Abstract
The nature of the interaction between magnetism and topology in magnetic topological semimetals remains mysterious, but may be expected to lead to a variety of novel physics. We systematically studied the magnetic semimetal EuAs_{3}, demonstrating a magnetisminduced topological transition from a topological nodalline semimetal in the paramagnetic or the spinpolarized state to a topological massive Dirac metal in the antiferromagnetic ground state at low temperature. The topological nature in the antiferromagnetic state and the spinpolarized state has been verified by electrical transport measurements. An unsaturated and extremely large magnetoresistance of ~2 × 10^{5}% at 1.8 K and 28.3 T is observed. In the paramagnetic states, the topological nodalline structure at the Y point is proven by angleresolved photoemission spectroscopy. Moreover, a temperatureinduced Lifshitz transition accompanied by the emergence of a new band below 3 K is revealed. These results indicate that magnetic EuAs_{3} provides a rich platform to explore exotic physics arising from the interaction of magnetism with topology.
Introduction
Topological semimetals (TSMs), including Dirac, Weyl, nodalline, and triplepoint semimetals, can be divided into two categories—nonmagnetic and magnetic TSMs depending on whether magnetism is involved^{1,2,3}. Compared with betterknown nonmagnetic TSMs, magnetic TSMs have unique properties due to their broken timereversal symmetry (TRS): for example, nonzero net Berry curvatures that can induce anomalous Hall or Nernst effects, only one pair of Weyl nodes for some magnetic Weyl semimetals, and a good ability to manipulate the spin for spintronics applications^{3}. Moreover, when magnetism is involved, interactions of the external magnetic field with the magnetic moments can result in exotic properties, such as Weyl states induced by magnetic exchange^{4,5}. However, in contrast to nonmagnetic TSMs, theoretical predictions and experimental studies on magnetic TSMs are rarer and more difficult due to the complexity of the magnetic configuration for calculations and the difficulty in synthesis of single crystals^{3}. In fact, the very nature of the interaction between magnetism and topology in magnetic TSMs remains mysterious. Given how few such compounds are known, seeking and fully characterizing new magnetic TSMs is a priority for the new light they may shed on these issues.
Recently, the nonmagnetic CaP_{3} family of materials was proposed as potential host of topological nodalline (TNL) semimetals^{6}, among which SrAs_{3} possesses a TNL feature at ambient pressure^{7,8,9} and exotic properties under high pressure^{10}. Isostructural with SrAs_{3}, EuAs_{3} orders in an incommensurate antiferromagnetic (AFM) state at T_{N} = 11 K, and then undergoes an incommensurate–commensurate lockin phase transition at T_{L} = 10.3 K, producing a collinear AFM ground state^{11,12,13,14,15,16}. Previous electrical transport studies found an extremely anisotropic magnetoresistance (MR), which is strongly related to the magnetic configuration of EuAs_{3}^{17}. However, experiments sensitive to the topology have not been reported on EuAs_{3}.
In this paper, we demonstrate a magnetisminduced topological transition from a TNL semimetal in the paramagnetic or the spinpolarized state to a topological massive Dirac metal in the AFM ground state. First, we explore the band structure in the AFM ground state through band calculations and transport measurements, demonstrating that EuAs_{3} is a magnetic topological massive Dirac metal. Second, Shubnikov–de Haas (SdH) oscillations and band calculations in the spinpolarized state are displayed, yielding a proposal that EuAs_{3} is a TNL semimetal with an extremely large magnetoresistance (XMR) of ∼2 × 10^{5}% at 1.8 K and 28.3 T. Third, our angleresolved photoemission spectroscopy (ARPES) results in the paramagnetic state verify the nodalline structure as predicted by band calculations. Ultimately, the origin of the XMR and a temperatureinduced Lifshitz transition are revealed.
Results
Topological massive Dirac metal state in the AFM state
EuAs_{3} crystallizes in a monoclinic structure (space group C2/m, No. 12), and the magnetic moments of Eu^{2+} are oriented parallel and antiparallel to the monoclinic b axis^{11,12,13,14,15,16}, as plotted in Fig. 1a. Figure 1b shows the bulk and (110) surface Brillouin zones (BZs) of EuAs_{3} in the doubled unit cell corresponding to its AFM ground state. The calculated band structure including spin–orbit coupling (SOC) in this magnetic ground state as determined by neutron diffraction experiments^{12} for EuAs_{3} is displayed in Fig. 1c. In addition to topological bands around the Γ point, several trivial bands cross the Fermi level, indicating that EuAs_{3} is a metal rather than a semimetal. In magnetic systems, TRS is broken. To preserve the Dirac node, extra symmetries, for example, the combination of inversion (I) and timereversal (T) symmetries, i.e., IT, are necessary^{3}. The Dirac band crossing is not topologically protected, and it can be gapped out by SOC to turn into a gapped dispersion of massive Dirac fermions^{3}. Following this clue, two massive Dirac points around Γ point are identified, as shown in the inset to Fig. 1c. The complicated Fermi surface is composed of two hole sheets and one electron sheet in the AFM state (Fig. 1d), all of threedimensional (3D) character. The electron sheet consists of two individual pockets, i.e., electron_1 and electron_2, which can both be detected by quantum oscillations.
Projected band structure analysis shows that the low energy states near the Fermi level are dominated by As4p states (Fig. 1e). There are clear signatures of band inversion between Asp_{x,y} and Asp_{z} orbitals at the Γ point. To identify the topological character, we calculated the Z_{2} invariant by employing the Willson loop method^{18}. Figure 1f, g show the evolution of the Wannier charge center on two representative planes of the bulk BZ. From the calculations, the Z_{2} invariant for the k_{z} = 0 plane is 1, whereas Z_{2} is 0 for the k_{z} = 0.5 plane, providing strong evidence for nontrivial topology. Moreover, topologically protected surface states are expected, and we can unambiguously identify nontrivial surface states in the surface spectrum for the semiinfinite (010) surface, as displayed in Fig. 1h, confirming further the nontrivial topology in the AFM state.
To verify the predictions from band calculations, we conducted electrical transport measurements. Resistivity in zero magnetic field is plotted in Fig. 2a, which displays typical metallic behavior with a lowtemperature peak corresponding to the magnetic transitions. The magnetic transitions were also found by thermodynamic measurements (Supplementary Fig. 1) to be consistent with previous reports^{11,12,13,14,15,16}. The inset to Fig. 2a shows the fit to the resistivity data below 2.5 K using a power law: ρ = ρ_{0} + AT^{2}, where ρ_{0} is the residual resistivity and A the electronic scattering coefficient. The fit gives a residual resistivity ρ_{0} of 2.6 µΩcm, and the residual resistivity ratio ρ_{300K}/ρ_{0} is ~72. Figure 2b shows the lowfield MR data with evident SdH oscillations. B_{M} in Fig. 2b denotes the critical field, above which the spins are fully polarized by the external magnetic field. The SdH oscillation amplitude can be described by the Lifshitz–Kosevich formula^{1,2}: \(\,\Delta {{\rho }}_{{xx}}{{{{{\rm{\propto }}}}}}\,\frac{2{{{{{{\rm{\pi }}}}}}}^{2}{k}_{{{{{{\rm{B}}}}}}}T/{\hslash {\omega}}_{{{{{{\rm{c}}}}}}}}{{{\sinh }}\left(2{{{{{{\rm{\pi }}}}}}}^{2}{k}_{{{{{{\rm{B}}}}}}}T/{\hslash {\omega}}_{{{{{{\rm{c}}}}}}}\right)}{e}^{2{{{{{{\rm{\pi }}}}}}}^{2}{k}_{{{{{{\rm{B}}}}}}}{T}_{{{{{{\rm{D}}}}}}}/{\hslash {\omega}}_{{{{{{\rm{c}}}}}}}}{{\cos }}2{{{{{\rm{\pi }}}}}}\,(\frac{F}{B}{\gamma }+{\delta }),\) where ω_{c} = eB/m* is the cyclotron frequency and T_{D} is the Dingle temperature. \({\gamma }=\frac{1}{2}\left(\frac{1}{2{\pi }}\right){\phi }_{{{{{{\rm{B}}}}}}}\) (0 ≤ γ ≤ 1) is the Onsager phase factor, and ϕ_{B} is a geometrical phase known as the Berry phase. For a topological system with peculiar electron state degeneracy and intraband coupling, a π Berry phase will be observed. 2πδ is an additional phase shift resulting from the curvature of the Fermi surface in the third direction, where δ varies from 0 to ±1/8 for a quasitwodimensional (quasi2D) cylindrical Fermi surface and a corrugated 3D Fermi surface, respectively^{7,8}. The cyclotron effective mass m* can be obtained from the thermal damping factor \({{R}}_{T}=\frac{2{{\pi }}^{2}{k}_{{{{{{\rm{B}}}}}}}T/{\hslash {\omega}}_{{{{{{\rm{c}}}}}}}}{{{\sinh }}\left(2{{\pi }}^{2}{k}_{{{{{{\rm{B}}}}}}}T/{\hslash {\omega}}_{{{{{{\rm{c}}}}}}}\right)}\).
By analyzing the oscillatory component (inset to Fig. 2c) below B_{M} via fast Fourier transform (FFT), four bands are uncovered, i.e., 156, 185, 217, and 7 T, referred to as α, β, γ^{1}, and γ^{2}, respectively, in line with the band calculations. To check their topological nature, a Landau index fan diagram is plotted in Fig. 2d, yielding intercepts of 0.6(2), 0.5(1), −0.03(9), and 0.07(8) for α, β, γ^{1}, and γ^{2}, respectively. Throughout this paper, we assign integer indices to the ∆ρ_{xx} peak positions in 1/B and half integer indices to the ∆ρ_{xx} valleys. According to the Lifshitz–Onsager quantization rule for a corrugated 3D Fermi surface, intercepts falling between −1/8 and 1/8 suggest nonzero Berry phase, while intercepts in the range 3/8–5/8 indicate trivial band topology. Therefore, the γ^{1} and γ^{2} bands may be topologically protected, while the other two are trivial. However, the index number is >20 (α, β, and γ^{1} pockets), and hence the extrapolation from the Landau fan plots may have biggish uncertainty. In order to validate the topological nature, more solid evidences are needed. Other parameters for these four bands, such as the Fermi energy E_{F}, extremal crosssectional areas A_{F}, Fermi momentum k_{F}, Fermi velocity v_{F}, cyclotron effective mass m^{∗}, and Dingle temperature T_{D}, are calculated and summarized in Table 1.
In TSMs, in addition to nonzero Berry phase, the nLMR induced by the chiral anomaly can also serve as a smoking gun for nontrivial topology^{19,20,21}. Figure 2e displays the nLMR of EuAs_{3} with magnetic field parallel to the electric current I. The kinks in the nLMR curves below the ordering temperature arise from the fieldinduced transitions^{15,16,17}, i.e., from a collinear AFM phase to incommensurate and commensurate spiral phases^{15,16,17}. Negative MR in magnetic systems is not uncommon^{19,20,21} when the applied magnetic field suppresses the inelastic magnetic scattering from local moments or magnetic impurities, leading to a negative MR for charge transport along all directions^{19,20,21}. However, in EuAs_{3} we only observed a nLMR when the magnetic field is applied parallel to the electric current (Supplementary Fig. 2). Furthermore, if the applied external magnetic field has a strong effect on the magnetic scattering and induces a nLMR, the changes in the nLMR will occur predominantly below and above the ordering temperature. This is not observed. Instead, we find several minor kinks arising from the magnetic transitions, on top of a much larger signal. Therefore, the suppression of magnetic scattering can be excluded as the origin of the nLMR in EuAs_{3}. The nLMR also displays a wide variety of temperature dependences, ruling out current jetting effects and the weak localization effect^{19,20,21}. Since nontrivial band topology has been suggested in EuAs_{3}, the chiral anomaly arising from Weyl fermions is the most likely mechanism behind the nLMR.
The nLMR induced by the chiral anomaly in TSMs can be analyzed through the Adler–Bell–Jackiw (ABJ) chiral anomaly equation^{19,20,21}: \({{{{{\rm{\sigma }}}}}}\left(B\right)=\left({1+C}_{{{{{{\rm{w}}}}}}}{B}^{2}\right)\left({\sigma }_{0}+a\sqrt{B}\right)+{{{{{{\rm{\sigma }}}}}}}_{{{{{{\rm{N}}}}}}}\), where σ_{0}, C_{w}, and \({\sigma }_{{{{{{\rm{N}}}}}}}^{1}={{\rho }}_{0}+A{B}^{2}\) denote the conductivity at zero field, a temperaturedependent positive parameter originating from chiral anomaly, and the conventional nonlinear band contribution around Fermi energy, respectively. Figure 2f shows the conductivity and the fit to the data below 3 T at various temperatures. The data above the ordering temperature are well described by the ABJ equation, while the data at lower temperatures do not fit as well, which may be ascribed to magnetic transitions or topological transitions. The inset to Fig. 2f shows the temperature dependence of C_{w}. At 2 K, C_{w} is 0.253(7) T^{−2}. With increasing temperature, a clear anomaly in C_{w} around the ordering temperature can be observed, verifying the proposal above. When T > T_{N}, C_{w} decreases monotonically, as observed in SrAs_{3}^{7}. Taken together, these results demonstrate that EuAs_{3} is a magnetic topological massive Dirac metal in its AFM ground state.
Topological state in the spinpolarized state
We now turn to the exploration of topology in the spinpolarized state, where in Fig. 2b we have already observed a clear change in the quantum oscillations. Figure 3a plots the MR of EuAs_{3} in higher magnetic field, and an unsaturated XMR ~2 × 10^{5}% at 1.8 K and 28.3 T is observed. By analyzing the oscillatory components above B_{M} (inset in Fig. 3b), frequency components are identified at F = 93, 158, 346, and 597 T, which are referred to here as the ξ, α′, ε, and η bands, respectively (Fig. 3b). These four bands are different from those in lower field (Fig. 2c), indicating that they are likely rooted in different band structure. This is unsurprising since the unit cell is no longer doubled by antiferromagnetism, but the fieldinduced spin polarization can also play a significant role. We thus conducted band calculations for the fieldpolarized state (Supplementary Fig. 3) and the paramagnetic state (Supplementary Fig. 4), and these are indeed quite different, as we discuss in more detail in Supplementary Notes 3 and 4.
In the fieldpolarized state, we find four Fermi surface sheets—two electron and two hole sheets and double nodal loops at the Y point, one each for the spinup and spindown channels (Supplementary Fig. 3d). To identify the topological nature of the four bands seen in quantum oscillations, a Landau index fan diagram is plotted in Fig. 3c, and the intercepts are −0.0(1), 0.67(3), 0.34(4), and 0.61(4) for the ξ, α′, ε, and η bands, respectively. Although the intercepts from the fit with large Landau index number cannot serve as a smoking gun for topology, we still use them, because it is difficult for us to evaluate the topological nature in the fully spinpolarized state above 11.0 T (the critical field is deduced from specific heat in Supplementary Fig. 1c). The intercepts give a hint that the ξ band is topologically protected, while the α′ and η bands are topologically trivial. The intermediate value for ε is suggestive of a possible nontrivial Berry phase but does not allow a strong conclusion and will require further verification. The cyclotron effective masses m* for these four pockets can be obtained by fitting the temperature dependence of the normalized FFT amplitude, as shown in the right inset to Fig. 3c. Other parameters can be also extracted, and all values are summarized in Table 1.
To better reveal the Fermi surface anisotropy and topology of EuAs_{3}, angledependent MR measurements have been performed at 1.8 K, in the experimental geometry shown in the inset to Fig. 3d. Upon rotating sample from 0° to 90°, the magnitude of the MR is reduced monotonically, as also seen in a polar plot of the MR (Supplementary Fig. 2b). We extract the frequency components for the ξ, α′, ε, and η bands by analyzing the oscillatory component (Fig. 3e) and summarize the results in Fig. 3f. The angle dependence of the ξ, α′, and η bands is of 3D character, while the ε band is well described below 50° by the formula F = F_{3D} + F_{2D}/cos(θ), where F_{2D} and F_{3D} denote 2D and 3D components, respectively. The ratio between the 2D and 3D components derived from the fit (F_{2D}/F_{3D}) is ∼1.76, suggesting that the ε pocket exhibits mainly 2D character although a 3D component also exists.
Now, we turn to the angle dependence of the Berry phase. As shown in Fig. 3g, the intercept for the topological ξ band shows strong angle dependence, similar to results in other systems such as Cd_{3}As_{2}^{22}, ZrSiM (M = Se, Te)^{23}, or ZrTe_{5}^{24}. For θ < 30° and θ ≥ 60°, the intercept falls between −1/8 and 1/8, while it falls between 3/8 and 5/8 for 30° ≤ θ < 60°. For the ε band, the intercept from 0° to 70° fluctuates between 1/8 and 5/8, averaging to 0.34(5), which is suggestive of trivial topology. However, when θ reaches 80° and 90°, this intercept falls between −1/8 and 1/8, implying nonzero Berry phase. For η and α′ bands, the intercepts at all angles remain between 1/8 and 5/8, averaging 0.4(2) and 0.5(2), respectively, indicating trivial topology. Figure 3h, i show Hall results, which will be discussed later.
TNL structure in the paramagnetic state
Since our band structure calculations identify nodal loops at Y and our quantum oscillation data indicate nontrivial band topology, we also directly investigated the band structure with ARPES (Fig. 4). Momentum analysis in this technique is incompatible with magnetic field, so we investigated the paramagnetic rather than the fieldpolarized state; however, as shown in more detail in Supplementary Figs. 3 and 4, a closed nodal loop persists at the Y point in the paramagnetic state. In order to visualize the nodal loop in EuAs_{3}, the photon energy dependence of the electronic structure along the k_{y} direction was investigated at 12 K within the vertical plane of the (010) cleaved surface, as sketched in Fig. 4c.
From the intensity plot of the Fermi surface at 12 K in the k_{y}–k_{z} plane (Fig. 4a) taken at E_{F} −0.2 eV, the pocket centered at the Y point (54 eV) can be easily identified, and two nodes arising from the crossing of the electronlike and holelike bands can be also observed in Fig. 4b, which agrees with the band calculations. As observed in SrAs_{3}, the drumheadlike surface state of EuAs_{3} is buried in the bulk state, so it cannot be resolved by ARPES. For ARPES cuts away from the Y point, the bandcrossing area shrinks gradually and finally disappears, and the topological nontrivial nodal loop encircled the Y point, illustrated by the red ellipse in Fig. 4d. Besides, the k_{y}dependent evolution of the band structure shows a good agreement with the calculations (the black dotted curves in Fig. 4d) and the corresponding energydistribution curves could further confirm the nodes introduced by the band crossing and their k_{y}dependent evolution in Fig. 4f (dashed line is a guide for the eyes to trace the dispersions). The evolution of the nodes along the k_{x}direction is presented in Fig. 4e, which shows the band dispersions along cuts 1–4 indicated in Fig. 4b (photoemission intensity map of constant energy contours at 0.5 eV below E_{F}). We noticed both the electron and holelike bands deplete their spectral weight from 1 to 4, consistent with the bandcrossing scenario. However, whether or not a gap opens in the nodes away from k_{x} = 0 remains vague due to the intrinsic broadness of the electronlike band. We also measure the electronic structure of another sample at 18 K, as shown in Supplementary Fig. 5, and obtain the same results. And we also estimate the Fermi momenta k_{F} and Fermi velocities v_{F} to be k_{F} = 0.12 and 0.14 Å^{−1} and v_{F} = 3.7 × 10^{5} and 1.17 × 10^{5} m/s, respectively, for the hole and electron bands, the same order of magnitude as for the ε and η bands (see Table 1). These data are extremely similar to what was found in SrAs_{3}^{9}.
The verification of the nodalline structure in the paramagnetic state by utilizing ARPES measurements and density functional theory (DFT) calculations shows remarkable agreement between the theoretical and experimental values. For the spinpolarized state, which is predicted to hosts closely similar but spin–split band structure to the paramagnetic state, nodalline structure is thus strongly expected to exist in spinpolarized EuAs_{3}. Very recently, lifted degeneracy of the Bloch bands was observed in the paramagnetic phase of EuCd_{2}As_{2}, producing a spinfluctuationinduced Weyl semimetal state^{25}. The magnetic susceptibility in EuAs_{3} reveals a positive Curie–Weiss temperature T_{CW} of 4.4 K for magnetic fields applied within the ab plane (Supplementary Fig. 6), suggestive of ferromagnetic fluctuations deep in the paramagnetic phase. The ferromagnetic correlations in EuAs_{3} may induce band splitting within the paramagnetic phase, which may be resolvable with higherresolution ARPES, such as laser ARPES.
Discussion
It is clear from our transport measurements that the electronic structure in the antiferromagnetically ordered state is very different from that found in the fieldpolarized or paramagnetic states. This is a consequence of the doubling of the unit cell due to AFM order and the coupling of this magnetic order to the electronic structure and is well described by our band calculations. However, a possible additional Lifshitz transition below 3 K has also been suggested.
Figure 3h shows the Hall resistivity (ρ_{xy}) from 0.3 to 30 K. The ρ_{xy} curves are clearly nonlinear, implying the coexistence of two types of carriers, as predicted by band structure calculations. On cooling, the slope of the curve changes from positive to negative, indicating an increased contribution from electron carriers. The carrier concentration and mobility are extracted by fitting the lowfield Hall conductivity with a twocarrier model, and results are summarized in Fig. 3i. For 3 ≤ T ≤ 30 K, the concentration of hole carriers is larger than that of electron carriers. Upon decreasing the temperature <3 K, the concentration of electron carriers is suddenly enhanced, accompanied by a sharp increase in the mobility of hole carriers. These indicate a possible Lifshitz transition.
Temperatureinduced Lifshitz transitions are also observed in other TSMs, for example, MTe_{5} (M = Zr, Hf)^{26,27}, InTe_{1δ}^{28}, ZrSiSe^{29}, WTe_{2}^{30}, and TaIrTe_{4}^{31}. Anomalies in both longitudinal resistivity and Hall resistivity/coefficient can be found in MTe_{5} (M = Zr, Hf)^{26,27}, InTe_{1δ}^{28}, and ZrSiSe^{29}, but not in WTe_{2}^{30} and TaIrTe_{4}^{31}. Since we have observed the change of Hall resistivity in EuAs_{3} (Fig. 3h), we wonder how the longitudinal resistivity evolves with decreasing temperature. The inset of Fig. 2a shows the lowtemperature resistivity from 0.3 to 2.5 K in zero field, and we did not observe any distinct anomaly. Considering that the variations in resistivity may be very weak and the temperature range from 0.3 to 2.5 K is not appropriate, we measured two more samples (denoted as Sample 4 and Sample 5 in Supplementary Fig. 7a), and found that there is a very weak anomaly at ~2.3 K in resistivity for both samples (see Supplementary Fig. 7b). Since the Lifshitz transition should also manifest in quantum oscillations, we further check the lowfield MR data below B_{M} in Fig. 2b and the FFT in Fig. 2c. One can see that, due to the limited oscillatory periods and/or noise at 3 K, the Lifshitz transition cannot be resolved from the lowfield quantum oscillation data. To verify it, other lowtemperature probes are needed, for example ARPES and scanning tunneling microscopy/scanning tunneling spectroscopy.
Now, we turn to the highfield state >B_{M}. The temperature dependence of Hall coefficient measured at 9 T for Sample 5 is shown in Supplementary Fig. 7c. With decreasing temperature, a small peak at ~3.6 K arises and Hall coefficient changes its sign from positive to negative at ~2.3 K. We then analyze the oscillatory component (∆ρ_{xy}) > B_{M}, and a new oscillation frequency of 374 T (denoted as the φ band) can be clearly distinguished at 0.3 K, as shown in Supplementary Fig. 8a. The trivial topology nature for φ band has also been demonstrated (see Supplementary Fig. 8b). Therefore, a temperatureinduced Lifshitz transition likely exists in both AFM and spinpolarized states, although the change of Fermi surface topology with temperature in these two states may be different. Generally speaking, Lifshitz transitions are related to electronic transitions at zero temperature and involve abrupt changes of the Fermi surface topology. However, in topological materials, Lifshitz transitions can also involve other types of zeroenergy modes, such as Weyl or Dirac nodes, nodal lines, flat bands, Majorana modes, etc.^{32}. It has been proposed that multiple types of novel Lifshitz transitions involving Weyl points are possible depending on how they connect Fermi surfaces and pockets. For instance, the Lifshitz transition can correspond to the transfer of Berry flux between Fermi pockets connected by typeII Weyl points^{33}. To understand the physics behind the lowtemperature Lifshitz transition in EuAs_{3}, more work is needed.
According to the conventional chargecarrier compensation picture for XMR, the ratio n_{h}/n_{e} should be unity^{1,2}. At 0.3 K, n_{h}/n_{e} for EuAs_{3} is ∼1.0, consistent with this picture. However, for 3 ≤ T ≤ 30 K, n_{h}/n_{e} varies between 1.5 and 2.5 while the MR remains large and unsaturated, evidently excluding the chargecompensation picture for EuAs_{3}. XMR is also frequently encountered in the cases of topologically protected electronic band structure and when open orbits contribute^{1,2,34,35}. According to the openorbit effect, the unsaturated XMR is only observed for current along the open orbits^{35}. However, the observation of the unsaturated XMR with different current direction in EuAs_{3} excludes the openorbit effect (see Supplementary Fig. 9). Besides, for both the chargecarrier compensation picture and openorbit effect, a B^{2} dependence of MR is suggested^{34,35}, which is different from the situation of EuAs_{3} reported here (Supplementary Fig. 9c). Since we have verified nontrivial band topology in EuAs_{3}, we consider this the more likely explanation.
In summary, combining band calculations, electrical transport, and ARPES measurements on the magnetic compound EuAs_{3}, we report a magnetisminduced topological transition from a TNL semimetal in the paramagnetic or the spinpolarized state to a topological massive Dirac metal in the AFM ground state. The paramagnetic and spinpolarized states differ by the splitting of a topological nodal line associated with the spin splitting of the band structure. An XMR of ∼2 × 10^{5}% and an asyetunexplained temperatureinduced Lifshitz transition <3 K have also been revealed. These results indicate that magnetic EuAs_{3} could serve as a unique platform to explore exotic physics at the interface of magnetism and topology.
Methods
Sample synthesis
Eu (99.95%, Alfa Aesar), As (99.999%, PrMat), and Bi (99.9999%, Aladdin) blocks were mixed in a molar ratio of 1:3:26 and placed into an alumina crucible. The crucible was sealed in a quartz ampoule under vacuum and subsequently heated to 900 °C in 15 h. After reaction at this temperature for 20 h, the ampoule was cooled to 700 °C over 20 h and then slowly cooled to 450 °C at −1 °C/h. The excess Bi flux was then removed using a centrifuge, revealing EuAs_{3} single crystals with black shiny metallic luster.
Electrical transport and thermodynamic measurements
For electrical transport measurements, a single crystal was cut into a bar shape. A standard fourprobe method was used for the longitudinal resistivity measurement. Data were collected in a ^{3}He and a ^{4}He cryostat. Magnetic susceptibility and specific heat measurements were performed in a magnetic property measurement system (MPMS, Quantum Design) and a physical property measurement system (PPMS, Quantum Design), respectively. Highfield measurements were performed at the Steady High Magnetic Field Facilities, High Magnetic Field Laboratory, Chinese Academy of Sciences in Hefei.
ARPES measurements
ARPES measurements were performed at beam line BL13U at the National Synchrotron Radiation Laboratory (NSRL), China (photon energy hν = 1238 eV); beam line BL03U of Shanghai Synchrotron Radiation Facility (SSRF), China (photon energy hν = 3490 eV). The samples were cleaved in situ at 18 K (12 K) and measured in ultrahigh vacuum with a base pressure of better than 3.5 × 10^{−11} (5 × 10^{−11}) mbar at NSRL (SSRF). Data were recorded by a Scienta R4000 at NSRL and SSRF. The energy and momentum resolution were 10 meV and 0.2°, respectively.
DFT calculations
Firstprinciples calculations were carried out within the framework of the projector augmented wave method^{36,37} and employed the generalized gradient approximation (GGA)^{38} with Perdew–Burke–Ernzerhof formula^{39}, as implemented in the Vienna ab initio Simulation Package^{40}. Two unit cells repeated along the b axis were adopted to simulate the AFM configuration indicated by neutron diffraction experiment for EuAs_{3}^{14}. The energy cutoff was chosen to be 500 eV. A Γcentered 8 × 6 × 14 Monkhorst–Pack kpoint grid was used to produce the wellconverged results for the AFM phase. For the spinpolarized and paramagnetic band calculations, the same unit cell was used. Γcentered 10 × 10 × 10 and 6 × 6 × 6 grids were used in the first BZ for the unit cell and supercell magnetic structures, respectively. The convergence criterion of energy in relaxation was set to be 10^{−6} eV and the atomic positions were fully relaxed until the maximum force on each atom was <0.02 eV/Å. The electronic correlations of Eu4f states were treated by the GGA + U method^{41}. SOC was considered in a selfconsistent manner. The Wannier90 package^{42} was adopted to construct Wannier functions from the firstprinciples results. The WannierTools code^{43} was used to investigate the topological features of surface state spectra.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
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Acknowledgements
This work is supported by the Natural Science Foundation of China (Grant Nos. 12034004, 11674367, 11674229, and 11874264), the Ministry of Science and Technology of China (Grant Nos. 2016YFA0300503 and 2017YFA0305400), the Shanghai Municipal Science and Technology Major Project (Grant No. 2019SHZDZX01), the Zhejiang Provincial Natural Science Foundation (Grant No. LZ18A040002), and the Ningbo Science and Technology Bureau (Grant No. 2018B10060). W.Z. is supported by the Shenzhen Peacock Team Plan (KQTD20170809110344233) and Bureau of Industry and Information Technology of Shenzhen through the Graphene Manufacturing Innovation Center (201901161514). Y.G. acknowledges research funds from the State Key Laboratory of Surface Physics and Department of Physics, Fudan University (Grant No. KF2019 06). C.X. was supported by the Users with Excellence Project of Hefei Science Center CAS (Grant No. 2018HSCUE015). D.C.P. is supported by the Chinese Academy of Sciences through 2018PM0036 and from the Deutsche Forschungsgemeinschaft (DFG), through project C03 of the Collaborative Research Center SFB 1143 (projectID 247310070). The authors are grateful for support from the Analytical Instrumentation Center (# SPSTAIC10112914), SPST, ShanghaiTech University. Part of this research used beamline 03U of the Shanghai Synchrotron Radiation Facility, which is supported by ME2 project under contract No. 11227902 from the National Natural Science Foundation of China.
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S.L. and Y.G. conceived the idea and designed the experiments. E.C. was responsible for electronic transport experiments. W.X., X.W., N.Y., and H.S. performed sample synthesis and partial data analysis. X.S., S.X., W.R., and W.Z. performed the electronic band calculations. C.X., L.W., and L.P. helped with the MR measurements in Hefei. H.F., C.W., Y.C., and Z.L. performed ARPES measurements and analysis. Z.L., Y.G., and S.L. supervised the project. E.C., D.C.P., Y.G., and S.L. analyzed the data and wrote the paper. All authors discussed the results and commented on the manuscript.
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Cheng, E., Xia, W., Shi, X. et al. Magnetisminduced topological transition in EuAs_{3}. Nat Commun 12, 6970 (2021). https://doi.org/10.1038/s41467021264827
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DOI: https://doi.org/10.1038/s41467021264827
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