Resonant magneto-optic Kerr effect in the magnetic topological insulator Cr:(Sbₓ,Bi₁₋ₓ)₂Te₃

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We report measurements of the polar Kerr effect, proportional to the out-of-plane component of the magnetization, in thin films of the magnetically doped topological insulator (Cr₀.₁₂Bi₀.₂₆Sb₀.₆₂)₂Te₃. Measurements of the complex Kerr angle, Θₖ, were performed as a function of photon energy in the range 0.8 eV<ℏω<3.0 eV. We observed a peak in the real part of Θₖ(ω) and zero crossing in the imaginary part that we attribute to resonant interaction with a spin-orbit avoided crossing located ≈ 1.6 eV above the Fermi energy. The resonant enhancement allows measurement of the temperature and magnetic field dependence of Θₖ in the ultrathin film limit, d≥2 quintuple layers. We find a sharp transition to zero remanent magnetization at 6 K for d<8 QL, consistent with theories of the dependence of impurity spin interactions on film thickness and their location relative to topological insulator surfaces.