Extended Data Fig. 9: Theoretical consideration for the electrical switching of the chiral AF order in Mn3Sn.
From: Perpendicular full switching of chiral antiferromagnetic order by current
a, configuration-(a): the kagome plane is perpendicular to the current I and parallel to the electrically injected carrier spin polarization p (thick red arrows in the W layer) (kagome ⊥ I || p). b, configuration-(b): the kagome plane is parallel to I and perpendicular to p (kagome || I ⊥ p). c, configuration-(c): the kagome plane is parallel to the current I and parallel to the electrically injected carrier spin polarization p (kagome || I || p). d, Schematics for the current-induced switching of the chiral AF order in the configuration-(b) (kagome || I ⊥ p) with the in-plane compressive strain (δ > 0 and ε < 0). Orange arrows represent the polarization direction of the cluster magnetic octupole. Large (small) green and purple arrows represent the electric current I || x (spin torque (Tcurrent) associated with the spin current with the polarization p, leading to the chiral spin rotation) and bias magnetic field H || z (spin torque (Tfield) associated with H), respectively. Here p is parallel to the spin moments of the spin current (antiparallel to the spin angular momentum). θM is the angle of the polarized direction of the cluster magnetic octupole. e-f, In-plane angle θM of the polarization direction of the cluster magnetic octupole as a function of time t in the W/Mn3Sn bilayer calculated numerically using the LLG equation in the configuration-(b), where the kagome plane is parallel to the current I and the magnetic field H, and perpendicular to the electrically injected carrier spin polarization p (Figs. 3, Methods, Extended Data Figure 9b). I with the current density Jwrite in the W layer is applied for 1 ns < t < 2 ns. A positive Jwrite is applied in (i) and (ii), and negative Jwrite is applied in (iii) and (iv) (See detailed configurations in Fig. 3b). The magnetic field is set to be 0.1 T. e, Perpendicular (chiral spin) switching of the chiral AF order under |Jwrite| = 64 MA cm−2 (corresponding to the region-(B) in Fig. 3c). f, Chiral spin rotation only for one ((ii) for Jwrite > 0 and (iii) for Jwrite < 0) of the initial states under |Jwrite| = 73.5 MA cm−2 (region-(C) in Fig. 3c). g, Chiral spin rotation for both initial states under |Jwrite| = 77.5 MA cm−2 (region-(D) in Fig. 3c). Inset: Magnified view of the in-plane angle θM of the octupole moment as a function of time.
