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Complex electronic structure evolution of NdSb across the magnetic transition

The rare-earth monopnictide (REM) family, which hosts magnetic ground states with extreme magnetoresistance, has established itself as a fruitful playground for the discovery of interesting topological phases. Here, by using high-resolution angle-resolved photoemission spectroscopy complemented by first-principles density functional-theory based modeling, we examine the evolution of the electronic structure of the candidate REM Dirac semimetal NdSb across the magnetic transition. A complex angel-wing-like band structure near the zone center and three arc-like features at the zone corner have been observed. This dramatic reconstruction of the itinerant bands around the zone center is shown to be driven by the magnetic transition: Specifically,, the Nd 5d electron band backfolds at the Gamma point and hybridizes with the Sb 5p hole bands in the antiferromagnetic phase. Our study indicates that antiferromagnetism plays an intricate role in the electronic structure of the REM family.

The rare-earth monopnictide (REM) family, which hosts magnetic ground states with extreme magnetoresistance, has established itself as a fruitful playground for the discovery of interesting topological phases. Here, by using high-resolution angle-resolved photoemission spectroscopy complemented by first-principles density-functional-theory based modeling, we examine the evolution of the electronic structure of the candidate REM Dirac semimetal NdSb across the magnetic transition. A complex angel-wing-like band structure near the zone center and three arc-like features at the zone corner have been observed. This dramatic reconstruction of the itinerant bands around the zone center is shown to be driven by the magnetic transition: Specifically, the Nd 5d electron band backfolds at the Γ point and hybridizes with the Sb 5p hole bands in the antiferromagnetic phase. Our study indicates that antiferromagnetism plays an intricate role in the electronic structure of the REM family.
NdSb has been suggested to host a Dirac-like dispersion at the corners of the Brillouin zone (BZ) in its paramagnetic (PM) phase. It undergoes an AFM transition at 15 K under zero magnetic field [7]. NdSb, thus, is an interesting platform for investigating effects of magnetism on the electronic structure and topology in the REM family. Neutron diffraction experiments on NdSb polycrystals in zero field at 2 K show commensurate AFM ordering with Nd magnetic moments directed along the ordering wavevector [30]. Resistivity measurements indicate that NdSb possesses extreme magnetoresistance of ∼ 10 4 %. NdSb displays a complex H-T phase diagram at high fields, with multiple first-order transitions [31]. However, the electronic structure of NdSb in the low-temperature regime (below 15 K) has not been investigated before and the present study will therefore be of great importance to understand the role of antiferromagnetism on the electronic structure of this material.
Here, we report the evolution of the complex electronic band structure of NdSb using high-resolution angleresolved photoemission spectroscopy (ARPES) across the magnetic phase transition. Interestingly, an angel-winglike feature appears at the zone center due to the backfolding of the Nd 5d electron pocket present at the X point as the material undergoes a transition from the PM to the AFM phase, which leads to hybridization between the Nd 5d and Sb 5p bands. Our study reveals the presence of Dirac-like states in both the PM and the AFM phases at the center and corners of the BZ.
Single crystals of NdSb were grown by the Sn flux technique as described elsewhere [32]. Details of experimental as well as theoretical techniques are given in the Supplementary Material (SM) [33]. NdSb crystallizes in a rocksalt type crystal structure with space group Fm3m ( Fig.  1(a)) with lattice constant, a = 6.319Å [34]. The bulk BZ of NdSb along with the projection on to the (001) surface is shown in Fig. 1 of a spherical and diamond-shaped pockets around the center Γ along with two concentric elliptical-electron-like pockets around the corner X of the BZ consistent with an previous study [7]. Theoretical Fermi surface including spin-orbit coupling (SOC) effects projected into the k x -k y plane is shown in Fig. 1(d), and is seen to be in excellent agreement with the corresponding experimental results of Fig. 1(c). This agreement implies significant k z dispersion of the bulk bands. The associated broadening of the bulk features allow surface states to stand out more clearly in our spectra.
The band structure along various k -directions calculated with the inclusion of SOC is presented in Figs. 1(ef), where the blue circles represent the contribution from Nd 5d orbitals and the red circles represent the contribution from the Sb 5p orbitals. One can see that the two hole pockets at the Γ point arise mainly from the Sb 5p orbitals, whereas the electron pocket at the X point arises due to the mixture of both Nd 5d and Sb 5p orbitals. From the orbital character plots, we can see the presence of a band inversion between the Nd 5d and Sb 5p orbitals at the X high-symmetry point. The WL spectra [35,36] at k z = 0 and k z =π have been calculated and shown in the SM, [33] which show strong topological index Z 2 = 1, suggesting the material to be topologically nontrivial.
In Figs. 2(a) and 2(b), we present the FS maps and the constant-energy-contour (CEC) plots in the PM (20 K) and AFM phases (7 K), respectively. A small circular pocket as indicated by an arrow in Fig. 2(b) left panel, which is absent in the PM phase, emerges at the cen-ter of the BZ in the AFM phase. This circular feature changes to an almost point like feature at around 60 meV below the Fermi level asserting the electron like nature of the band. At this binding energy, one can begin to resolve another larger circular pocket, which decreases in size on going further down to 120 meV, where the first circular pocket completely vanishes. Interestingly, at 300 meV below the Fermi level in the AFM phase, the circular pocket appears to be enlarged in size indicating the hole-like nature of the carriers at this binding energy. Moving further towards higher binding energies, the circular pocket enlarges, but the size of this hole pocket is smaller in the AFM phase compared to the PM phase, indicating that the hole band is pushed downwards in energy in the AFM phase.
To observe the possible effect of magnetism on the band dispersion, temperature dependent measurements along the Γ−X high-symmetry direction were performed as shown in Fig. 3 for both the PM and the AFM phase. In the PM phase, there are two hole-like bands crossing the Fermi level along with a linear Dirac-like band at the Γ point denoted as α (see SM [33] for a clearer view). With the onset of antiferromagnetism, significant changes in the electronic structure are observed as shown in Fig. 3(b). The band denoted as α 1 shows signature of a Dirac-like band in the AFM phase. An additional band denoted as α 2 is also observed in the AFM phase due to exchange splitting of the α 1 band. Apart from the changes discussed above, a huge transformation of the electronic structure due to the emergence of a number of folded bands in the AFM phase is observed. In particular, at the zone center near the Fermi level, a complex angel-wing-like structure is observed in the AFM phase which has been denoted as β (see SM [33]). This structure is reproducible even after thermal recycling of the sample, thus suggesting that these states are very robust and arise only through the effect of magnetic transition in this material as shown in the SM [33]. The calculated band structures of NdSb (001)-surface for the PM and AFM phases are shown in Fig. 3 for comparison with the ARPES data where the bright red bands represent surface states. AFM calculations were performed by considering the ordering wavevector aligned along the c-axis. The comparison of the DFT band structure with the ARPES data suggests that the Dirac-like bands observed at the Γ point denoted as α in the PM phase, α 1 in the AFM phase and the Dirac-like bands at the X point are surface states. Our DFT calculations are able to reproduce the experimental ARPES data suggesting that the extra bands at the Γ point in the AFM phase arise due to the zone-folding effect. The extra bands at the Γ point may also originate due to the splitting of the bands when the magnetic moment is aligned along the caxis in the AFM phase compared to the PM phase, thus further complicating the band structure. To determine the orbital character of the bands at the Γ point, we have plotted the band structure in detail as shown in SM [33], which clearly shows that the angel wing-like structure arises mainly due to the Nd 5d states. The Dirac-like bands shown by arrows in Fig. 3(b) have contributions from both the Nd 5d and the Sb 5p orbitals. This suggests that the Nd 5d electron-like pocket at the X point backfolds at the Γ point due to the onset of AFM transition. We have unfolded the band structure in the AFM phase and compared it with the bands in the PM phase. Both the band structures show the band inversion at X. Other than that, we did not find any other band inversion in the AFM phase suggesting that the AFM is also topologically nontrivial. From our slab calculations as shown in the right panel of Fig. 3(a, b), we can see the presence of two surface states at the X high symmetry point (red-colored bands) within the inverted band gap. The two surface states are observed because two distinct X points in the bulk BZ are projected to an X point in the surface BZ. In addition to this, according to Ref [6], we can suggest the mirror Chern number, C+ = +1 for NdSb as the two surface states at the X point are gapped due to hybridization. The presence of one odd surface state at Γ and two surface states at the X point, which is demon- The dispersion maps were taken along the Γ−X −Γ direction. The green arrows indicate the additional bands in the AFM phase. All the measurements were performed at a photon energy of 50 eV. strated in Fig. 3 (a, b) strongly supports our conclusion about the nontrivial band topology induced by the observed parity inversion. The Dirac-like state at the X point of the BZ can be seen more clearly when the band structure is measured along the M − X − M direction as shown in Fig. 3(c,d) and is in good agreement with a previous report [7]. The DFT results are shown in the right panel of Fig. 3 (c,d) and reproduce the obtained ARPES results. Interestingly, DFT calculation shows a small band gap at the X point which can be seen from the zoomed in view of the data presented in Fig. 3(e,f). However, the ARPES data suggests a large band gap for the surface states at the X point in both the magnetic and paramagnetic phases. The Fermi level is also slightly shifted in the experiments compared to the DFT calculations. This discrepancy between the experimental and the theoretical results are likely due to the inaccuracy of DFT calculations for these low carrier density systems which has been observed in some other reports [37][38][39]. An additional reason may be due to the significant effect of the f electrons in the electronic structure of NdSb at low temperatures which has been ignored as f states are assumed to be completely localized in our calculations. To observe the effect of the magnetic transition at the corner of the BZ, a zoomed in view of the Fermi surface at the X point is shown in Fig. 4(a) for both the PM and the AFM phase. We can clearly see the presence of additional features in the AFM Fermi surface (shown by arrows in Fig. 4(a)). To visualize the changes more clearly, the band dispersion along the Γ − X − Γ direction has been plotted. An electron like pocket and a linear Dirac-like state is observed at the X point for both the PM and the AFM phase. Furthermore, in the AFM phase, several extra features can be observed near the Fermi level denoted as γ 1 , γ 2 and γ 3 , which is absent in the PM phase and is consistent with our Fermi surface measurements [see Fig. 4(a)]. Particularly, three small features are observed within the close proximity of the Fermi level. These features are also reproducible as the temperature is recycled and arises only in the AFM phase (see SM [33]). These robust complex features observed at the X point could not be observed from our DFT calculations. Further study is required in order to completely understand these extra features observed at the X point.
In summary, we have carried out an ARPES study along with parallel first-principles modeling of the electronic and magnetic structures of the rare-earth monopnictide NdSb in the PM and the AFM phases. A significant reconstruction of the electronic states is found to take place with the onset of antiferromagnetic transition. A complex angel-wing-like band structure near the zone center and three arc-like features at the zone corner are observed. We demonstrate the presence of a linear, Dirac-like band at Γ and two Dirac-like bands at the X point in the BZ in both the PM and the AFM phase indicating the non-trivial topology of the material. Our study, thus, highlights the interplay between magnetism and topology in the rare-earth monopnictides.