Study of magnetism in Cr doped (Bi$_{1-x}$Sb$_x$)$_2$Te$_3$

The quantum anomalous Hall (QAH) effect was first observed in Cr doped films of the topological insulator (TI) (Bi$_{1-x}$Sb$_x$)$_2$Te$_3$. This ferromagnetic TI opens a gap at the Dirac point and, when the Fermi energy lies inside this gap, a quantized QAH conductance can be observed. The origin of ferromagnetism in this material is still not well understood with the mechanism typically attributed to either a high van-Vleck susceptibility or a carrier mediated RKKY like interaction. To elucidate this we have studied Cr$_y$(Bi$_{1-x}$Sb$_x$)$_{2-y}$Te$_3$ thin films grown by MBE on SrTiO$_3$ (STO) substrates using polarized neutron reflectivity (PNR) while in-situ backgating the film to change the position of the Fermi energy. The films are also characterized by XRD, AFM, TEM and low temperature transport measurements. PNR measurements provide a direct measure of the depth dependent magnetization of a sample. We use this to study how the magnetization changes as the Fermi energy is moved towards the Dirac point. Funded by DARPA and ARO-MURI.