RKKY signals characterizing the topological phase transitions in Floquet Dirac semimetals

Recently, the Floquet ${\rm Na_3Bi}$-type material has been proposed as an ideal platform for realizing various phases, i.e., the spin-degenerate Dirac semimetal (DSM) can be turned into the Weyl semimetal (WSM), and even to the Weyl half-metal (WHM). Instead of the conventional electrical methods, we use the RKKY interaction to characterize the topological phase transitions in this paper. It is found that detecting the Ising term $J_I$ is feasible for distinguishing the phase transition of DSM/WSM, since the emergence of $J_I$ is induced by the broken spin degeneracy. For the case with impurities deposited on $z$ axis (the line connecting the Weyl points), the Heisenberg term $J_H$ coexists with $J_I$ in the WSM, while $J_H$ is filtered out and only $J_I$ survives in the WHM. This magnetic filtering effect is a reflection of the fully spin-polarized property (one spin band is in the WSM phase while the other is gapped) of the WHM, and it can act a signal to capture the phase transition of WSM/WHM. This signal can not be disturbed unless the direction of the impurities greatly deviates from $z$ axis. Interestingly, as the impurities are moved into the $x$-$y$ plane, there arises another signal (a dip structure for $J_H$ at the phase boundary), which can also identify the phase transition of WSM/WHM. Furthermore, we have verified that all magnetic signals are robust to the term that breaks the electron-hole symmetry. Besides characterizing the phase transitions, our results also suggest that the Floquet DSMs are power platforms for controlling the magnetic interaction.