Magnetism-induced topological transition in EuAs3

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 EuAs3, demonstrating a magnetism-induced topological transition from a topological nodal-line semimetal in the paramagnetic or the spin-polarized state to a topological massive Dirac metal in the antiferromagnetic ground state at low temperature. The topological nature in the antiferromagnetic state and the spin-polarized state has been verified by electrical transport measurements. An unsaturated and extremely large magnetoresistance of ~2 × 105% at 1.8 K and 28.3 T is observed. In the paramagnetic states, the topological nodal-line structure at the Y point is proven by angle-resolved photoemission spectroscopy. Moreover, a temperature-induced Lifshitz transition accompanied by the emergence of a new band below 3 K is revealed. These results indicate that magnetic EuAs3 provides a rich platform to explore exotic physics arising from the interaction of magnetism with topology.

To avoid any influence from the metamagnetic transition and investigate the fully spinpolarized state, we collected our quantum oscillation data above 11.0 T (Figs. 3(b) and 3(e) in the main text). showing typical twofold anisotropy. Compared with θ, the AMR for  is much more complicated, which is ascribed to the field-induced magnetic transitions 1 . For  ∼ 90, i.e., magnetic field parallel to electric current I, a negative MR is observed. According to Supplementary Fig. 2(b) and 2(c), the scenario that external magnetic field suppresses the inelastic magnetic scattering from local moments or magnetic impurities and then induces a negative MR along all directions can be excluded.

Supplementary Note 3: Band structure in the spin-polarized state
The GGA+U (U = 5 eV) band structures of the spin-up and spin-down electrons, We also re-measure the electronic structure of another EuAs3 single crystal at 18 K within the vertical plane of the (010) cleaved surface, as shown in Supplementary   Fig. 5. From the intensity plot of the Fermi surface in the ky-kz plane ( Supplementary   Fig. 5(a)), the pocket centered at the Y point (17 eV) can be easily identified, and two nodes arising from the crossing of the electronlike and holelike bands can be also observed in Supplementary Fig. 5(b), which agrees with the band calculations (red lines). For ARPES cuts away from the Y point ( Supplementary Fig. 5(b)), the bandcrossing area shrinks gradually and finally disappears. This is highlighted by an orange ellipse, and represents the nodal loop predicted by our band structure calculations. Supplementary Fig. 7(a) shows the low-temperature resistivity of two more samples (Sample 4 and Sample 5), and the antiferromagnetic and incommensurate-tocommensurate lock-in transitions take place at 11 K and 10.3 K, respectively. As displayed in the inset of Fig. 2(a) in the main text, we didn't observe any distinct anomalies below 2.5 K. To check this, the low-temperature resistivity measurements  Fig. 8(b), and there is no any distinct anomaly below 3 K. Considering that the variation in resistivity may be very weak and the weak signal may be covered by noise, we use a polynomial to reproduce the experimental data (the red solid lines in Supplementary Fig. 7(b)), and obtain the derivative from the simulated data.

Supplementary
Surprisingly, a broad peak locating at ~2.3 K has been found in both Sample 4 and inset shows the extrapolation of 1/B to zero.
To check the temperature-induced Lifshitz transition, we analyze the oscillatory component (∆ρxy) (displayed in the inset to Supplementary Fig. 8(a)) via FFT, and a new band (denoted as ) with oscillation frequency of 374 T has been identified, demonstrating the Lifshitz transition. We then check the topology of the φ band, as plotted in Supplementary Fig. 8(b). We assign integer indices to the ∆ρxy peak positions 3, magnetic field is applied along the c axis, and electric current I along the a axis. c B 2 as a function of MR for three different samples. The data for Sample 1 is taken from that in Fig. 2(b). With changing the direction of electric current, the unsaturated XMR persists, excluding the open-orbit effect.
To exclude the open-orbit effect which may also induce the XMR in EuAs3, we a b c performed the MR measurements with electric current I applied along different crystallographic axis, as shown in Supplementary Fig. 9. Supplementary Fig. 9(a) shows the MR of Sample 2 with magnetic field parallel to c axis and electric current applied along the [110] direction, which is the same as Sample 1 (Fig. 2(b)). Compared with Sample 1, the MR of Sample 2 with RRR ∼ 61 is smaller than that of Sample 1, indicating that the quality of single crystal may have a great effect on the magnitude of MR. For Sample 3 with smaller RRR ∼ 52, the MR is smaller than those of Sample 1 and Sample 2. For comparison, we plot the B2 dependence of MR for these three samples, as shown in Supplementary Fig. 9(