Fig. 1. (a) Schematic of the SHEL on an MO oxide multilayer. A linearly polarized light beam is incident on the structure composed of Ce1Y2Fe5O12, cerium-substituted yttrium iron garnet (CeYIG), yttrium iron garnet (YIG) film, and the silicon substrate, and the reflected beam splits into left and right circularly polarized light. The applied magnetic field is perpendicular to the incident plane and provided by an electromagnet. (b) Experimental setup: a half-wave plate (HWP) is used for beam intensity adjustment, and L1 (f=100  mm) and L2 (f=250  mm) are lenses for beam focusing and collimation, respectively. Polarizers P1 and P2 are used to determine the pre-selected and post-selected state. CCD, charge-coupled device (Coherent LaserCam HR).

Fig. 2. (a) Fresnel reflection coefficient of the multilayer structure without an applied magnetic field. (b) Relative change of reflectivity caused by magnetic field directions, which is obtained by using the MO transfer matrix method.

Fig. 3. (a) Original SHEL shift (left-handed circularly polarized) in the TMOKE condition for different CeYIG thicknesses. The inset shows spin-dependent splitting of left-handed and right-handed circularly polarized light when dCeYIG=50  nm. (b) SHEL shifts with opposite magnetic fields (black solid and red dotted line) and the shift difference δMO=δ(H−)−δ(H+) (green solid line) after weak measurements amplification, where Δ=2  deg.

Fig. 4. (a) Theoretical (solid and dashed lines) and experimental (dot marks) results of the amplified SHEL shifts in the transverse magnetic field with opposite directions, where the incident angle is 73.9 deg. (b) and (c) Amplified SHEL shifts without the applied magnetic field, where the incident angle is 55.5 deg and 80.5 deg, respectively.