Ferromagnetic Quantum Phase Transition in a Dirac Semimetal*

We investigate the quantum ferromagnetic transition in a Dirac Semimetal (DSM) doped away from the charge neutrality point. In an ordinary Fermi liquid the coupling of the magnetization to the fermions is known to drive the transition first order [1]. In a DSM the spin dependence of the Hamiltonian requires a re-analysis of this problem. Our theory is general, and allows us to consider both the DSM case as the limit of strong spin-orbit coupling, and ordinary metallic magnets with a weak spin-orbit interaction.

[1] M. Brando, D. Belitz, F.M. Grosche, and T.R. Kirkpatrick, Rev. Mod. Phys. 88, 025006 (2016).