Competition between terahertz magnetoelectric and N\'eel spin-orbit torque driven spin dynamics in metallic antiferromagnets

Although magnetoelectric effects in metals are usually neglected, assuming that applied electric fields are screened by free charge carriers, the skin depth, defining the penetration depth of the fields, is non-zero and for THz electric fields typically reaches 400 nm. Hence, if the thickness of an antiferromagnetic film is of the order of tens of nm, electric field induced effects cannot be neglected. Here, we theoretically study the THz electric field induced spin dynamics in the metallic antiferromagnet $\mathrm{Mn}_{2}\mathrm{Au}$, whose spin arrangements allow it to exhibit a linear magnetoelectric effect. We show that the THz magnetoelectric torque in metallic antiferromagnets is proportional to the time derivative of the polarization induced by the THz electric field. Our simulations reveal that the magnetoelectric driven spin dynamics is indeed not negligible, and for a fair explanation of previously published experimental results in $\mathrm{Mn}_{2}\mathrm{Au}$ competition between THz magnetoelectric and N\'eel spin-orbit torques must be taken into account. Thus, it is shown that even in metallic antiferromagnets the THz magnetoelectric effect on spins can be strong and thus cannot be neglected.