Fig. 4.

Schematic diagram of the origin of the MA engineering. (A) MA energy of LSMO. The anisotropy energy is defined by the formula $E=K·{\text{M}}^4{\text{sin}}^{2}2\theta$, where M is the in-plane magnetization and $\theta$ is the angle to [100] (red arrows). The MCA of LSMO (K_c <0) favors the $\langle 110\rangle$ easy axis as shown by the black solid lines (energy minimum). (B) SIO-induced MA energy (K_in >0), which favors the $\langle 100\rangle$ easy axis. (C) Effective MA energy of SL31, in which the K_in overcomes K_c. Therefore, SL31 shows π/4 shift of the easy axis compared with LSMO. (D) Schematic diagram of the anisotropy contributions. The SIO-induced anisotropy is determined by the interfacial exchange coupling to the emergent weak ferromagnetism in SIO (green arrows), which effectively shifts the magnetic easy axis of LSMO by π/4. (E) Thickness evolution of the MA of the superlattice and the emergent magnetism in the strong SOC SIO (FM, ferromagnetic; PM, paramagnetic).