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[Tomomi Furuhashi](https://orcid.org/0009-0008-8017-5375), Keisuke Hozawa, [Yusuke Kozuka](https://orcid.org/0000-0001-7674-600X), [Yoshihiro Tsujimoto](https://orcid.org/0000-0003-2140-3362), [Kazunari Yamaura](https://orcid.org/0000-0003-0390-8244), [Jun Fujioka](https://orcid.org/0000-0003-1340-0268)

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[Doping-induced variation of anomalous Hall effect in the magnetic Weyl-Kondo metal candidate                    <math>                      <mrow>                        <msub>                          <mi>CeCo</mi>                          <mrow>                            <mn>1</mn>                            <mo>−</mo>                            <mi>x</mi>                          </mrow>                        </msub>                        <msub>                          <mi>Fe</mi>                          <mi>x</mi>                        </msub>                        <msub>                          <mi>Ge</mi>                          <mn>3</mn>                        </msub>                      </mrow>                    </math>](https://mdr.nims.go.jp/datasets/da1ae039-c050-42db-849e-3e10f2442d1d)

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Doping-induced variation of anomalous Hall effect in themagnetic Weyl-Kondo metal candidate CeCo1 − xFexGe3Tomomi Furuhashi,1, ∗ Keisuke Hozawa,1 Yusuke Kozuka ,2Yoshihiro Tsujimoto ,2 Kazunari Yamaura ,2 and Jun Fujioka 3, 41Graduate School of Science and Technology,University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan2Research Center for Materials Nanoarchitechtonics (MANA),National Institute for Materials Science (NIMS),Namiki, Tsukuba, Ibaraki 305-0044, Japan3Department of Materials Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan4Research Center for Organic-Inorganic Quantum Spin Science and Tchnology (OIQSST),University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan(Dated: October 22, 2025)1AbstractWe have investigated the doping-induced variation of magnetic and charge transport properties ofsingle crystalline CeCo1− xFexGe3 with a noncentrosymmetric tetragonal BaNiSn3-type structure.The magnetization measurements revealed that, with increasing doping level x, the antiferromag-netic phase for x = 0 turns into a ferromagnetic one at x = 0.15, a cluster-glass like phase atx = 0.46, and eventually evolves into a paramagnetic phase above x = 0.67. For 0 ≤ x < 0.46wherein the electrical resistivity shows the Fermi liquid behavior, the coefficient of the T 2-termof resistivity is small for 0 ≤ x ≤ 0.33 but increases sharply at around x ∼ 0.42, indicating theenhancement of density of state near the Fermi energy. Hall resistivity measurements indicatethat, at 2 K in the ferromagnetic phase, the anomalous Hall conductivity remains nearly constantover the range 0.15 ≤ x ≤ 0.42 but markedly decreases with increasing x beyond 0.42. Notably, ananomalous Hall component that is not proportional to magnetization is observed for x ≥ 0.42. Itis anticipated that the Berry curvature in momentum space significantly changes across the tran-sition from the ferromagnetic phase to cluster-glass like phase, driven by a change in the Kondohybridization in the present materials.INTRODUCTIONThe quantum phenomena arising from the interplay between topology and electron cor-relation in solids have attracted great interest in condensed matter physics. One of the mostprominent examples is the correlated Weyl semimetal, where relativistic electrons exhibita variety of collective phenomena associated with the Mott transition or heavy-fermion be-havior. A characteristic feature of Weyl semimetals is the emergence of the Weyl nodesnear the Fermi energy, which correspond to the source or the sink of the Berry curvaturein momentum space [1–4]. In particular, the Berry curvature acts as the fictitious magneticfield to the conduction electrons [5], leading to significant intrinsic anomalous Hall effects,anomalous Nernst effects [6], and nonlinear Hall effects [7, 8]. On the other hand, a fea-ture of strongly correlated electrons is the emergence of various electronic orderings such asmagnetic, orbital and charge ordering, whose phase transitions are often accompanied bythe dramatic reconstruction of electronic structure. Accordingly, strongly correlated Weylsemimetals provide a fertile playground for exploring emergent quantum states and transi-2tions. A prototypical example is d-electron-correlated electron systems in proximity to theMott transition [2, 9–14]. For example, it is argued that antiferromagnetic Weyl semimetallicphase appears in a narrow phase space between the antiferromagnetic Mott insulating phaseand the paramagnetic metallic phase in the pyrochlore iridates. In particular, several Weylsemimetallic phases compete with each other near the Mott criticality, and their transitionscan be induced by the application of magnetic field or hydrostatic pressure, which manifestas significant variation of the anomalous Hall response [12, 15].Recent theoretical studies predict that the heavy-mass quasiparticles in heavy-fermionsystems can also induce a Weyl semimetallic phase, that is, Weyl-Kondo semimetal. Forexample, it has been argued that Weyl-Kondo semimetallic states are responsible for a giantspontaneous Hall effect in the noncentrosymmetric Ce3Bi4Pd3 [16–18]. Moreover, a largeanomalous Hall/Nernst effect in the ferromagnetic USbTe [19] and UCo0.8Ru0.2Al [20] hasbeen also understood from the Weyl semimetallic state originating from U-5f electrons. Inheavy-fermion systems, the electronic state often undergoes significant changes due to thevariation of Kondo hybridization [21–24]. Consequently, the Berry curvature in magneticWeyl-Kondo metals would also significantly change, a subject that has not been sufficientlyexplored so far. In particular, it is still unclear whether topological phase transitions due tomagnetic fields, similar to those observed in the Weyl semimetal near the Mott transition,also occur near the suppression of magnetic order in heavy-fermion systems.In this context, the heavy-fermion compound CeCo1− xFexGe3 is a promising candidatefor exploring the interplay between magnetism and Dirac/Weyl electrons as the Kondohybridization is tuned. CeCo1− xFexGe3 crystallizes in the noncentrosymmetric tetragonalBaNiSn3-type structure with space group I4mm, as shown in Fig. 1(a) [25–28]. The cornersand the body center of the tetragonal structure are occupied by Ce-atoms, which show 4f -magnetic-moment with the easy axis anisotropy along the c-axis for x = 0 [29–31]. At zeromagnetic field, CeCoGe3 exhibits three successive antiferromagnetic transitions at TN1=21K, TN2=12 K, and TN3=8 K, respectively [25, 26, 30]. Neutron scattering studies on singlecrystals have identified the propagation vectors as q=(0, 0, 2/3) for TN2 < T < TN1, q=(0,0, 5/8) for TN3 < T < TN2, and q=(0, 0, 1/2) for T < TN3 [30]. Figure 1(a) illustratesan example of the magnetic structure with the propagation vector q=(0, 0, 2/3). Thenonmagnetic Co-3d states are hybridized with the Ce-4f states [26, 32, 33], and the partialsubstitution of Co with Fe enhances the Kondo hybridization [34]; in CeCo1− xFexGe3, the3magnetic ordering is suppressed with increasing x and vanishes around x ∼ 0.6 [28, 34–37]. Recent theoretical studies argue that several Weyl nodes can emerge near the Fermilevel due to the noncentrosymmetric crystal structure [38, 39]. Given these properties,CeCo1− xFexGe3 appears to be an excellent platform to explore how the transport propertyof Dirac/Weyl electrons evolves as the Kondo hybridization strength is changed. However,there is no report on the magneto-transport property for the CeCo1− xFexGe3 (0 < x < 1)to the best of our knowledge, so far [19]. To precisely characterize the magnetic/magneto-transport property in materials with relatively large magnetic anisotropy, measurements onsingle crystalline samples are essential. Here, we investigated the doping-induced variationof magnetization, resistivity and Hall resistivity to get an insight into the variation of Berrycurvature characteristic of Weyl-Kondo semimetal in CeCo1− xFexGe3 single crystals.METHODSSingle crystals of CeCo1− xFexGe3with x < 0.5 were grown by the Bi-flux method [26, 40].The starting materials were mixed with the molar ratio Ce : Co : Fe : Ge : Bi = 1 : 1 − x :x : 3 : 10–15, placed in alumina crucibles. The crucible sealed under vacuum in a quartztube, was kept at 1050 ◦C for 24 h and was subsequently cooled down to 650–850 ◦Cover130 h. Then, the sealed ampoule was centrifuged to remove the Bi-flux. To obtain samplesof sufficient size for magnetization measurements, single crystals of CeCo1− xFexGe3withx > 0.6were grown by Sn-flux methods. The synthesis procedure was similar to that forBi-flux, with an initial composition of Ce : Co : Fe : Ge : Sn = 1.2 : 1− x : x : 3.5–3.7 : 30, amaximum temperature of 1130 ◦C, a cooling time of 130–310 h, and a quench temperatureof 600 ◦C. The crystals were characterized by X-ray powder diffraction using a Rigaku X-ray diffractometer with Cu-Kα radiation [see Fig. S1] [41]. The doping level of Fe (x) isdetermined by the energy dispersive X-ray spectroscopy (EDX) analysis [see Fig. S2] [41].The doping level exhibits relatively large sample-to-sample variation, whereas no significantspatial inhomogeneity was detected within a single sample [see Fig. S3].Measurements of resistivity and Hall resistivity were performed using the standard four-terminal method. The measurements were done using the Physical Property MeasurementSystem (Quantum Design) from 2 K to 300 K under the magnetic field up to 9 T. The magne-tization measurements were performed using the Dynacool System equipped with the VSM4option from 2 K to 300 K under the magnetic field up to 9 T. Several samples with differentshapes show nearly identical magnetization profiles, suggesting that the demagnetizationfactor is not significant.RESULTSFigure 1(b) shows the temperature dependence of magnetization for CeCo1− xFexGe3with various x for magnetic field (B) along the c-axis [see also Figs. S4 and S5] [41].Magnetic transitions manifest as multiple anomalies in the magnetization for x ≤ 0.48. Forx = 0, the magnetization exhibits three anomalies at the transition into qz = 2/3-phase,qz = 5/8-phase, and qz = 1/2-phase at TN1=20 K, TN2=11.6 K, and TN3=6 K, respectively,which are roughly consistent with the previous reports [25, 26, 30]. For x = 0.13, themagnetization exhibits only two anomalies at TN1 and TN2, whereas a single ferromagnetictransition is observed for x = 0.19 and 0.42. For x = 0.48, the temperature dependence ofmagnetization shows a broad hump-like structure around 6.7 K, whereas no clear anomalyis observed for x = 0.76. The magnetization curves for various x are shown in Fig. 1(c). Forx = 0, the magnetization plateau due to qz = 5/8 phase, qz = 2/3 phase, and ferromagneticphase are observed at 2 K as previously reported [26], while a simple ferromagnetic hysteresiswith the saturation magnetization about 0.4 µB/f.u. is observed for x = 0.19. For x = 0.48,the magnetization curve no longer shows the ferromagnetic hysteresis and smoothly increasesas a function of magnetic field. For x = 0.76, the magnetization exhibits nearly B-linearbehavior characteristic of the paramagnetic state.Figure 2(a) shows the magnetic phase diagram based on the results of magnetization.With increasing x, the transition temperature of the qz = 2/3-phase decreases while thoseof qz = 5/8- and 1/2-phases rather increase with increasing x. At around x = 0.15, thesephases evolve into the ferromagnetic phase, which is then likely replaced by a differentstate around x = 0.46. Overall, this suggests that the Kondo hybridization suppressesthe RKKY interaction and magnetically ordered phase, in qualitatively agreement withthe previous results [33, 34]. It is known that, in Ce-based ferromagnets, the increase ofKondo interaction tends to promotes the antiferromagnetic interaction before reaching thequantum critical point, which often causes the Kondo-cluster glass state [42, 43]. Thereforeconsidering the broad hump-like anomaly in temperature dependence of magnetization as5well as the smooth MH-curve, it is likely that the Kondo-cluster glass state appears below 6K in the present material. Although the results around x = 0.5–0.6 are missing due to thelack of single crystalline samples, x = 0.67 exhibits paramagnetic behavior in the range of2–300 K (shown as a green cross in Fig. 2(a)). Therefore, the cluster-glass like phase likelyvanishes around x = 0.5–0.6, which is consistent with previous reports [28, 34–37].Figures 3(a) and (b) show the temperature dependence of resistivity (ρxx) at B = 0 T. Allthe samples show metallic behavior, and a clear kink is observed at the magnetic transitiontemperature for x ≤ 0.42 [see Fig. 3(a)]. In contrast, no clear kinks are visible for x ≥ 0.46[see Fig. 3(b)]. For x ≤ 0.42, ρxx shows the Fermi liquid behavior ρxx(T ) = AT 2 + ρ0with A and ρ0 being the constant and residual resistivity, respectively at low temperatures(T < 5 K) [see Fig. S6]. It is known that A is related to the density of states near theFermi energy through the Kadowaki-Woods relation A/γ2 ∼ 1.0× 10−5 µΩcm(K ·mol/mJ)2in various heavy-fermion systems [44]. Here, γ is the electronic specific heat coefficient. Fig.2(b) shows the doping dependence of A. As a function of x, A gradually increases in the lowdoping regime but is sharply enhanced above x ∼ 0.4, suggesting that the density of statesnear the Fermi energy increases significantly above x ∼ 0.4 due to the delocalization ofCe-4f state. A similar behavior has been demonstrated in polycrystalline samples [34, 36].For x = 0.48, ρxx(T ) exhibits a nearly T -linear behavior rather than the conventional Fermiliquid behavior at low temperatures [see the inset to Fig. 3(b)], which is often observed nearthe quantum critical point in heavy fermion systems [45, 46].Figures. 4(a)–(d) show the magnetic field dependence of the Hall resistivity for x = 0,0.19, 0.33, and 0.48, respectively. For x = 0, ρyx is small and exhibits an almost lineardependence on magnetic field (B) at 100 K, but is remarkably enhanced at 20 K, showingthe nonlinear B-dependence [see Fig. 4(a)]. With further lowering temperature, ρyx is ratherreduced, and a jump (or kink) due to the metamagnetic transition becomes remarkable. Forx = 0.19 which lies in ferromagnetic phase, ρyx shows a step around B = 0, followed bya nearly linearly increase at a higher field region, corresponding to the anomalous Halleffect and ordinary Hall effect, respectively. The sign of the anomalous Hall resistivity ispositive at 15 K but changes to negative at low temperatures [see the inset to Fig. 4(b)].A similar behavior is observed for x = 0.33; the sign of anomalous Hall effect is reversedby changing the temperature, while the sign of ordinary Hall effect remains to be positiveat all temperatures [see Fig. 4(c)]. For x = 0.48, ρyx exhibits a sign change, similar to the6anomalous Hall component for x = 0.19 and 0.33, while complex behavior emerges near andbelow TN in the low field regime; a peak feature appears around 2 T and 6 K, which evolvesinto a dip structure below 4 K. Although ρyx for x = 0 and x = 0.48 exhibit complicatedfield-dependence, it is likely that, in the low-field regime below 1 T, the primary contributionto ρyx is commonly ascribed to the anomalous Hall term.To qualitatively evaluate the temperature dependence of the anomalous Hall term, weplot ρyx at 0.2 T (ρyx(0.2 T)) as a function of temperature in Fig. 4(e). For x = 0, withdecreasing temperature, ρyx(0.2 T) gradually increases, maximizes near or slightly higherthan TN and finally becomes vanishingly small below 10 K. For x = 0.19 and 0.33, ρyx(0.2T) shows a maximum near TC analogous to the behavior of x = 0, but its sign changes tonegative below 15 K. A similar behavior is observed for x = 0.48. To visualize the dopingevolution of ρyx(0.2 T), we show the contour plot of ρyx(0.2 T) on the x-T plane in Fig.4(f). Above the transition temperature, ρyx(0.2 T) is positive in wide range of temperaturesand doping levels. In particular, the positive region extends up to about 100 K for x = 0,which gradually shrinks with increasing x and nearly vanishes around x = 0.48. In themagnetically ordered phase, ρyx(0.2 T) is negligibly small in the antiferromagnetic phasefor 0 ≤ x < 0.15, whereas it becomes significantly large in magnitude and negative in signboth in the ferromagnetic phase and cluster-glass like phase for 0.15 ≤ x ≤ 0.48. In heavyfermion systems, it is well known that the anomalous Hall effect arises predominantly fromincoherent skew scattering in the vicinity of, and above, the magnetic transition temperatureor the coherence temperature. In contrast, at lower temperatures, the anomalous Hall effectis mainly attributed to coherent skew scattering or intrinsic mechanisms [47–49]. Indeed, itis demonstrated that the temperature dependence of ρyx(0.2 T) exhibits a broad peak nearand above the transition temperature of antiferromagnetic ordering in CeAl3 and CeCu2Si2[49]. In this context, it is likely that the substantial positive component near and above themagnetic transition temperature originates from the incoherent skew scattering, whereasthe negative component in the ferromagnetic/cluster-glass like phase can be attributed tocoherent skew scattering or intrinsic mechanisms in the present system.To clarify the mechanism of negative component, we plot the anomalous Hall conductivityσMxy at 2 K, defined as the zero-field Hall conductivity (B = 0 T), as a function of longitudinalelectrical conductivity σxx for several ferromagnetic samples with 0.15 ≤ x ≤ 0.33 [see Figs.5(a) and 6(a)]. σMxy at 2 K is found to be almost independent of σxx, indicating that the7negative component of σMxy originates from the intrinsic mechanism, i.e. the Berry curvaturein the momentum space [50, 51].To separate the contribution from the ordinary Hall effect and anomalous Hall effect, weanalyzed the Hall conductivity in both the ferromagnetic phase and the cluster-glass likephase using the following formulaσxy = σNxy + σMxy + σresxy (1)The first, second, and third terms represent the ordinary Hall term (σNxy =∑inieµ2iB1+(µiB)2),the anomalous Hall term in proportion to M (σMxy = SAM), and the residual component(σresxy ), which is neither proportional to B nor to M , respectively. Here, ni and µi are thedensity and mobility of i-th carrier, respectively, and SA is the anomalous Hall coefficient.The analyzed results at 2 K for x = 0.15, x = 0.29, x = 0.33, x = 0.42 and x = 0.48 areshown in Figs. 5 (a)–(c). For x = 0.15, x = 0.29 and x = 0.33, which is located in themiddle of ferromagnetic phase, σxy is well reproduced by the simple summation of σNxy andσMxy (σNxy + σMxy) [see Fig. 5(a)]. On the contrary, for x = 0.42, which is the ferromagneticphase in vicinity to the cluster-glass like phase, a small deviation between σxy and σNxy +σMxyis seen below 2 T (|B| < 2 T) [see Fig. 5(b)]. The deviation becomes more significant forx = 0.48 which lies in the cluster-glass like phase [see Fig. 5(c)]; σxy is well reproducedby σNxy + σMxy above 3 T, whereas a significant deviation is observed near 2 T, indicating asubstantial contribution from σresxy . Figures 5(d)–(f) show the magnetic field dependence ofσresxy at 2 K for representative compositions. Although there is no systematic or reproduciblepeak/dip for 0.15 ≤ x ≤ 0.33, pronounced peaks are observed at x = 0.42 and x = 0.48.DISCUSSIONFigures 6(b) and (c) summarize the doping dependence of σMxy and σresxy as well as themagnetization at 2 K. The magnetization measured at 7 T is nearly constant for 0.15 ≤x ≤ 0.33 and slightly decreases for x ∼ 0.42. In contrast, σMxy remains nearly constantfor 0.15 ≤ x ≤ 0.33 but drops abruptly at x ∼ 0.42, indicating that the Berry curvaturein momentum space rapidly changes around x = 0.42. As previously mentioned, the A-coefficient sharply increases around x = 0.42, which is attributed to the delocalization ofCe-4f electrons [see Fig. 2(b)]. The theoretical study argues that the structure of Weyl8nodes is reconstructed when the Ce-4f state is hybridized with the states near the Fermienergy in CeCo1− xFexGe3 [38]. Therefore, it is likely that the Berry curvature in momentumspace changes rapidly with respect to x around x = 0.42, resulting in the suppression of σMxy.Figure 6(c) shows the maximum of −σresxy (−σres,maxxy ) plotted as a function of x. −σresxyis nearly constant for 0.15 ≤ x ≤ 0.33 and rises above x = 0.42, implying that σresxy isalso closely linked to the reconstruction of the Ce-4f electronic state. A similar peak/dipstructure of Hall conductivity is often seen in magnetic Weyl semimetals [52, 53]. Forexample, in the perovskite-type EuTiO3, an anomalous Hall component not proportional tomagnetization has been observed during the field-induced spin-reorientation process, whichis attributed to the field-induced shift of Weyl nodes located in proximity to the Fermi energy[52]. In the present system, at x = 0.48, the cluster-glass like state seems to change into theforced ferromagnetic phase by the application of a magnetic field. It is anticipated that thestructure of Weyl nodes is modulated in the course of the magnetization process, leadingto the non-monotonic field dependence of anomalous Hall effect. Another possibility is thefield-induced variation of Kondo hybridization. It is known that Ce-based heavy-fermionsystems on the verge of the quantum critical point often show the field-induced variation ofKondo hybridization. A prominent example is CeRu2Si2, a paramagnetic compound closeto a quantum critical point, which exhibits a metamagnetic-like transition into the enforcedferromagnetic phase [54, 55]. This phenomenon is attributed to the field-induced suppressionof Kondo hybridization. In the present case, a slight change in the Kondo hybridization dueto the magnetic field could change the Berry curvature in the momentum space. Suchdoping/field-sensitive anomalous Hall effect may be a hallmark of Weyl semimetal close toquantum phase transition in a heavy-fermion system.In summary, we have investigated the magnetic and charge transport properties for heavy-fermion systems CeCo1− xFexGe3. Magnetization measurements reveal that the magneticordering evolves from an antiferromagnetic phase to a ferromagnetic phase around x = 0.15,and then to a cluster-glass like phase around x = 0.46. In particular, the transition tempera-ture of magnetic ordering gradually decreases with increasing x, and finally the paramagneticstate appears around x = 0.5–0.6. This is in parallel with enhanced T 2 coefficient of resis-tivity, implying that the delocalized Ce-4f state starts to be formed near the Fermi energyfor x > 0.42. Above the magnetic transition temperature, the Hall resistivity in the low fieldregime is likely dominated by the anomalous Hall effect of incoherent skew scattering mecha-9nism, while the intrinsic anomalous Hall effect is observed in the ferromagnetic/cluster-glasslike phase. The magnitude of anomalous Hall conductivity is nearly x-independent for0.1 ≤ x ≤ 0.33, but rapidly decreases for x ≥ 0.42. Moreover, the peculiar anomalous Hallresponse emerges in and near the cluster-glass like phase, which cannot be explained byconventional contributions that scale monotonically with magnetic field or magnetization.These results suggest that the Weyl nodes near the Fermi energy undergo significant changesunder the influence of external fields or varying doping levels, especially in the vicinity ofthe localization-delocalization crossover of the Ce-4f state.ACKNOWLEDGEMENTSThe EDX analysis was carried out with TM4000 (Hitachi High-Tech.) at R&D Center forInnovative Material Characterization and the Organization for Open Facility Initiatives, Uni-versity of Tsukuba. This work was partly supported by Grant-In-Aid for Science Research(Nos. 18H01171, 21K18813, 22H01177, 25K01657) from the Mext, by Iketani Foundation forMaterials Science and Engineering, Japan, by JST FOREST Program (Grant Number: JP-MJFR203D) MANA is supported by World Premier International Research Center Initiative(WPI), MEXT, Japan and by JST SPRING (Grant Number: JPMJSP2124).∗ furuhashi.tomomi.tkb go@u.tsukuba.ac.jp[1] S. Murakami, New J. Phys. 9, 356 (2007).[2] X. Wan, A. M. Turner, A. Vishwanath, and S. Y. Savrasov, Phys. Rev. B 83, 205101 (2011).[3] N. P. Armitage, E. J. Mele, and A. Vishwanath, Rev. Mod. Phys. 90, 015001 (2018).[4] Z. Fang, N. Nagaosa, K. S. Takahashi, A. Asamitsu, R. Mathieu, T. Ogasawara, H. Yamada,M. Kawasaki, Y. Tokura, and K. Terakura, Science 302, 92 (2003).[5] D. Xiao, M.-C. Chang, and Q. Niu, Rev. Mod. Phys. 82, 1959 (2010).[6] N. Nagaosa, J. Sinova, S. Onoda, A. H. MacDonald, and N. P. Ong,Rev. Mod. Phys. 82, 1539 (2010).[7] K. Kang, T. Li, E. 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Crystallogr. 44, 1272 (2011).13Fig. 1Magnetization (μB/f. u. )-0.4-0.20.00.20.4x=0.762 K6 K10 KCeCo1-xFexGe3a bcCeCoGe-0.4-0.20.00.20.4-4 0 4Magnetic field (T)x=0 B∥c2 K 15 K30 K(a) (c)(b)-0.4-0.20.00.20.4x=0.482 K6 K 10 K-0.4-0.20.00.20.4x=0.19 10 K2 K30 KFIG. 1. (a) The illustration of the crystal structure of CeCoGe3with up-up-down-type magneticstructure (qz=(0, 0, 2/3)) [56]. Arrows denote the Ce-4f magnetic moment. (b) The temperatureand (c) magnetic field dependence of magnetization for the magnetic field (B) along the c-axis forrepresentative compositions of CeCo1− xFexGe3. Solid circles, open triangles, and solid squaresdenote the magnetic transition temperature at TN1, TN2, and TN3, respectively. Open circlesdenote the characteristic temperature of cluster-glass like state. The transition temperature wasdetermined from the kink in the temperature dependence of magnetization. When it was difficultto determine the transition temperature by the kink, the transition temperature was determinedusing the peak of the second derivative of magnetization with respect to temperature.14Fig. 2FMqz=2/3qz=5/8qz=1/2cluster-glassPM0.30.20.10.00.80.60.40.20.0 x3020100 B∥cCeCo1-xFexGe3(b)(a)図を分割(c), (d)はFig. 6へFIG. 2. (a) The magnetic phase diagram for CeCo1− xFexGe3. Here, qz represents the wave numberof magnetic modulation along the c-axis. Solid circles, open triangles, and solid squares denotethe magnetic transition temperature at TN1, TN2, and TN3, respectively. Open circle denote thetransition temperature of cluster-glass like state. Cross denotes the samples for which no magnetictransition was observed in the 2–300 K range. (b) The A-coefficient in the T 2 term of the electricalresistivity as a function of x.1512080400ρ xx (μΩcm)403020100Temperature (K)x=0.80x=0.76x=0.48x=0.46Fig. 3(a) (b)12080400ρ xx (μΩcm)403020100Temperature (K)x=0x=0.13x=0.19x=0.33x=0.42CeCo1-xFexGe3ρ xx (μΩcm)FIG. 3. The temperature dependence of resistivity (ρxx) at B=0 T for (a) 0 ≤ x ≤ 0.42 and(b) 0.46 ≤ x ≤ 0.80. Solid triangles denote the kink at the magnetic transition temperaturedetermined from the temperature dependence of magnetization. The inset shows the magnifiedview of low-temperature region for x = 0.48. The solid line in the inset denotes the fitting-resultsby ρxx(T ) = ATα + ρ0 (α = 1).160.600.500.400.300.200.100.00100806040200Temperature (K)x=0x=0.19x=0.33x=0.48CeCo1-xFexGe3×5ρ yx (μΩcm)Fig. 4(b)ρ yx (μΩcm) (c)(e)(f)(d)-0.050.000.050.4-0.4B (T)ρ yx (μΩcm)ρ yx(μΩcm)(a)FIG. 4. The magnetic field dependence of the Hall resistivity for CeCo1− xFexGe3 with (a) x = 0,(b) x = 0.19, (c) x = 0.33 and (d) x = 0.48. The inset to (b) is a magnified view of the low fieldregion. (e) Temperature-dependence of ρyx at B=0.2 T for x = 0, 0.19, 0.33, and 0.48. Arrowsdenote the magnetic transition temperature. (f) The contour plot of ρyx at B=0.2 T in the x-Tplane. Solid circles, open triangles, and solid squares denote the magnetic transition temperatureat TN1, TN2, and TN3, respectively. Open circles denote the transition temperature of cluster-glasslike phase.17σ xy(Ω-1cm-1)σ xy(Ω-1cm-1)Fig. 5σ xy(Ω-1cm-1)(a)(b)(c)-σxy(Ω-1cm-1)res-σxy(Ω-1cm-1)res-σxy(Ω-1cm-1)res(d)(e)(f)組成の対応が分かりやすいように変更。図を分割(スケーリングプロットはFig. 6へ)FIG. 5. The magnetic field dependence of Hall conductivity at 2 K for (a) the samples locatedin the middle of ferromagnetic phase (x = 0.15, x = 0.29, x = 0.33), (b) the sample located nearthe phase boundary (x = 0.42), and (c) the sample that in the cluster-glass like phase (x = 0.48)respectively. The dashed curve denotes the σNxy + σMxy . (d)–(f) The magnetic field dependenceof Hall conductivity which is proportional neither to B nor to M (−σresxy ) corresponding to eachcomposition shown in (a)–(c). The solid triangles denote the peak of −σresxy .18101102103104105σxx (Ω-1cm-1)2 K, 0 Tcluster-glass like(x=0.48)FM (0.15 ≤ x ≤ 0.33)x=0.42CeCo1-xFexGe3Fig. 6Fig. 2、Fig. 5の分けた分を移動(a)組成に相の名前を追加(b), (c)基底状態を記載＋磁場の向きを追加見やすいように(c)の色とマーカーを変更組成の範囲を0~0.8から0~0.6に変更(a)AF FMCluster-glassPM1050-5-100.60.50.40.30.20.10.0x40020000.40.20.0→←2 K, 7 T (B∥c)(b)(c)FIG. 6. (a) The anomalous Hall conductivity −σMxy at 2 K, which is defined by the Hall conductivityat B=0 T as a function of electrical conductivity σxx. Open triangles denote samples located inthe middle of ferromagnetic phase (0.15 ≤ x ≤ 0.33), the solid triangle denote the sample locatednear the phase boundary (x = 0.42) and solid circle denote the sample that in the cluster-glasslike phase (x = 0.48). (b) The magnetization at 2 K, 7 T (open squares) and Hall conductivityproportional to M (σMxy) at 2 K, 7 T (solid circles), (d) The maximum value of the residual Hallconductivity at 2 K(−σres,maxxy ) as a function of x. Since systematically-changed peak/dip of −σresxyis not observed for 0.15 ≤ x ≤ 0.33 [see also Fig. 5(d)], the maximum and minimum values of−σresxy are shown by error bars and their average values are plotted.19