where < > refers to the spatial average over the plane of the layers (for a fixed ρ
1?ρ
2). Due to the much stronger PMA of the bottom CoFeB layer (
FIG. S3), the change in magnetic properties of top CoFeB layer by voltage to be much larger than that of bottom CoFeB, which is supported by
FIG. 6B. Assuming that the applied voltage from the positive to negative polarity results in a change of the correlation function from the correlated (ξ
12>0) to the anti-correlated (ξ
12<0) state, i.e., the oxidation level (therefore the induced moment from Gd ions) of the two interfaces is likely similar if |ρ
1?ρ
2|<r
0 for a positive voltage, where r
0 is the correlation length. For a negative voltage, the oxidation level of the two interfaces is likely to be less similar, giving rise to ξ
12<0. With the above assumptions, the coupling field H
IC≡?δE/δδm
1 can be estimated. The z-component of the coupling field is thus,