Anomalous transport in magnetic topological materials

Abstract

The interplay between symmetry breaking and topological electronic structure is crucial to design anomalous transport properties in materials. Materials with strong or quantum electromagnetic responses have an extensive impact on the development of data storage, information processing, energy conversion, etc. In magnetic materials, the anomalous transport of anomalous Hall effect, anomalous Nernst effect, and magneto-optical effect et al. can be understood from the Berry curvature of the electronic band structures. Two typical band structures of Weyl points and nodal line band structures host strong local Berry curvature. Since the Berry curvature is time-reversal symmetry odd, such strong Berry curvatures can lead to strongly enhanced anomalous transport signals. With this guiding principle, we studied the anomalous Hall effect in magnetic Weyl semimetal Co3Sn2S2 [1-3] and magnetic nodal line semimetal in Heusler compound Co2Mn(Ga/Al) [4].With a mirror symmetry, the inverted band structure forms a nodal loop in the absence of spin-orbital coupling. This nodal line can be broken by spin-orbital coupling and a bandgap opens, which generates non-zero Berry curvature in the bandgap and forms a hot loop, see Figure 1a-b. Such strong Berry curvature in the magnetic system can lead to a strongly enhance or even quantized anomalous Hall effect. We applied this idea to real materials of magnetic Heusler compounds Co2Mn(Ga/Al). Protected by mirror symmetries the band inversion between the bands with opposite mirror eigenvalue forms three gapless nodal lines in the kx=0, ky=0, and kz=0 mirror planes, respectively. With spin-orbital coupling, the symmetry of the system is reduced. Taking magnetic along z, the mirror symmetries in kx=0 and ky=0 planes are broken, which leads to band anti-crossings with strong local Berry curvature locating in the opened bandgap around original nodal lines, see Figure 1d. Integral of the Berry curvature in the whole k-space gives a large intrinsic anomalous Hall conductivity reaching ~1500 to ~2000 S/cm [4].Weyl points is another typical band structure and present as the Berry curvature monopole, and therefore naturally results in a strong anomalous Hall effect. In ideal models with only one pair of Weyl points locating at the Fermi level, the intrinsic anomalous Hall conductivity can be presented as the combination distance of Weyl points and the quantized anomalous Hall conductance. Inspired by these excellent relations, we studied the anomalous Hall effect in Co3Sn2S2, and a new record of three-dimensional anomalous Hall angel (~20%) was observed, which offers the 1st three-dimensional material with both strong anomalous Hall conductivity and anomalous Hall angle [1]. It indeed shows as a Weyl semimetal from electronic band structure analysis. One crucial symmetry in Co3Sn2S2 is the three mirror planes parallel to the c direction, which results in three pairs of nodal lines connected by a c3z rotation symmetry. Because the magnetization is aligned along the z-direction, the mirror symmetries are broken by spin-orbital coupling. Meanwhile, one pair of Weyl points with opposite chirality remains along each of the former nodal lines, leading to the so large anomalous Hall effect.Though the strong anomalous Hall effect provides a promising signature for the existence of Weyl and nodal line band structure. Our transport work about Co3Sn2S2 and Co2MnGa/Al inspired the direct band structure detection by ARPES and STM [5-7], and they are in turn became the 1st experimentally verified magnetic Weyl semimetal and nodal line semimetal, respectively.Applying temperature gradient instead of the electrical field, the Weyl points and nodal lines induced Berry curvature can also lead to strongly enhanced anomalous Nernst effect. From our theoretical calculations and experimental measurements, the anomalous Nernst conductivity can reach around 3 and 6 A/(m-K) in Co3Sn2S2 [8] and Co2MnGa [9], respectively, with Co2MnGa keeping the record. Owing to the large anisotropy, Co3Sn2S2 is, so far, the only material with a large anomalous Nernst effect with zero magnetic fields. In addition, very recently, a giant magneto-optical response was observed in Co3Sn2S2 with the applied field from polarized light [10].Very recently, a strong interest in antiferromagnets is rising. In an antiferromagnet without such kind of joint TO symmetry to reverse Berry curvature, it allows the existence of anomalous Hall effect, anomalous Nernst effect, magneto-optical responses, and special spin current, etc. The nonzero anomalous Hall effect in antiferromagnets was proposed as early as 2001 in distorted non-linear magnetic structures [11]. However, its experimental realization was not successful until 2015 [12-16]. This understanding can be further expanded into collinear antiferromagnets. Different from non-linear antiferromagnets, the collinear antiferromagnetic structure can be usually understood from two sublattices connected by translation of inversion operation. Therefore, there are mainly two ways to break the joint symmetry, to replace the magnetic atoms connected by the joint TO symmetry, or change the the nonmagnetic sites. With this understanding, we predicted the anomalous Hall and Nernst effect in anti-Heusler Weyl semimetal Ti2MnAl [17-18]. **