High-field Studies on Layered Magnetic and Polar Dirac Metals: Novel Quantum Transport Phenomena Coupled with Spin-valley Degrees of Freedom

Recently, the interplay between the Dirac/Weyl fermion and various bulk properties, such as magnetism, has attracted considerable attention, since unconventional transport and optical phenomena were discovered. However, the design principles for such materials have not been established well. Here, we propose that the layered material $A$Mn$X_2$ ($A$: alkaline and rare-earth ions, $X$: Sb, Bi) is a promising platform for systematically exploring strongly correlated Dirac metals, which consists of the alternative stack of the $X^-$ square net layer hosting a 2D Dirac fermion and the $A^{2+}$-Mn$^{2+}$-$X^{3-}$ magnetic block layer. In this article, we shall review recent high-field studies on this series of materials to demonstrate that various types of Dirac fermions are realized by designing the block layer. First, we give an overview of the Dirac fermion coupled with the magnetic order in EuMnBi$_2$ ($A$=Eu). This material exhibits large magnetoresistance by the field-induced change in the magnetic order of Eu layers, which is associated with the strong exchange interaction between the Dirac fermion and the local Eu moment. Second, we review the Dirac fermion coupled with the lattice polarization in BaMn$X_2$ ($A$=Ba). There, spin-valley coupling manifests itself owing to the Zeeman-type spin-orbit interaction, which is experimentally evidenced by the bulk quantum Hall effect observed at high fields.