Spontaneous Hall effect in the Weyl semimetal candidate of all-in all-out pyrochlore iridate

ARTICLE DOI: 10.1038/s41467-018-05530-9 OPEN Spontaneous Hall effect in the Weyl semimetal candidate of all-in all-out pyrochlore iridate 1234567890():,; Kentaro Ueda1, Ryoma Kaneko1, Hiroaki Ishizuka1, Jun Fujioka1,2, Naoto Nagaosa1,3 & Yoshinori Tokura1,3 Topological quantum states of matter, characterized by geometrical features of electronic band structures, have been extensively studied. Among them, the topological electronic state with magnetic order remains elusive because of a scarce number of examples. Here we present experimental observations proving that the pyrochlore iridate, when electronically tuned, can be a topological Weyl semimetal as predicted by recent theories. We observe a sizable spontaneous Hall conductivity with minimal magnetization only within a few Kelvin below the all-in all-out magnetic ordering temperature. Our theoretical calculation, which is quantitatively consistent with the observation, suggests that the presence of linearlydispersing crossing points (Weyl points), acting as a source/sink of a quantized magnetic flux, potentially gives rise to such an enormous effect. The manifestation of the salient Hall response provides one important example of topological states, which promotes a better understanding of Weyl semimetal and indicates the new research direction for the topological-materials design. 1 Department of Applied Physics, University of Tokyo, Tokyo 113-8656, Japan. 2 PRESTO, Japan Science and Technology Agency, Kawaguchi, Saitama 3320012, Japan. 3 RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan. Correspondence and requests for materials should be addressed to K.U. (email: ) NATURE COMMUNICATIONS | (2018)9:3032 | DOI: 10.1038/s41467-018-05530-9 | www.nature.com/naturecommunications 1 ARTICLE O NATURE COMMUNICATIONS | DOI: 10.1038/s41467-018-05530-9 rigins of anomalous Hall effect (AHE), conventionally produced by the presence of the magnetization, have been a longstanding issue in condensed matter physics since its discovery more than a century ago1. An intrinsic mechanism of AHE was first proposed by Karplus and Luttinger who attributed it to the electronic band structure with spin–orbit interaction2, which generates an additional contribution in a Hall current with no energy consumption. Recently, this mechanism has been reformulated in terms of the Berry curvature, i.e., the quantum geometric/topological property of the Bloch wave functions3. Since the concept of the topological nature was appreciated, the intrinsic mechanism has received a renewed interest from a broader perspective over the past few decades; the Berry phase is now considered as the key concept for AHE, successfully explaining AHEs observed in a number of magnetic materials4–9. Recently, Weyl semimetal (WSM) has drawn much attention as a unique class of materials that potentially shows an enormous Hall response10,11. WSM is the semimetal or zero-gap semiconductor in which the two non-degenerate bands cross linearly at the band-touching points, i.e., Weyl points (WPs)10–13. Intriguingly, WP can be regarded as a magnetic monopole of Berry curvature in k-space, and therefore, its position is expected to be manifested in AHE. A family of pyrochlore iridates R2Ir2O7 is the first existing compound that is proposed to realize a magnetic WSM by a firstprinciple calculation10. The pyrochlore iridates host symmetry identical to the diamond lattice (Fig.1a) and are considered to be a fertile ground to potentially produce topologically-nontrivial electronic states14. Furthermore, the magnetic ordering configuration shows the all-in all-out (AIAO, 4/0) state which breaks the time-reversal symmetry without reducing the cubic lattice symmetry (Fig. 1b). These conditions are remarkably suitable for the realization of topological states. The recent angle-resolved photoemission (ARPES) study has revealed that the ground state of the paramagnetic metal R = Pr is a unique semimetal with a quadratic-band-touching point right across the Fermi level, which evolves into abundant topologically-nontrivial phases by symmetry-breaking perturbations15,16. When the time-reversal symmetry is broken by the AIAO magnetic order, for instance, WSM is predicted to emerge with 8 WPs for intermediate electron-correlation strengths12,13. In general, WSM is stable against perturbations as each WP is protected by the topological charge. In fact, the R = Nd compound undergoes the AIAO magnetic order below TN, accompanying a metal-insulator transition (Fig. 1c); the theories10,12,13 predict the AIAO WSM state in the vicinity of the AIAO charge-gapped state. Nonetheless, the experimental confirmation of WSM under zero magnetic field turns out to be challenging because the charge gap appears to open so easily by the pair annihilation of WPs which quickly immigrate as a function of the magnetic order parameter and collide with each other at the zone boundaries, consequently leaving metallic fragments only in magnetic domain walls as remnants of the surface state in the gapped state13,17,18. Therefore, WSM is expected in an extremely narrow temperature region right below TN, still being missed so far19. Here we exploit the electronic transport measurements on pyrochlore Nd2Ir2O7 and (Nd0.5Pr0.5)2Ir2O7 by applying pressure and magnetic field to search for the smoking gun of the predicted WSM state. A salient spontaneous Hall effect accompanied by a vanishingly small magnetization is observed only within the narrow temperature window right below TN. Assuming that the observed Hall effect is provoked by the emergence of WPs which can be regarded as a source or sink of the quantized magnetic flux in k-space, we carry out the numerical analysis of the Hall conductivity. As a result, the minimal tilting of the magnetic moment deviating from the ideal AIAO state is proved to cause such an 2 enormous Hall effect. The qualitative consistency with the experiment indicates that the WSM can be realized in pyrochlore iridates, offering a significant step towards the material design for magnetic topological systems. Results Phase diagram for pyrochlore iridates and spontaneous hall effect. To explore the WPs in this system, we take advantage of the Hall effect which is sensitive to the Berry phase3. For this purpose, high-quality single crystals of R = Nd (Nd2Ir2O7) were prepared for transport measurements under fine control of temperature, hydrostatic pressure, and magnetic field. Figure 1d shows the phase diagram as a function of magnetic field for Nd2Ir2O7 (R = Nd) at the pressure P = 1.4 GPa. At zero magnetic field, the magnetic transition occurs at 12 K from paramagnetic to AIAO state. The application of the field along [111] crystalline direction modulates the AIAO pattern by flipping one of four magnetic moments on vertices of a tetrahedron, referred to as 3in 1-out (3/1) configuration. In accordance, the electronic transport properties change dramatically (Fig. 1e); as the field increas (...truncated)