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[Tomo Higashihara](https://orcid.org/0009-0007-6718-6566), Ryotaro Asama, Ryoya Nakamura, [Mori Watanabe](https://orcid.org/0000-0003-0664-6323), [Nanami Tomoda](https://orcid.org/0000-0003-4273-7644), [Thomas Johannes Hasiweder](https://orcid.org/0000-0002-8421-1897), [Yuita Fujisawa](https://orcid.org/0000-0002-5436-0883), Yoshinori Okada, [Takuya Iwasaki](https://orcid.org/0000-0002-1103-2433), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Nan Jiang](https://orcid.org/0000-0002-5489-7410), [Yasuhiro Niimi](https://orcid.org/0000-0003-1659-0634)
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[Magnetotransport properties in van der Waals ](https://mdr.nims.go.jp/datasets/a0e045f1-1bcb-4377-8226-8cfb0a89649b)
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Magnetotransport properties in van der Waals $R{\rm Te}_3$ ($R$ = La, Ce, Tb)PHYSICAL REVIEW B 109, 134404 (2024)Editors’ SuggestionMagnetotransport properties in van der Waals RTe3 (R = La, Ce, Tb)Tomo Higashihara ,1 Ryotaro Asama,1 Ryoya Nakamura,1 Mori Watanabe ,1 Nanami Tomoda ,2Thomas Johannes Hasiweder ,2 Yuita Fujisawa ,2 Yoshinori Okada,2 Takuya Iwasaki ,3 Kenji Watanabe ,3Takashi Taniguchi ,3 Nan Jiang ,1,4,5,* and Yasuhiro Niimi 1,4,51Department of Physics, Graduate School of Science, Osaka University, Toyonaka 560-0043, Japan2Okinawa Institute of Science and Technology Graduate University, Okinawa 904-0495, Japan3National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan4Center for Spintronics Research Network, Osaka University, Toyonaka 560-8531, Japan5Institute for Open and Transdisciplinary Research Initiatives, Osaka University, Suita 565-0871, Japan(Received 19 January 2024; accepted 12 March 2024; published 2 April 2024)Rare-earth tritellurides are van der Waals antiferromagnets which have been attracting attention as materialsnot only with high mobility, but also with various states such as superconductivity under high pressure,incommensurate charge density wave (CDW) phase, and multiple antiferromagnetic phases. In this paper, weperform longitudinal resistivity and Hall resistivity measurements simultaneously in exfoliated RTe3 (R =La, Ce,Tb) thin film devices, in order to investigate the influence of magnetic ordering on transport properties in van derWaals magnetic materials. We obtain carrier mobility and concentration using a two-band model, and we observean increase in carrier mobility in the antiferromagnets CeTe3 and TbTe3 due to the magnetic transition. Especiallyin CeTe3, the carrier concentration changes drastically below the magnetic transition temperature, suggesting theinteraction between the CDW and antiferromagnetic phases. In addition, the analysis of the Shubnikov–de Haasoscillations in CeTe3 supports the possibility of Fermi surface modulation by magnetic ordering. This researchwill pave the way not only for spintronic devices that take advantage of high mobility, but also for the study ofthe correlation between CDW and magnetism states in low-dimensional materials.DOI: 10.1103/PhysRevB.109.134404I. INTRODUCTIONIn recent years, magnetic van der Waals (vdW) materialshave been attracting much attention due to motivation towardsnext-generation spintronic and twistronic devices. The easeof thin film fabrication down to a single atomic layer, alongwith the large degree of freedom in fabrication of high qualityheterostructures via the dry transfer techniques, has lead tofruitful reports of unique transport phenomena [1–7].Among these magnetic vdW materials, rare-earth tritel-lurides RTe3 (R =Y, La-Tm) have high electronic mobilities[8]. RTe3 has an orthorhombic crystal structure described bythe space group Cmcm as shown in Fig. 1(a). It consistsof R-Te slabs which are responsible for its magnetic prop-erties, sandwiched between two Te square-net sheets whichare responsible for the highly two-dimensional (2D) electrictransport [9,10]. The Te sheets are parallel to the a-c plane,and the out-of-plane direction of RTe3 is the b axis [9,11]. Theadjacent Te layers are coupled by weak vdW forces, whichallows fabrication of thin films by mechanical exfoliation. Thenesting of the Fermi surfaces (FSs) produced by the px and pzorbitals of Te atoms and the three-dimensional (3D) folding ofTe sheet stacking lead to the formation of one (R = Gd, Sm,and lighter) or two (R = Tm, Er, Ho, Dy, Tb) charge densitywave (CDW) states [12–15], which have been extensivelystudied in recent years. However, there are still only a few*nan.jiang@phys.sci.osaka-u.ac.jpreports that systematically study the effect of the magnetismorder on transport properties. Recent observations of quantumoscillations in several RTe3 systems have revealed that RTe3has small FS pockets, originating from the partially openedCDW gap, and exhibits highest mobility carriers among vdWmagnetic materials [8,16,17].Another interesting property of RTe3 is the interaction be-tween the CDW state and an antiferromagnetic (AFM) statethat appears at a sufficiently lower temperature than the Peierlstransition [18–20]. Although the CDW order often competeswith magnetic order [21], recent discoveries of CDW-AFMcoexistence [22,23] have led to an observation of unique trans-port phenomena such as the topological Hall effect [24].In this paper, we have systematically evaluated the effectof magnetic ordering on transport properties of RTe3 throughmagnetoresistance (MR) and Hall measurements for threematerials LaTe3, CeTe3, and TbTe3. We have derived car-rier mobility and concentration using a two-band model. Theevaluated carrier mobilities are comparable to some of theprevious studies [8,17,25]. In particular, by comparing the car-rier mobilities and concentrations of AFM CeTe3 and TbTe3with those of nonmagnetic LaTe3, we have obtained indica-tions of CDW and AFM ordering interactions via couplingof conduction electrons and magnetic moments, particularlylarger in CeTe3. This result is consistent with a previous re-port that discussed the 4 f -2p hybridization energy due to theCDW distortion of CeTe3 and TbTe3 [26]. Furthermore, in thepresent experiment, we observed Shubnikov–de Haas (SdH)oscillations as already reported in our previous study [16,27].2469-9950/2024/109(13)/134404(8) 134404-1 ©2024 American Physical Societyhttps://orcid.org/0009-0007-6718-6566https://orcid.org/0000-0003-0664-6323https://orcid.org/0000-0003-4273-7644https://orcid.org/0000-0002-8421-1897https://orcid.org/0000-0002-5436-0883https://orcid.org/0000-0002-1103-2433https://orcid.org/0000-0003-3701-8119https://orcid.org/0000-0002-1467-3105https://orcid.org/0000-0002-5489-7410https://orcid.org/0000-0003-1659-0634https://crossmark.crossref.org/dialog/?doi=10.1103/PhysRevB.109.134404&domain=pdf&date_stamp=2024-04-02https://doi.org/10.1103/PhysRevB.109.134404TOMO HIGASHIHARA et al. PHYSICAL REVIEW B 109, 134404 (2024)abcFIG. 1. (a) Crystal structure of RTe3. Black line rectangle andpurple sheets represent a unit cell and Te square-net sheets, respec-tively. (b) An optical microscope image of a LaTe3 thin film device.The scale bar corresponds to 20 µm. The purple and blue flakes areLaTe3 and hBN, respectively. (c) The temperature dependence ofthe electrical resistivity for LaTe3 (green dot), CeTe3 (blue dot), andTbTe3(red dot) devices.Together with the Hall measurement results, we show the pos-sibility of FS modulation caused by the magnetic transition.II. EXPERIMENTAL DETAILSSingle crystals of RTe3 were grown by a self-flux method[9,28,29]. The mixture of R and Te elements in a molar ratioof 1 : 30 was placed in an evacuated quartz tube. The ampulewas heated to approximately 900 ◦C and cooled to 500 ◦Cat a speed of 2 ◦C/h in a furnace. The RTe3 single crystalsand Te flux were separated by a centrifuge immediately afterremoving the ampule from the furnace. The x-ray diffractionconfirms RTe3 crystalline phases. Depending on the ionic ra-dius of R, the b-axis lattice constant is systematically changed:LaTe3 (26.22 Å), CeTe3 (26.02 Å), and TbTe3 (25.64 Å).To fabricate the device, Au/Ti (40 nm/5 nm) electrodepatterns were first deposited on a thermally oxidized siliconsubstrate. It should be noted that all the following fabricationprocesses were carried out inside a glovebox with an Ar purityof 99.9999% since RTe3 is extremely sensitive to ambientair [30]. To fabricate thin film devices from the bulk RTe3,we used the mechanical exfoliation technique using scotchtapes. The exfoliated flakes were transferred from scotch tapesto transparent polydimethylsiloxane polymers, and the RTe3flakes were released onto the prepatterned electrodes alignedunder an optical microscope. In addition, flakes were cappedwith high quality hexagonal boron nitride (hBN) to preventoxidation during taking devices from the glovebox and settingthem to the measurement system. To check the reproducibility,we fabricated at least two different devices for each RTe3. Themain results (obtained with no. 1) are shown in the main text,while the additional results (obtained with no. 2) are displayedin Supplemental Material [31]. For simplicity, we omit thedevice number in the main text.Figure 1(b) shows a typical device structure taken by anoptical microscope. The purple flake in the center is a 25-nm-thick LaTe3 film, while the blue area is the hBN filmcap. Electrical transport measurements were performed by theconventional four-probe method with a constant alternatingcurrent of 10 or 30 µA for all devices using a lock-in amplifier.The device was cooled with a variable temperature insert us-ing liquid 4He down to 1.7 K. The external magnetic field wasapplied using a superconducting magnet up to 8 T perpendicu-lar to the a-c plane. The thicknesses of all measured thin filmswere confirmed by using an atomic force microscope, whichwere 25, 24, and 47 nm for LaTe3, CeTe3, and TbTe3 devices,respectively. It should be noted that this device fabricationmethod cannot rule out the possibility of a finite strain dueto deformation induced in the thin-film devices. As detailedin the following section, however, the effect of such a strainwould be negligibly small on transport properties because wedid not observe a significant change in the magnetic transitiontemperature and the temperature dependence of the resistivity,compared to those measured with bulk samples [9,11,25,32].III. RESULTS AND DISCUSSIONSA. Longitudinal and Hall resistivitiesThe temperature dependence of the longitudinal resistiv-ity ρxx for LaTe3, CeTe3, and TbTe3 devices are shown inFig. 1(c). All these show metallic temperature dependencieseven below the CDW transition. This is due to the partial gapopening, caused by the imperfect nesting of the FS [13]. Theresidual resistivity ratios (RRRs) [= ρxx(290 K)/ρxx(3.0 K)],which are indicators of the purity of the devices, were 98 forLaTe3, 17 for CeTe3, and 45 for TbTe3. These values are largerthan previous studies for TbTe3 films [33] and comparableto our previous study for CeTe3 [16]. Although no previousstudies have been reported for LaTe3 thin films, the RRRvalues are comparable to the bulk counterpart [25].We next performed longitudinal MR and Hall resistancemeasurements at various temperatures from around 100 Kdown to 1.7 K. The longitudinal and Hall resistances aresymmetrized and antisymmetrized with respect to the mag-netic field to extract only their respective components. InFigs. 2(a)–2(c), we show the magnetic field dependence ofthe MR ratio defined as �ρxx/ρ0 ≡ ρxx (Hz )−ρxx (Hz=0)ρxx (Hz=0) for (a)LaTe3, (b) CeTe3, and (c) TbTe3 devices. For all the devices,a nonsaturating and large positive MR were observed. Theseare characteristics of materials with high carrier mobilities μ(μ is larger than ≈103 cm2/V s). Especially for LaTe3, theMR ratio reached up to 2250% at 2.7 K, which is larger thanits bulk counterpart by a rough factor of 3 [25]. This is likelydue to the increase in the crystallinity of the thin film device,134404-2MAGNETOTRANSPORT PROPERTIES IN VAN DER WAALS … PHYSICAL REVIEW B 109, 134404 (2024)FIG. 2. (a)–(c) Longitudinal magnetoresistance (MR) ratio �ρxx/ρ0 and (d)–(f) Hall resistivity ρyx under a magnetic field up to 8 Tmeasured at several temperatures for LaTe3, CeTe3, and TbTe3 devices, respectively.compared to the bulk counterpart, by exfoliation and selectionof clean flakes. In contrast to the parabolic field dependenceof MR due to the usual Lorentz force contribution in CeTe3,linear MRs were observed for both LaTe3 and TbTe3 at lowenough temperatures. These linear MRs were also observedin previous studies of bulk LaTe3 and thin film TbTe3 de-vices [25,33–35]. Furthermore, in the AFM phase of TbTe3below the Néel temperature (TN1 ≈ 6.6 K), the slope of MR ischanged at μ0H = 3–4 T [see T = 1.7 K in Fig. 2(c)]. Thismagnetic field of the change of the MR slope is close to thephase transition magnetic field reported in the previous study[32]. It seems that the AFM structure has a notable effect onthe electrical transport properties.The Hall resistance, which was taken simultaneously withthe MR, is shown as the Hall resistivity ρyx in Figs. 2(d)–2(f) for (d) LaTe3, (e) CeTe3, and (f) TbTe3 devices. Allthe curves show nonlinear external field dependencies. Thisbehavior was reproducible for all of LaTe3, CeTe3, and TbTe3devices, suggesting that these materials possess multiple car-riers. From the Hall curves, we derived the carrier mobilitiesand concentrations, which will be detailed in the next sub-section. It should be noted that quantum oscillations wereobserved in the case of CeTe3 both in the longitudinal andHall resistivities. The observation of quantum oscillation inthe longitudinal MR is consistent with our previous studies[16,27], while the emergence of the quantum oscillation inthe Hall effect can be attributed to the multicarrier effect [36].The analysis of this SdH signal will be discussed in Sec. III C.B. Effect of magnetic order on the electrical transportIn order to investigate the effect of magnetic order onthe electrical transport, we have analyzed the temperaturedependence of the zero field longitudinal resistivity, car-rier mobility, carrier concentration, and MR ratio for eachmaterial as shown in Fig. 3. First, we discuss the temper-ature dependence of the longitudinal resistivity in the lowtemperature region. In CeTe3 and TbTe3 which are knownto have a multi-AFM phase, reductions in the zero fieldresistivity were observed below the first magnetic transitiontemperature T CeTe3N1 ≈ 3.0 K and T TbTe3N1 ≈ 6.6 K, respectively[11,32]. Enlarged views of the low temperature region ofthe electrical resistivities of CeTe3 and TbTe3 with magnetictransition points are shown in Figs. 3(b) and 3(c), respectively.The electrical resistivity of nonmagnetic LaTe3 is shown inFig. 3(a) for comparison, where no characteristic reductionwas observed. These reductions in ρxx for CeTe3 and TbTe3can be attributed to the suppression of magnetic scatteringby magnetic ordering. It is clear that this effect is especiallypronounced in CeTe3 compared to TbTe3. This result indicatesthat the Ruderman-Kittel-Kasuya-Yosida (RKKY) interactionplays an important role in the magnetism and transport prop-erties in CeTe3. In fact, the electrical resistivity of CeTe3 alsohas a small bump at around 5 K as shown in Fig. 3(b)[16].This is likely due to a weak Kondo effect [9], which is furthersupportive evidence of the AFM coupling in the conductionelectron of CeTe3.Next we discuss the temperature dependence of the car-rier mobility and concentration calculated from the MR andthe Hall resistivity. Assuming the presence of independentelectron and hole carriers, we have considered the conven-tional two-band model for analysis and used the followingequations:σxx = enhμh11 + (μhB)2+ eneμe11 + (μeB)2, (1)σxy =(nhμ2h11 + (μhB)2− neμ2e11 + (μeB)2)eB, (2)where σxx = ρxxρ2xx+ρ2yxand σxy = ρyxρ2xx+ρ2yxare the longitudinal andHall conductivities, respectively, e is the elementary charge,B is the applied magnetic field, nh and ne are the carrierconcentrations of hole and electron, and μh and μe are thecarrier mobilities of hole and electron, respectively. Here wehave assumed ρxx = ρyy and used Onsager’s reciprocal re-lation ρxy = −ρyx to derive the electrical conductivity fromthe electrical resistivity. Carrier mobilities and concentrations134404-3TOMO HIGASHIHARA et al. PHYSICAL REVIEW B 109, 134404 (2024)FIG. 3. (a)–(c) The low temperature portions of the electrical resistivity of LaTe3, CeTe3, and TbTe3 devices, respectively. (d)–(f) Thecarrier mobilities and (g)–(i) the carrier concentrations of electron and hole obtained by the two-band model. The error bar added in thefigure indicates the standard deviation errors computed by covariance matrix. (j)–(l) The temperature dependence of the MR ratio at 8 T.have been determined by fitting the measured data by thetwo-band model in Eqs. (1) and (2) simultaneously.Although the equations have been well fitted in most tem-peratures, some discrepancy from the data has been observedat the lower temperatures, as shown in Fig. S1 (in Supple-mental Material [31]). This could be due to the followingthree main reasons. The first reason is the linear MR; whilethe linear MR was clearly observed, the MR described by theusual two-band model is parabolic in the magnetic field, lead-ing to a difference in fitting. The second possibility would beanisotropy in the electrical resistivity; the assumption ρxx =ρyy was used in the conversion from electrical resistivity toconductivity, but it is known that the RTe3 system exhibitssignificant anisotropy of electrical resistivity with respect tothe crystal axis below the CDW transition temperature. Infact, enhancement of the anisotropy at lower temperatures hasbeen reported in some RTe3 materials, [32,37], which could bethe cause of errors in the fitting. The third possibility wouldbe multicarriers; although two-band carriers are consideredhere for simplicity, it is likely that more types of carrierscontribute to transport in reality, and the equation for the two-band model may not reflect the actual situation. In fact, in theRTe3 system, the existence of more than two carriers has beensuggested from measurements of SdH quantum oscillations[8,17]. In addition, it is possible that the transport propertiesunique to the magnetic structure, such as the anomalous Halleffect, may also contribute to the discrepancy.The results of carrier mobilities and concentrations forelectron and hole obtained by the two-band model are shownin Figs. 3(d)–3(f) and 3(g)–3(i) for LaTe3, CeTe3, and TbTe3134404-4MAGNETOTRANSPORT PROPERTIES IN VAN DER WAALS … PHYSICAL REVIEW B 109, 134404 (2024)devices, respectively. The electron mobility of LaTe3 is μe =12 000 cm2/V s at 2.7 K, which is notably high, and the orderof magnitude is comparable to that of GdTe3 [8], NdTe3 [17],and bulk LaTe3 [25], which were reported as high mobilityRTe3 systems. The high mobility common to the RTe3 systemoriginates from the small pocket created by the reconstructionof the FS due to the CDW ordering [38]. In terms of the effectof the magnetic ordering, enhancements of carrier mobilitiesbelow TN1 are observed for AFM TbTe3 and CeTe3. As forCeTe3, the carrier mobilities reach up to a total enhancementof 44%. The only other RTe3 material reported to have sucha large mobility enhancement below its magnetic transitiontemperature is NdTe3 [17]. Similar to the temperature depen-dence of longitudinal resistivity, the origin of this behaviorwould be the enhancement of electron relaxation time due tothe suppression of magnetic scattering by magnetic ordering.The effect of magnetic ordering is also observed in thetemperature dependence of the MR ratio. In Figs. 3(j)–3(l),we have plotted the temperature dependence of the MR ratioat 8 T for (j) LaTe3, (k) CeTe3, and (l) TbTe3 devices. While agradual increase in the MR ratio with decreasing temperatureis observed for the nonmagnetic LaTe3, discontinuous en-hancements of the MR ratio below the first magnetic transitiontemperature are observed for CeTe3 and TbTe3. In particular,a sharp increase of 111% is observed for CeTe3 below TN1.These enhancements of the MR ratio can be explained by theincrease in the carrier mobility below TN1. On the other hand,we did not observe any negative MR which is often observedin typical magnetic materials. This is likely attributed to thefact that the positive MR effect caused by high carrier mobilityoverwhelms the negative MR component.Let us mention the change in the temperature dependenceof carrier concentration below and above TN1 observed forCeTe3, as shown in Fig. 3(h). Although the transport phenom-ena discussed in this section can be attributed to the scatteringby the fluctuating magnetic moments, the change in nh andne cannot be explained by the same mechanism. Usually,magnetic transition is not accompanied by a drastic change inits carrier concentration. Rather, we believe that modulation ofthe CDW, which is closely related to the band structure of thematerial, could be the direct cause of the carrier concentrationtemperature dependence. Given that this behavior occurs atTN1, the data imply that there is some coupling of the CDWand magnetic order. As far as we know, neutron diffractionexperiments have been conducted for TbTe3 [18,19], wherein addition to the commensurate AFM and CDW orders,new magnetic peaks were observed whose propagation vectorequals the sum of the AFM and CDW propagation vectors,revealing a coupling between the orders. Although there is noevidence for CeTe3, the magnetic ordering in CeTe3 may mod-ulate the CDW state, resulting in a change of the temperaturedependence in nh and ne. It is also interesting to note that thiseffect is pronounced in CeTe3, indicating that the RKKY inter-action, which is more significant in CeTe3, is a possible originof the coupling between the CDW and the magnetic order.C. Shubnikov–de Haas oscillationsSdH oscillations have been reported in several RTe3 ma-terials [8,17,39,40], where the structure of the FS plays animportant role [13,38]. In this subsection, we discuss the effectof magnetic order on the SdH oscillations. As mentioned inSec. III A, in CeTe3, SdH oscillations were observed in theMR, i.e., ρxx(B) [see Fig. 2(b)]. In addition, quantum oscil-lations with the same period as the SdH oscillations werealso observed in the Hall resistivity component, i.e., ρyx(B)[see Fig. 2(e)]. In general, SdH oscillations are discussed forρxx(B). It is known that the SdH oscillations are also reflectedin ρyx(B) for multicarrier materials [36]. The amplitude of theoscillations in ρyx(B) becomes larger than that in ρxx(B). Thus,we have used the oscillatory component of ρyx(B) for thefollowing analysis of the quantum oscillations, but as shownin Fig. S3 (in Supplemental Material [31]), we have obtainedessentially the same result in ρxx(B).In general, the SdH oscillation is described by the fol-lowing Lifshitz-Kosevich (L-K) formula with �ρ ′ as theoscillating component of resistance, given as�ρ ′ ∝ λ(B)Tsinh {λ(B)T }e−λ(B)TD cos{2π(FB− 12+ β + δ)},(3)where TD is the Dingle temperature which corresponds to theblurring of the Landau level, and F is the frequency of the SdHoscillation. 2πβ is the Berry phase and δ is the phase shift thattakes zero in 2D and ± 18 in 3D systems. λ(B) is defined byλ(B) = 2π2kBm∗/(h̄eB), where kB is the Boltzmann constant,h̄ is the reduced Planck constant, and m∗ is the effectivecyclotron mass.First, we analyze the SdH frequency in order to determinethe FS structure responsible for the oscillation, using the equa-tion S = 2πeFh̄ where S is the extremal surface area of theFS pocket. For the analysis, the background resistivity ρBGyxwas first subtracted from the Hall resistivity in the magneticfield range from 5 to 8 T and the oscillatory component�ρ ′yx = ρyx − ρBGyx was obtained as shown in Fig. 4(a). Wethen performed the fast Fourier transformation (FFT) to ex-tract the oscillation frequency. A single oscillation frequencyof F (α) = 31.8 T was observed as shown in Fig. 4(b), whichis consistent with our previous study [16]. Given that the 3Dunit cell of RTe3 is equal to the unit cell of a single Te squarenet rotated by 45◦ and multiplied by 2 [41], the size of theBrillouin zone of CeTe3 can be calculated as SBZ = 122πa2πc ,where a = 4.384 Å, c = 4.403 Å [42]. Therefore, we de-termine that the measured SdH oscillation originates from aFS pocket equivalent to 0.30% of the entire Brillouin zone,which is likely the small FS pocket frequently labeled asthe α pocket in RTe3. This pocket arises due to the recon-struction of the FS under the CDW ordering, and was alsoobserved in other RTe3 [0.28% for LaTe3 [40], 0.27% forGdTe3 [8], 0.2% for NdTe3 [17], and 0.16±0.1% for NdTe3measured by angle-resolved photoemission spectroscopy(ARPES) [38].Next, we discuss the temperature dependence of the SdHoscillation amplitude, from which the conduction electroneffective mass and mobility can be evaluated. The SdH oscil-lation amplitude has a characteristic temperature dependencethat is proportional to λ(B0 )Tsinh{λ(B0 )T } , where B0 is the mean valueof the analyzed magnetic field range. By fitting the FFT134404-5TOMO HIGASHIHARA et al. PHYSICAL REVIEW B 109, 134404 (2024)FIG. 4. (a) SdH oscillation component of CeTe3 plotted againstthe reciprocal of the applied magnetic field for several differenttemperatures. The inverted triangle is an eye guide to show shiftsin the positions of the oscillation peaks. (b) The fast Fourier trans-formation (FFT) of the oscillation component for several differenttemperatures. The correspondence between color and temperature isthe same as in (a).amplitude with the above function as shown in Fig. 5(a),the effective mass m∗ can be obtained. We note that datafrom multiple samples are plotted in Fig. 5(a), which arenormalized by the FFT amplitude at 5 K. The results are listedin Table I. Above TN1, the effective mass is 0.042me, whichis comparable to our previous work [16]. A large deviationfrom the L-K formula has been observed below TN1. Thus,we performed separate fits for the effective mass above andbelow TN1, resulting in a large enhancement of effective massTABLE I. Comparison of effective cyclotron mass, Dingle tem-perature, scattering relaxation time, and carrier mobility for PM andAFM regions of CeTe3.Region m∗/me TD (K) τq (s) μq (cm2/V s)PM (10 K) 0.042 48.3 2.51×10−14 1056AFM (1.7 K) 0.37 2.53 4.80×10−13 2266FIG. 5. (a) The temperature dependence of the FFT amplitudesat 31.8 T with fitting curves of the L-K formula. (b) The temperaturedependence of β + δ. The error bar added in the figure indicates thestandard deviation errors computed by covariance matrix.(0.37me) below TN1. The quantum lifetime τq = h̄/(2πkBTD)and the carrier mobility μq = eh̄/(2πkBm∗TD) can also beevaluated as listed in Table I. We have observed an enhance-ment in all m∗, τq, and μq below TN1. It is important tonote that these enhancements provide further supportive ev-idence of our discussion based on the MR and Hall resistivityin Sec. III B. The enhancement of m∗ below TN1 is mostlikely attributed to some modulation of the band structurenear the FS from the magnetic order, which is consistentwith our analysis of the temperature dependence of the carrierconcentrations. The enhancement of carrier mobility is alsoconsistent with the temperature dependence of longitudinaland Hall resistivities. It should originate from the increase inrelaxation time of the carriers as the fluctuations of magneticmoments are suppressed below TN1.Finally, we point out the β + δ term in Eq. (3). As men-tioned, the β and δ terms correspond to the Berry curvatureand the dimension of the FS pocket, respectively. The temper-ature dependence of β + δ is shown in Fig. 5(b), where a peakstructure is observed at TN1. This phase shift can also be seenin the shift of the position of the oscillation peaks shown inFig. 4(a). Although further study is required to elucidate theorigin of this behavior, it is another supportive result whichindicates the modulation of the band structure near the FSaround TN1, since this quantity should be sensitive to the FStopology.134404-6MAGNETOTRANSPORT PROPERTIES IN VAN DER WAALS … PHYSICAL REVIEW B 109, 134404 (2024)IV. CONCLUSIONIn this paper, we have focused on RTe3, a van der Waalsmaterial with high mobility. We performed systematic lon-gitudinal resistivity and Hall resistivity measurements onsingle-crystal thin films of nonmagnetic LaTe3 and antifer-romagnetic CeTe3 and TbTe3. We have observed a peculiarlinear magnetoresistance in LaTe3 and TbTe3, the magneticfield dependence of nonlinear Hall resistance in all samples,and a SdH oscillation in CeTe3. Carrier concentration andmobility are derived using a two-band model. Both CeTe3and TbTe3 show decreases in longitudinal resistivity and in-creases in carrier mobility below TN1. Combined with thequantum mobility obtained from the SdH oscillation in CeTe3,we conclude that the behavior is caused by the suppressionof magnetic scattering due to the magnetic ordering. Fur-thermore, a change in the temperature dependence of thecarrier concentration is also observed in CeTe3 below andabove its magnetic transition temperature. Combined withthe results of L-K formula fitting, we have found that theband structure near the FS may be modulated by the mag-netic ordering. This indicates that the magnetic ordering andCDW ordering are coupled via the RKKY interaction. Itis expected that further ARPES experiments before and af-ter the magnetic transition will be performed to search forinteresting properties in the system where CDW and mag-netic order are strongly coupled. Our results demonstratenot only possibilities of two-dimensional devices with highmobility and magnetic order, but also a testbed towardsthe understanding of new phenomena due to the coexis-tence of magnetic order and CDW order in low-dimensionalmaterials.The data that support the findings of this paper are availablefrom the corresponding author upon reasonable request.ACKNOWLEDGMENTSWe thank S. Nakaharai for his technical support and fruitfuldiscussions. 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