"Dirac semimetal" is a class of materials in which electrons show a linearly dispersed band structure, obeying the Dirac equation. 3-dimensional (3D) Dirac semimetals have recently been synthesized successfully in several compounds, and are now attracting a great interest as a system to observe various nontrivial properties proposed in the context of high-energy physics. Dirac semimetals are now intensely studied for spintronic applications, due to "spin-momentum locking" nature of electrons arising from strong spin-orbit coupling, which is equivalent to the locking of helicity under chiral symmetry.

In this talk, I will introduce my recent theoretical work on spin correlations in magnetically-doped 3D Dirac semimetals [1]. Localized magnetic moments, introduced by magnetic impurities in the material, become correlated via itinerant Dirac electrons. We find that the correlation becomes anisotropic due to spin-momentum locking, which may give rise to some topologically nontrivial excitations in addition to the normal ferromagnetic ground state. I will also talk about the dispersion of spin waves (magnons), which appear as Nambu-Goldstone modes, related to the spontaneous breaking of a new continuous symmetry involving both the real O(3) space and the spin SU(2) space.

[1] Y. Araki and K. Nomura, paper in preparation.