Although Weyl fermions have proven elusive in high-energy physics, their existence as emergent quasiparticles has been predicted in certain crystalline solids in which either inversion or timereversal symmetry is broken [1][2][3][4]. Recently they have been observed in transition metal monopnictides (TMMPs) such as TaAs, a class of noncentrosymmetric materials that heretofore received only limited attention [5][6][7]. The question that arises now is whether these materials will exhibit novel, enhanced, or technologically applicable electronic properties. The TMMPs are polar metals, a rare subset of inversion-breaking crystals that would allow spontaneous polarization, were it not screened by conduction electrons [8][9][10]. Despite the absence of spontaneous polarization, polar metals can exhibit other signatures of inversion-symmetry breaking, most notably second-order nonlinear optical polarizability, χ (2) , leading to phenomena such as optical rectification and second-harmonic generation (SHG). Here we report measurements of SHG that reveal a giant, anisotropic χ (2) in the TMMPs TaAs, TaP, and NbAs. With the fundamental and second harmonic fields oriented parallel to the polar axis, the value of χ (2) is larger by almost one order of magnitude than its value in the archetypal electrooptic materials GaAs [11] and ZnTe [12], and in fact larger than reported in any crystal to date.The last decade has witnessed an explosion of research investigating the role of bandstructure topology, as characterized for example by the Berry curvature in momentum space, in the electronic response functions of crystalline solids [13]. While the best established example is the intrinsic anomalous Hall effect in time-reversal breaking systems [14], several nonlocal [15,16] and nonlinear effects related to Berry curvature generally [17,18]and in WSM's specifically [19,20] have been predicted in crystals that break inversion symmetry. Of these, the most relevant to this work is a theoretical formulation [21] of SHG in terms of the shift vector, which is a quantity related to the difference in Berry connection between two bands that participate in an optical transition. * Electronic address: liangwu@berkeley.edu † Electronic address: jworenstein@lbl.gov Fig. 1a and caption provide a schematic and description of the optical set-up for measurement of SHG in TMMP crystals . Figs. 1b,c show results from a (112) surface of TaAs. The SH intensity from this surface is very strong, allowing for polarization rotation scans with signal-to-noise ratio above 10 6 . In contrast, SHG from a TaAs (001) surface is barely detectable (at least six orders of magnitude lower than (112) surface). Below, we describe the use of the set-up shown in Fig. 1a to characterize the second-order optical susceptibility tensor, χ ijk , defined by the relation,As a first step, we determined the orientation of the high-symmetry axes in the (112) surface, which are the [1,-1,0] and [1,1,-1] directions. To do so, we simultaneously rotated the linear polarization of th...

When a polarized light beam is incident upon the surface of a magnetic material, the reflected light undergoes a polarization rotation1. This magneto-optical Kerr effect (MOKE) has been intensively studied in a variety of ferro- and ferrimagnetic materials because it provides a powerful probe for electronic and magnetic properties2, 3 as well as for various applications including magneto-optical recording4. Recently, there has been a surge of interest in antiferromagnets (AFMs) as prospective spintronic materials for high-density and ultrafast memory devices, owing to their vanishingly small stray field and orders of magnitude faster spin dynamics compared to their ferromagnetic counterparts5–9. In fact, the MOKE has proven useful for the study and application of the antiferromagnetic (AF) state. Although limited to insulators, certain types of AFMs are known to exhibit a large MOKE, as they are weak ferromagnets due to canting of the otherwise collinear spin structure10–14. Here we report the first observation of a large MOKE signal in an AF metal at room temperature. In particular, we find that despite a vanishingly small magnetization of M ~0.002 µB/Mn, the non-collinear AF metal Mn3Sn15 exhibits a large zero-field MOKE with a polar Kerr rotation angle of 20 milli-degrees, comparable to ferromagnetic metals. Our first-principles calculations have clarified that ferroic ordering of magnetic octupoles in the non-collinear Néel state16 may cause a large MOKE even in its fully compensated AF state without spin magnetization. This large MOKE further allows imaging of the magnetic octupole domains and their reversal induced by magnetic field. The observation of a large MOKE in an AF metal should open new avenues for the study of domain dynamics as well as spintronics using AFMs.

We report measurements of optical absorption in the zigzag antiferromagnet α-RuCl_{3} as a function of temperature T, magnetic field B, and photon energy ℏω in the range ∼0.3-8.3 meV, using time-domain terahertz spectroscopy. Polarized measurements show that threefold rotational symmetry is broken in the honeycomb plane from 2 to 300 K. We find a sharp absorption peak at 2.56 meV upon cooling below the Néel temperature of 7 K at B=0 that we identify as the magnetic-dipole excitation of a zero-wave-vector magnon, or antiferromagnetic resonance (AFMR). With the application of B, the AFMR broadens and shifts to a lower frequency as long-range magnetic order is lost in a manner consistent with transitioning to a spin-disordered phase. From a direct, internally calibrated measurement of the AFMR spectral weight, we place an upper bound on the contribution to the dc susceptibility from a magnetic excitation continuum.