acrossTC . To better demonstrate this distinct temperature be-havior, we plot the temperature-dependent shift for thosewith an onset primarily at T∗ in Fig. 2(e), and those withan onset primarily at TC in Fig. 2(f), all referenced tothe final band position at 200 K. The dichotomy of thetemperature behaviors is clearly contrasted.As there are no known phase transitions above TC ,the high temperature scale in the band evolution is likelyassociated with the response of the electronic structureto fluctuation effects associated with the FM order. InCr2Ge2Te6, it has been reported that the lattice pa-rameter a (inset in Fig. 2(e)) shows a negative ther-mal expansion with an onset temperature near 100 K,well above TC [26]. To investigate the direct impactof a temperature-dependent lattice change on the elec-tronic structure, we performed DFT calculations usingthe temperature-dependent lattice parameters refined at5 K, 70 K and 150 K by neutron scattering experiment(Fig. S6). However, both the direction and magni-tude of band shifts are not consistent with the observedband shifts, suggesting that the changes in the electronicstructure, particularly those that set in at high tempera-tures, cannot be directly accounted for the temperature-induced lattice change.To gain insights into the possible origin of the highertemperature band evolution, we consider that for a quasi-2D magnet, while the in-plane and out-of-plane spin cor-relations both diverge at the same rate near TC , the in-plane correlations, due to larger in-plane exchange inter-actions, would exceed several lattice constants at highertemperatures compared to that of the out-of-plane cor-relations, manifesting in a 2D to 3D crossover behav-ior, as has been reported for the iron-based supercon-4FIG. 3. Neutron scattering and Monte Carlo simulations.(a)-(b) Magnetic excitations measured via inelastic neutronscattering along [H H 0] and [0 0 L] as a function of temper-atures across TC , the solid lines are Gaussian fits. (c) Theelastic peak width of the (110) peak measured by neutrons;(d) The two-axis measurement at wavevector (1, 1, 3.43). (e)The simulated change in the in-plane ξ‖ and out-of-plane ξ⊥correlation lengths, in units of the nearest-neighbor latticespacing, as well as their ratio, as a function of temperature.The crossover scale T2D ∼ 2Tc when ξ‖ = 1. The horizontaldotted line is a guide to the eye denoting the nearest-neighborspacing with T2D indicated here as the point where ξ‖ beginsto exceed this distance.ductors [27]. In order to investigate this behavior, weprobed the magnetic correlations by neutron scattering.First, we observe no broadening of the (110) nuclear andmagnetic elastic peaks around TC (Fig. 3(c)). Second,we performed a two-axis experiment at (H,K,L)=(1, 1,3.43). The wave-vector-dependent magnetic susceptibil-ity is proportional to the signal integrated over the en-ergy transfer E=ki2−kf22mn, with mn being the mass of neu-tron [28]. This integration is achieved with triple-axisspectrometer by removing the analyzer to accept all neu-trons along the final wave vector kf , which was set ||c. If the magnetic fluctuation is 2D in the ab-plane, themagnetic scattering forms a ridge along the [1 1 L] direc-tion. Only at a particular L value, 3.43 in this case, canthe condition for the integration over the magnetic ridgebe met. Therefore, the two-axis experiment can probeinstantaneous spin correlations. No critical 2D diver-gence in the instantaneous correlations is observed at thiswavevector across TC , as expected since ultimately this isa 3D phase transition (Fig. 3(d)). Interestingly, previousexperiments report a set of critical exponents consistentwith those near a 3D tricritical point–a second order tofirst order crossover point [29, 30]. To further determinethe temperature dependent spin excitations across TC ,we performed inelastic neutron scattering experiments,where we measured the spin excitation spectrum at dif-ferent temperatures around TC . From Fig. 3(a) we seethat the in-plane spin excitations do not vanish up to75 K and independent measurements show that in-planespin excitations persist up to at least 150 K (see Fig. S4in SM), indicating the existence of short-range spin-spincorrelations above TC . For comparison, we measured theout-of-plane spin excitations (Fig. 3(b)), which shows adiffusive pattern instead of well-defined spin excitationsat 75K, confirming that the out-of-plane spin correlationlength drops below a lattice constant at temperaturesslightly above TC while the in-plane short-range orderpersists to temperatures well above TC . This behavior isconsistent with the expected development of spin corre-lations in quasi-2D magnets.To substantiate this understanding, we carried outclassical Monte Carlo simulations using a classicalHeisenberg model with the anisotropic exchange cou-plings from previous reports [2]. As shown in Fig. 3(e),while both the in-plane correlation length ξ‖ and the out-of-plane correlation length ξ⊥ diverge at TC , where theratio of ξ‖/ξ⊥ is constant, ξ‖ grows beyond the nearest-neighbor spacing (ξ > 1) at a temperature scale (T2D)much higher than that for the out-of-plane correlation.Hence we can understand that in the range TC T > TC , we sim-ulate the in-plane FM spin correlations via A-type AFMspin arrangement, where in-plane spins are co-aligned.The lowest temperature T < TC is the FM order whereall spins are aligned along the c direction. The orbitalprojected DFT calculations for these three different mod-els are plotted on top of the corresponding ARPES data(Fig. 4). For the lowest temperature phase (T < TC),the dip-like shape for the α and β band top and the linearγ branch in ARPES data are all reproduced by the DFTcalculations (Fig. 4(b),(e)). As the temperature risesabove TC (T2D > T > TC), the α and β band top evolveinto two hole-like bands centered at Γ. The β branchwith a larger slope and higher energy band top crosses5FIG. 4. Spin correlation model and DFT calculations. (a) Schematic for the temperature evolution of spin correlations. Startingwith no spin correlations at high temperatures, the in-plane correlations length exceeds the lattice constant first, followed by out-of-plane correlations length, leading to long range FM order at TC . (b)-(d) Second energy derivatives of ARPES spectra fromthe three temperature regimes, with eye guides for dominant spectral change. (e)-(g) Same spectra images with correspondingDFT calculations for FM, A-type AFM and G-type AFM to simulate the three regimes, respectively. The green and yellowlines represent the band structures contributed by Cr 3d and Te 5p projected orbitals, respectively.the other branch, consistent with the DFT calculations.When the temperature goes up to 200 K (T > T2D), theγ band disappears, again consistent with the disappear-ance of this feature in the DFT model. The consistencybetween the DFT calculations for the three models andthe measured temperature evolution of the band disper-sions indirectly confirms our understanding that the bandevolution manifests the response of the electronic bandstructure to the sequential development of spin correla-tions from 2D to 3D.Overall, supported by our combination of ARPES,neutron scattering, DFT calculations and Monte Carlosimulations, we come to a comprehensive understandingof the development of the FM order in Cr2Ge2Te6. Localmoments from Cr d orbitals appear at very high temper-atures, resulting in an electronically gapped system. Dueto the much larger exchange coupling in the in-plane di-rection, the correlation length in the in-plane directionexceeds that of a characteristic length scale first, caus-ing bands with predominantly Cr 3d character to startevolving well above TC . With further lowering of thetemperature, the out-of-plane correlation length reachesthe characteristic length scale near TC , and is manifestedmost strongly in the bands associated with Te pz orbitals,which play a critical role in bridging the magnetism alongthe c-direction via the Cr-Te-Cr superexchange interac-tions. The development of spin correlations is typicallyprobed by neutron scattering, which is limited to bulkcrystals and not applicable for exfoliated vdW flakes. Asa vdW system with a single untangled magnetic order,Cr2Ge2Te6 allows us to clearly demonstrate the sensi-tivity of using orbital-dependent electronic structure totrack and resolve the development of spin correlationsthrough the dimensional crossover of the magnetic orderin quasi-2D magnets. We anticipate that this sensitiv-ity can be potentially useful in probing the developmentof spin correlations in the few layer or even monolayerregime, and contribute to the understanding of low di-mensional magnetism in the wider class of vdW magnetswith more complex order parameters.ACKNOWLEDGMENTSThis research used resources of the Advanced LightSource, and the Stanford Synchrotron Radiation Light-source, both U.S. Department Of Energy (DOE) Officeof Science User Facilities under contract nos. DE-AC02-05CH11231 and AC02-76SF00515, respectively. RiceARPES work is supported by the U.S. DOE grant No.DE-SC0021421 and the Gordon and Betty Moore Foun-dation’s EPiQS Initiative through grant no. GBMF9470.The neutron scattering and single crystal synthesis workat Rice was supported by US NSF-DMR-2100741 andby the Robert A. Welch Foundation under Grant No.C-1839, respectively (P.D.). Work at University of Cal-ifornia, Berkeley, is funded by the U.S. Department ofEnergy, Office of Science, Office of Basic Energy Sci-ences, Materials Sciences and Engineering Division underContract No. DE-AC02-05-CH11231 (Quantum Materi-als program KC2202). Work at Los Alamos was carriedout under the auspices of the U.S. Department of En-ergy (DOE) National Nuclear Security Administration(NNSA) under Contract No. 89233218CNA000001, andwas supported by LANL LDRD Program and in part byCenter for Integrated Nanotechnologies, a DOE BES userfacility, in partnership with the LANL Institutional Com-puting Program for computational resources. A portionof this research used resources at the High Flux IsotopeReactor and Spallation Neutron Source, a DOE Officeof Science User Facility operated by the Oak Ridge Na-tional Laboratory. M.W.B. was funded by the Robert A.Welch Foundation grant no. C-1818. A.H.N. acknowl-edges the support of the National Science Foundation6grant no. 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