High magnetic field induced crossover from the Kondo to Fermi liquid behavior in 1T-VTe_{2} single crystals
Xiaxin Ding, Jie Xing, Gang Li, Luis Balicas, Krzysztof Gofryk, Hai-Hu Wen
HHigh magnetic field induced crossover from the Kondo to Fermi liquid behavior in1 T -VTe single crystals Xiaxin Ding , , ∗ Jie Xing , Gang Li , Luis Balicas , Krzysztof Gofryk , and Hai-Hu Wen Idaho National Laboratory, Idaho Falls, Idaho, 83402, USA. Center for Superconducting Physics and Materials,National Laboratory of Solid State Microstructures and Departmentof Physics, Nanjing University, Nanjing 210093, China and National High Magnetic Field Laboratory, Florida State University, Tallahassee-FL 32310, USA
The magnetic and magnetotransport properties of metallic 1 T -VTe single crystals were investi-gated at temperatures from 1.3 to 300 K and in magnetic fields up to 35 T. Upon applying a highmagnetic field, it is found that the electrical resistivity displays a crossover from the logarithmicdivergence of the single-impurity Kondo effect to the Fermi liquid behavior at low temperatures.The Brillouin scale of the negative magnetoresistivity above the Kondo temperature T K = 12 Kindicates that the Kondo features originate from intercalated V ions, with S = 1/2. Both magneticsusceptibility and Hall effect show an anomaly around T K . By using the modified Hamann expres-sion we successfully describe the temperature-dependent resistivity under various magnetic fields,which shows the characteristic peak below T K due to the splitting of the Kondo resonance. I. INTRODUCTION
Layered transition metal dichalcogenides (TMDCs)have attracted enormous attention because they exhibita rich variety of physical properties and a striking poten-tial for applications [1–3]. The wide range of transportproperties of bulk TMDCs varies from conventional su-perconductivity [4] via charge density wave (CDW) [5]to exceedingly large positive magnetoresistivity (MR) [6]at low temperatures. Furthermore, layered TMDCs areeasily intercalated with metallic ions due to their lay-ered structures [7]. For example, Cu intercalated TiSe exhibits a CDW to superconducting transition upon dop-ing [8]. When magnetic 3 d transition metals (Co, Ni andFe) are intercalated into TiSe , the Kondo effect is in-duced in the dilute limit [9]. Similarly, the Kondo effecthas been reported in bulk VSe , probably due to the in-terlayer V ions [10]. In addition, TMDCs are ideal forstudying the interplay between electronic properties andcrystalline dimensionality. With the development of ex-foliation and epitaxial techniques, monolayered TMDCscould be successfully produced demonstrating distinctproperties from their bulk counterparts. In contrast toparamagnetism in bulk VSe , ferromagnetism is observedin monolayer VSe at room temperature [11]. In mono-layer VTe , which is isostructural to VSe , the suppres-sion of a CDW transition is a matter of debate [12–15].In bulk VTe , a CDW transition occurs upon coolingacross 480 K, which is accompanied by a structural phasetransition from the high-temperature trigonal phase (1 T structure) to the low-temperature monoclinic phase [16–19]. Using the vapor transport method, the single crys-talline VTe has a monoclinic structure corresponding tothe low-temperature polymorph [20]. By contrast, high-temperature polymorph 1 T -VTe single crystals can be ∗ [email protected] successfully grown via the molten-salt method. Further-more, this reveals characteristics of the Kondo effect atlow temperatures [21], which was later found in 1 T -VTe nanoplates [22].In this manuscript, we study the evolution of theKondo effect under high magnetic fields in 1 T -VTe sin-gle crystals. The Kondo effect, discovered in 1930 byMeissner and Voigt [23] and then explained by Kondo in1964 [24], has recently generated recently renewed inter-est due to progress in nanotechnology [25, 26]. In con-densed matter physics, it also provides clues to allow un-derstanding of the electronic properties of various strangemetals, such as superconductors and heavy-fermion ma-terials. The spin-exchange process between localized im-purities and itinerant electrons of the metallic host gener-ates a new state at the Fermi level, known as the Kondoresonance or Abrikosov-Suhl resonance peak [27]. Thefirst hint of this new state manifests itself as an anoma-lous upturn in the resistivity below the Kondo temper-ature T K , which is the energy scale dependent on spin-exchange coupling and limiting the validity of the Kondoeffect. Specifically, the temperature-dependent resistiv-ity ρ ( T ) of the Kondo system shows the approximatelogarithmic increase with decreasing temperature in asmall range below T K and T Fermi liquid behavior for T (cid:28) T K . Moreover, the splitting of the Kondo reso-nance under the applied magnetic field correlates with acharacteristic peak in the temperature and magnetic fielddependence of the resistivity ρ ( T, B ). These transportproperties for a single Kondo impurity can be calculatedby a nonperturbative approach, such as the numericalrenormalization group (NRG) method [28, 29]. However,despite all of these advances, the lack of a systematic un-derstanding remains on the low-temperature behavior ofthe electrical resistivity, especially in the presence of highmagnetic fields [30].Here, we systematically study the transport and mag-netic properties of 1 T -VTe single crystals under highmagnetic fields. The temperature and magnetic field de- a r X i v : . [ c ond - m a t . s t r- e l ] F e b pendence of the magnetization, resistivity, and Hall ef-fect reveal Kondo effect characteristics with T K = 12 K.Both magnetic susceptibility and MR measurements de-termined that the local magnetic moments arise from theintercalated V ions with S = 1/2. The characteristicpeaks in ρ ( T, B ) are observed below T K and can be ana-lyzed by a modified Hamann expression. By applying amagnetic field up to 35 T, the Kondo effect is graduallysuppressed, and the Fermi liquid behavior emerges at lowtemperatures. II. EXPERIMENTAL DETAILS T -VTe single crystals were grown by the flux methodusing KCl as the flux. First, we prepared the polycrys-talline samples by a solid-state reaction method, with Vpowders (purity 99.5%, Alfa Aesar) and Te grains (purity99.5%, Alfa Aesar) in the ratio of 1 : 2. The mixture wascompressed into a pellet, then loaded into an aluminacrucible and sealed in an evacuated quartz tube, subse-quently heated up to 750 ◦ C for 20 h. Second, powderswith a molar ratio of KCl : VTe = 4 : 1 were heatedup to 950 ◦ C for 2 days, followed by cooling down to800 ◦ C at a rate of 1 ◦ C/h. Finally, we obtained sin-gle crystals with lateral sizes of 2-4 mm and thickness ofabout 10-50 µ m by dissolving the flux in deionized water.The samples are stable in water and display silver color.All the weighing, mixing, grinding and pressing proce-dures were finished in a glovebox under Ar atmosphere.X-ray diffraction (XRD) measurements were performedusing a Bruker D8 Advanced diffractometer with Cu K α radiation. The energy dispersive X-ray (EDX) spectrummeasurements were performed on a scanning electron mi-croscope under an accelerating voltage of 20 kV (HitachiCo., Ltd.). The magnetization measurements were car-ried out using a SQUID-VSM-7T Quantum Design de-vice. The small enhancement, around 50 K in the tem-perature dependence of the magnetic susceptibility at 1T, is induced by an antiferromagnetic transition due to asmall amount of solid oxygen in the measurement cham-ber. Electrical transport measurements were done in aQuantum Design PPMS-16T instrument using a stan-dard four-probe method, with the electrical current ap-plied along the plane of samples. The high field MR wasmeasured at the National High Magnetic Field Labora-tory in Tallahassee. III. RESULTS AND DISCUSSIONA. X-ray diffraction
The XRD pattern of the as-grown 1 T -VTe single crys-tals at room temperature is shown in Fig. 1. Similar toits sister compounds [18, 31–33], our VTe single crystalsdisplay a trigonal CdI -type structure (1 T phase) with V
10 20 30 40 50 60 700.00.51.0 I n t en s i t y ( a r b . un i t ) q ( ) ( ) ( ) ( ) * * ** VTe
FIG. 1. (color online) X-ray diffraction patterns of 1 T -VTe single crystals. Asterisks mark peaks that do not belong tothe trigonal phase. Inset: Schematic atomic structure of 1 T -VTe . Olive and purple circles represent V and Te atoms,respectively. atoms (olive circles) located at the center of the octahe-dra formed by Te atoms (purple circles), as shown inthe inset of Fig. 1. The V-Te layers are stacked alongthe c -axis by the van der Waals-like forces. As sug-gested by the transport and magnetic properties shownbelow, there is no additional structural transition downto 1.3 K. Sharp (00 l ) Bragg peaks can be observed andyield a lattice constant c = 6.456 ˚A, which is similarto those of 1 T -V . Ti . Te single crystals [18] and 1 T -VTe nanoplates [22]. For single crystals made by thevapor transport method, the resulting CDW state leadsto a monoclinic structure with c = 9.069 ˚A [17, 20]. Asmarked by asterisks in Fig. 1, a very small amount ofunknown impurity phases has been identified. It corre-sponds to less than 2% of the sample volume and doesnot impact our studies or conclusions presented in thepaper. The EDX analysis performed at different loca-tions on the crystal surface of 1 T -VTe yields a V:Tecomposition close to (1.01 ± B. Resistivity and magnetic susceptibility
The temperature dependence of the electrical resistiv-ity ρ ( T ) is illustrated in Fig. 2(a). At 300 K, the valueof ρ is about 172.5 µ Ω cm, close to that of V . Ti . Te single crystals [18] while about an order of magnitudesmaller than that of VTe nanoplates [22]. In contrast tothe CDW transition observed in ρ ( T ) of V − x Ti x Te sin-gle crystals [18], no signature for a structural transition isfound down to 2 K in VTe single crystals. The ρ ( T ) de-creases from room temperature to a minimum value near16 K. Rather than saturating at low temperatures, asexpected for simple metals, the resistivity displays an in- r ( m W c m ) T (K) (a) c ( - e m u / m o l ) T (K) (b) B || c r ( m W c m ) T (K) M ( m B /f. u . ) B (T) 2 KB || c FIG. 2. (color online) (a) Temperature dependence of the in-plane electrical resistivity of VTe . Red curve is the fittingresult of Eq. 1. Inset: An enlarged view of low tempera-tures in semi-log plots. Blue dashed line is a guide for the eyeand shows a - lnT dependence. (b) Semi-log plots of the tem-perature dependence of the magnetic susceptibility of VTe ,measured under several magnetic fields applied along the c -axis. Red line is the Curie-Weiss fit in the temperature rangefrom 5 - 300 K at 1 T. Inset: Magnetic field dependence ofthe magnetization measured at 2 K. Blue line is calculated M ( B ) using the Brillouin function Eq. (4). crease with decreasing temperature below the minimum.The inset of Fig. 2(a) shows the low-temperature behav-ior on semi-log plots. The logarithmic increase below 16K is characteristic of Kondo systems and it is due to acontribution from the conduction electron-magnetic im-purity interaction [24]. Moreover, there is a divergencefrom the logarithmic increase below 5 K, mainly dueto the spin-compensated state or the Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions between magneticimpurities [34, 35]. The residual-resistivity ratio, definedas ρ (300 K)/ ρ (16 K), is relatively small and estimatedto be only 2.2 in VTe single crystals. This is consistent with the presence of small amounts of impurities in theKondo system. Therefore, the measured resistivity is thesum of the typical electron-phonon and electron-electroninteractions, and the spin scattering of the conductionelectrons by the magnetic impurity characteristic of theKondo effect. First, we focus on the high-temperaturebehavior of the resistivity and consider the Kondo term ρ K as a constant. As shown by the red line in Fig. 2(a),we fit ρ ( T ) of 1 T -VTe in the temperature range 50 - 300K to the formula ρ ( T ) = ρ + ρ K + aT + ρ ph ( T ) , (1)where ρ + ρ K = 79.68 µ Ω cm is the sum of the resid-ual resistivity and the Kondo contribution, the aT termrepresents the electron-electron interaction, and ρ ph ( T )arises from electron-phonon interactions and is expressedby the Bloch-Gr¨ueisen formula ρ ph ( T ) = α (cid:18) T Θ R (cid:19) (cid:90) ΘR T x ( e x − − e x ) dx. (2)In the model, α is a constant proportional to the electron-phonon coupling and Θ R is the Debye temperature. Thevalue Θ R = 274 K obtained from our electrical resistivityanalysis is close to Θ D = 267 ±
20 K, as obtained fromheat capacity measurement of VTe polycrystals [36].This approach fails to describe the low-temperature be-havior of VTe which can be well explained by includingthe Kondo effect. The analysis of the low-temperaturepart of ρ ( T ) will be discussed below.Figure 2(b) shows the temperature dependence of themagnetic susceptibility χ ( T ), measured under several val-ues of the magnetic field along the c -axis. The suscepti-bility increases monotonically with decreasing tempera-ture under 1 T. No magnetic order is observed down to2 K. As shown by the red curve, the χ ( T ) data from 5- 300 K could be well fitted to a modified Curie-Weissformula χ ( T ) = χ − f T + CT − θ , (3)where χ = 1 . × − emu/mol is the Pauli susceptibil-ity of conduction electrons in the host VTe . In general,the Pauli susceptibility of a metallic sample is tempera-ture independent. However, in our case, a phenomeno-logical fitting term − f T with f = 2 . × − emu/(molK) needs to be added. The temperature-dependent Paulisusceptibility might be due to the change of relative sizesof the Fermi surface and Brillouin zones, where the crys-tal contract anisotopically with decreasing temperature.For instance, such behavior has been observed in α -Usingle crystals [37]. Similar linear temperature depen-dence for χ has been observed in the sister compoundNiTe [38], in which spin-polarized topological surfacestates were observed [39]. The third term is the Curie-Weiss susceptibility coming from Kondo impurities. Asshown in the main frame of Fig. 2(b), the deviation of χ ( T ) below 4 K from the fitting is further indication ofKondo behavior. It demonstrates the Kondo screening ofthe magnetic moment on the impurity from the surround-ing cloud of negatively polarized conduction electrons,combined with the possible onset of short range order,mediated by an RKKY interaction between the interca-lated V impurities. As the temperature decreases, themagnetic moment of the Kondo impurity crossover fromlocalized behavior at high temperatures, described bythe Curie-Weiss law, to a fully compensated moment atlow temperatures, where temperature-independent Paulisusceptibility is formed [40]. We obtain the values ofthe Curie constant C = 0.0246 emu K/mol and theCurie-Weiss temperature θ = -0.676 K. According to theEDX analysis, there are no other magnetic elements inthe sample. Furthermore, layered compounds are eas-ily intercalated with metallic guests due to their low-dimensional structures [7]. Thus, we assume that theintercalated V ions are indeed the magnetic impurities inthe VTe sample. Taking the spin of the localized V ( S = 1/2) into account, the theoretical magnetic moment ofeach scattering center is µ V = g (cid:112) S ( S + 1) µ B = 1 . µ B ,where g = 2 assuming quenched orbital contribution. Us-ing the effective moment of the sample µ eff ≈ √ C =0.443 µ B /f.u., we estimate that the molar fraction of in-tercalated V ions is N = µ /µ = 0.066. As shown inFig. 2(b), similar to VSe [10], the deviation of the sus-ceptibility with respect to the Curie-Weiss law is moresignificant at higher magnetic fields. Moreover, the de-crease of the saturated susceptibility indicates a reduc-tion in the compensated moment of the impurity by themagnetic field. The inset of Fig. 2(b) shows the mag-netic field dependence of the magnetization at 2 K. Theinduced magnetization is only 0.05 µ B at 2 K and 7 T. Bytaking account the N value obtained above, the magne-tization could be calculated using the Brillouin function B J ( x ) with J = 1/2 as M cal = N gµ B B J (cid:18) g µ B JBk B T (cid:19) . (4)As shown by the blue line in Fig. 2(b), the M cal ( B ) curveis compared to the measured data. The deviation above0.3 T is mainly related to the splitting of the Kondoresonance under magnetic fields. C. Magnetoresistivity
To further evaluate the magnetic Kondo impurity, wesystematically measured the magnetic field dependenceof MR, ∆ ρ/ρ (0) = [ ρ ( B ) − ρ (0)] /ρ (0) × c -axis at different temperatures. The results are presentedin the inset of Fig. 3(a). At 25 K, the negative MR( B )shows a convex shape in the entire field range. In con-trast, the nonlinear MR at 2 K slightly bends upwardsunder high fields and reaches -3.7% at 14 T. The nega-tive MR has been derived by Yosida from the first-order r ( m W c m ) T (K) B || c (b) r ( m W c m ) T (K )
10 K6 K4 K2 K | D r / r ( ) | / B/T (T/K) B || c (a)
12 K15 K20 K25 K D r / r ( ) ( % ) B (T) 2 K25 K8 K FIG. 3. (color online) (a) Square root of | ∆ ρ/ρ (0) | as a func-tion of B/T measured at various temperatures. Pink line isthe Brillouin function with a scaled magnitude. Inset: Mag-netic field dependence of the MR at different temperatures.(b) Temperature dependence of the resistivity under differentmagnetic fields. Solid lines are fits to the modified Hamannexpression Eq. (6) and (8). Inset: An enlarged view of thefitting curve under zero magnetic field is shown by the redline. Black dashed line is a guide for the eye and shows a - T dependence. perturbation of the s - d exchange interaction [41]. If mag-netic moments existed, the magnitude of the negativeMR should be proportional to the square of the impuritymagnetization, for T > T K and in the low B/T limit [42].Accordingly, we plot | ∆ ρ/ρ (0) | as a function of B/T fordifferent temperatures in Fig. 3(a). It is clear that thenegative MR above 12 K collapses and can be scaled bythe Brillouin function ( J = 1/2) (cid:12)(cid:12)(cid:12)(cid:12) ∆ ρρ (0) (cid:12)(cid:12)(cid:12)(cid:12) = λB J (cid:18) gµ B JB k B T (cid:19) , (5)where λ is a scaling constant. These results stronglysupport the scenario of the localized V impurity with S = 1/2. The gradual deviation from the scaling functionbelow 12 K indicates the screening conduction electrons,which is a scale determined by many-body interactions.Thus, we obtain the Kondo temperature T K = 12 K,where the Kondo resonance is gradually formed.In order to analyze the Kondo effect in VTe in greaterdetail, we focus on the low-temperature behavior of theresistivity in this system. Fig. 3(b) shows the tempera-ture dependence of resistivity from 2 to 25 K and underdifferent magnetic fields applied along the c -axis. Sincethe phonon contribution is small at low temperatures anddoesn’t change under magnetic fields, we analyze the low-temperature data by taking into account the Fermi liquidbehavior and the contribution from the Kondo scatteringonly. The Hamann expression, yielding a new solution forthe s - d exchange model, is mostly used for analyzing theKondo effect in the low-temperature electrical resistivity.It was reduced from Nagaoka’s self-consistent equationsto a single nonlinear integral equation [43]. However, itsapplicability is limited to temperatures T ≥ T K . For T < T K , the Hamann expression gives low values for theimpurity spin S due to inadequacies in the Nagaoka’s ap-proximation [44]. To account for this issue, we replacethe variable T with T eff = (cid:112) T + T , where k B T W is theeffective RKKY interactions [34, 45]. As demonstratedby the red line, ρ ( T ) under zero field can be analyzed bythe formula ρ ( T ) = ρ + aT + ρ H ( T eff ) , (6)where ρ is the residual resistivity, ρ H ( T eff ) is the mod-ified Hamann expression [34, 43, 45], which leads to thecrossover region and to saturation at low temperatures,and is given by ρ H ( T eff ) = ρ K (cid:34) − ln ( T eff /T K ) (cid:112) ln ( T eff /T K ) + π S ( S + 1) (cid:35) , (7)where ρ K is a temperature-independent constant, T W =5 .
18 K is related to the average RKKY interactionstrength between V impurities and its value is close tothe deviation temperature of the logarithmic increase.According to the above MR analysis, the spin of the mag-netic impurities S and the Kondo temperature T K arefixed to 1/2 and 12 K, respectively. As shown in the in-set of Fig. 3(b), in the Kondo regime at T (cid:28) T K , the redfitting curve exhibits the - T dependence below 2 K, char-acteristics of single-impurity Kondo effect and Nagaokatheory [34, 44, 46, 47]. Thus, the modified Hamann ex-pression gives a phenomenologically satisfactory descrip-tion of the logarithmic increase with decreasing temper-ature in a small range below T K and the - T behavior at T (cid:28) T K in ρ ( T ) [48].Because the system shows negative MR, it is expectedthat the upturn of ρ ( T, B ) is suppressed with increasingmagnetic fields. Moreover, the splitting of the Kondo resonance under applied magnetic fields correlates withthe electrical transport property, in which ρ ( T, B ) showsan extra increase with decreasing temperature below T K .As shown in Fig. 3(b), a finite temperature peak is ob-served when the applied magnetic field is larger than3 T. With increasing magnetic field, the peak becomesbroader and shifts to higher temperatures. Motivatedby previous theoretical calculations [42] and experimen-tal analysis of Ce x La − x Al alloys [30], an impurity spinpolarization function [1- L ( x )] is added to the modifiedHamann expression in Eq. (7) for the analysis of ρ ( T, B ).Not only magnetic impurities interact with the conduc-tion electrons below T K , but also the relaxation time de-scribing the Kondo resonance is different for up spins anddown spins when a large enough magnetic field is ap-plied [41]. Therefore, we use the Langevin function L ( x )instead of the Brillouin function B J ( x ) for the analysisof ρ ( T, B ) [30]. Furthermore, the variable
B/T of theLangevin function is replaced by
B/T eff ρ H ( T eff , B ) = ρ K (cid:34) − ln ( T eff /T K ) (cid:112) ln ( T eff /T K ) + π S ( S + 1) (cid:35) · (cid:26) − L (cid:20) µBk B T eff (cid:21)(cid:27) , (8)where µ is the effective magnetic moment of the vana-dium impurity. The values for T K and S , as fixed inthe fitting of the zero-field resistivity, are left unchanged.As shown in Fig. 3(b), the change of MR at 1 T is rel-atively small. This indicates that magnetic field mightnot be strong enough to split the Kondo resonance at fi-nite temperatures [29]. Also, for a reliable analysis of theresult by Eq.(8) at low magnetic fields, measurements atlower temperatures are required (below 2 K). All fittingparameters are listed in Table I. The term ρ + ρ K grad-ually decreases with an increasing magnetic field, whichis consistent with the negative MR. The reduction of µ indicates that the impurity gradually loses its magneticcharacter under magnetic fields. This is also reflected inthe magnetic susceptibility measurements in Fig. 2(b).The 3 d vanadium impurity is unique, because its mag-netic moment varies from 0 in bulk V and clusters of Vatoms, via 3/5 µ B in the atomic model, to a maximumof 3 µ B in the d resonance model [49]. In VSe , previ-ous work suggests that the intercalated V ion produces anet paramagnetic moment of 2.5 µ B [10, 50]. A relatedpoint to consider is that a magnetic moment as large as6.5 µ B was reported for V impurities in thin films of Nahost, indicating a polarization of the host [49]. In the lastsection, we used the magnetic moment of quenched V ions to estimate the molar fraction of V impurities. Here,using µ (3 T) = 2 . µ B from the Langevin function fit,the molar fraction is estimated to be N = µ /µ =0.033, which is closer to the EDX result for the deviationfrom stoichiometry N = 0.01 ± r ( m W c m ) T (K ) B ^ c FIG. 4. (color online) Resistivity as a function of T mea-sured under different magnetic fields applied perpendicularlyto the c -axis. Discrete data points were determined from themeasurements by sweeping the magnetic field at a fixed tem-perature. Solid lines are fits at different magnetic fields (seetext). NRG calculation has previously been done for the ρ ( T, B )of dilute magnetic alloy Ce x La − x Al , x = 0 . ρ ( T, B ) to T (cid:28) T K . It is worth mentioning that, in heavyfermion Ce x La − x Cu , a continuous crossover from thesingle impurity Kondo system to the coherent Kondo lat-tice occurs with increasing the Ce impurity concentra-tion [52]. The resistivity for the concentrated Ce samples( x > T K , which drops steeplywith decreasing temperature. This type of maximum in ρ ( T ) under zero magnetic field, observed in Kondo lat-tice materials, is due to the RKKY interactions betweena periodic arrangement of Kondo ions.To systematically study the characteristic peaks in ρ ( T, B ) of 1 T -VTe single crystals, further investigationof the magnetic-field-induced splitting of Kondo reso-nance is provided by the MR measurements performedunder very high magnetic fields up to 35 T (the mag-netic field is applied perpendicular to the c -axis). At1.3 K, the negative MR reaches -5.2% at 35 T. Figure 4shows the resistivity versus T measured under differentmagnetic fields. As can be seen, the peak in ρ ( T, B ) isclearly visible at lower fields, but flattens out with in-creasing magnetic fields. For magnetic fields below 23 T,the data were analyzed by using the modified Hamannexpression Eq. (6) and (8). At high magnetic fields, theanomaly is no longer detectable, and the temperaturedependence of the resistivity above 23 T could be fittedto ρ ( T ) = ρ + ρ K + aT . It is clear that the negativeMR does not saturate after the anomaly is suppressed.This might indicate that higher magnetic fields are re-quired to fully suppress the Kondo effect. The fitting TABLE I. Parameters obtained from analysis of ρ ( B, T ) inFig. 3 and Fig. 4 where S =1/2 and T K = 12 K are fixed. B (T) ρ + ρ K ( µ Ω cm) a ρ K ( µ Ω cm) T W (K) µ ( µ B ) B (cid:107) c B ⊥ c parameters are included in Table I. It is worth notingthat the Fermi liquid behavior (the a coefficient, in par-ticular) at high temperatures T > T K and zero magneticfield is roughly the same as the Fermi liquid slope at lowtemperatures and 35 T (see Table I). As shown by theNRG calculations [29], the magnetic field splits and sup-press the Kondo resonance which is due to the interactionbetween the magnetic impurity and the conduction elec-trons. Our results demonstrate that the Kondo effect isgradually suppressed and the system shows a crossoverto the Fermi liquid state under high magnetic fields. D. Hall effect
Figure 5(a) shows the magnetic field dependence ofthe Hall resistivity ρ yx ( B ) measured at different tem-peratures up to 10 T. The red line is a linear fit of ρ yx ( B ) from 0 to 5 T, characteristic of the ordinary Halleffect. By having a scrutiny to ρ yx ( B ), the deviationfrom the linearity occurs at high magnetic fields below T K , which is consistent with the splitting of the Kondoresonance by the magnetic field. The Hall coefficient, R H = ρ yx /B at 5 T, is plotted versus temperature inFig. 5(b). The positive R H over the whole temperaturerange reveals that the electrical conduction is dominatedby hole-type charge carriers. In contrast to the electron-type carriers in the VTe nanoplates [22], our results areconsistent with the hole-like bands in the monolayer 1 T -VTe [13] and the result of recent angle-resolved photoe-mission spectroscopy measurements of 1 T -V − x Ti x Te ,which characterize the circular and triangular hole-type R H ( - m / C ) T (K) n ( c m - ) (b)
15 K 30 K 45 K r yx ( m W c m ) B (T) (a) m ( c m V - s - ) T (K) FIG. 5. (color online) (a) Magnetic field dependence of Hallresistivity at various temperatures of VTe . Red lines arelinear fit from 0 to 5 T. (b) Temperature dependence of theHall coefficient and effective charge carrier density. Inset:Hall mobility µ H vs temperature at B = 5 T. Fermi surfaces around Γ and K points, respectively [19].As shown in Fig. 5(b), the R H exhibits a temperaturedependency that differs from the expected one band ap-proximation in simple metals. This might indicate acomplex electronic structure in VTe , where the bandshave temperature-dependent carrier concentrations andmobilities. Furthermore, R H increases with decreasing temperature with an anomaly at T ∼ T K , which is char-acteristic for the Kondo effect [48]. The blue curve dis-plays the temperature dependence of the effective charge-carrier density n , obtained by the formula R H = 1 /ne (one band approximation). At 45 K, the estimated con-centration of free electrons is 6 . × cm − . This valueof n , due to the crude approximation that neglects thesemimetallic character of the compound, can be consid-ered as an upper limit of the real concentration in thismaterial. The temperature dependence of the Hall mo-bility µ H ( T ) calculated with the single-band scenario at5 T is shown in the inset of Fig. 5(b). At 35 K, the valueof µ H is 12.42 cm V − s − . IV. CONCLUSIONS
In summary, we have successfully synthesized singlecrystals of 1 T -VTe and measured their detailed mag-netic and magnetotransport properties at low tempera-tures and under high magnetic fields. The magnetic sus-ceptibility, electrical resistivity, and Hall effect are sys-tematically studied revealing the presence of the Kondobehavior in this material. From the negative MR mea-surements, we point out that the intercalated V mayact as the Kondo impurities. The observation of a peakbelow T K in ρ ( T, B ) reflects the splitting of the Kondoresonance. The analysis by using the modified Hamannexpression is in good agreement with the experimentalresults. Furthermore, we directly show that the Kondobehavior is suppressed by strong magnetic fields, and forthe fields above 23 T the bulk VTe material behaves asan ordinary Fermi liquid system. V. ACKNOWLEDGMENTS
This work is supported by the National Natural Sci-ence Foundation of China (Grant No. A0402/11534005and A0402/11674164). X.D. acknowledges support fromINLs LDRD program (19P43-013FP). K.G. acknowl-edges support from the US DOE BES Energy FrontierResearch Centre ”Thermal Energy Transport under Irra-diation” (TETI). L.B. is supported by DOE-BES throughaward DE-SC0002613. The National High MagneticField Laboratory is supported by the National ScienceFoundation Cooperative Agreement No. DMR-1644779and the State of Florida. [1] J. Wilson and A. Yoffe, The transition metal dichalco-genides discussion and interpretation of the observed op-tical, electrical and structural properties, Advances inPhysics , 193 (1969).[2] Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Cole-man, and M. S. Strano, Electronics and optoelectronics of two-dimensional transition metal dichalcogenides, Na-ture nano. , 699 (2012).[3] M. Chhowalla, H. S. Shin, G. Eda, L.-J. Li, K. P. Loh,and H. 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