  Topological crystalline insulator (TCI) is a recently-discovered topological
phase of matter. It possesses multiple Dirac surface states, which are
protected by the crystal symmetry. This is in contrast to the time reversal
symmetry that is operative in the well-known topological insulators. In the
presence of a Zeeman field and/or strain, the multiple Dirac surface states are
gapped. The high-Chern-number quantum anomalous Hall (QAH) state is predicted
to emerge if the chemical potential resides in all the Zeeman gaps. Here, we
use molecular beam epitaxy to grow 12 double layer (DL) pure and Cr-doped SnTe
(111) thin film on heat-treated SrTiO3 (111) substrate using a quintuple layer
of insulating (Bi0.2Sb0.8)2Te3 topological insulator as a buffer film. The Hall
traces of Cr-doped SnTe film at low temperatures display square hysteresis
loops indicating long-range ferromagnetic order with perpendicular anisotropy.
The Curie temperature of the 12DL Sn0.9Cr0.1Te film is ~ 110 K. Due to the
chemical potential crossing the bulk valence bands, the anomalous Hall
resistance of 12DL Sn0.9Cr0.1Te film is substantially lower than the predicted
quantized value (~1/4 h/e2). It is possible that with systematic tuning the
chemical potential via chemical doping and electrical gating, the
high-Chern-number QAH state can be realized in the Cr-doped SnTe (111) thin
film.
