Chromium-induced ferromagnetism with perpendicular anisotropy in topological crystalline insulator SnTe (111) thin films

Topological crystalline insulator 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 $\mathrm{SrTi}{\mathrm{O}}_3$ (111) substrate using a quintuple layer of insulating ${\left(\mathrm{B}{\mathrm{i}}_{0.2}\mathrm{S}{\mathrm{b}}_{0.8}\right)}_2\mathrm{T}{\mathrm{e}}_3$ 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 $12\mathrm{DL}\mathrm{S}{\mathrm{n}}_{0.9}\mathrm{C}{\mathrm{r}}_{0.1}\mathrm{Te}$ film is ∼110 K. Due to the chemical potential crossing the bulk valence bands, the anomalous Hall resistance of $12\mathrm{DL}\mathrm{S}{\mathrm{n}}_{0.9}\mathrm{C}{\mathrm{r}}_{0.1}\mathrm{Te}$ film is substantially lower than the predicted quantized value $\left(\sim 1/4h/e^2\right)$. 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.

Figure 1

Cr-doped SnTe (111) films. (a) Schematics of the crystal structure of Cr-doped SnTe (111) films. (b) Brillouin zone of pure SnTe (111) film when the chemical potential is near the charge-neutral point. Four Dirac cones are found at time-reversal-invariant momenta of the Brillouin zone, one is at $\overline{\mathrm{\Gamma }}$ point and the other three are at $\overline{M}$ points. (c) Brillouin zone of Cr-doped SnTe (111) film when the chemical potential is near the charge-neutral point. All Dirac cones are gapped due to the presence of the ferromagnetic order.

Figure 2

Characterizations of MBE-grown Cr-doped SnTe (111) films. (a)–(c) RHEED patterns of the heat-treated $\mathrm{SrTi}{\mathrm{O}}_3$ (111) substrate (a), 1-QL insulating ${\left(\mathrm{B}{\mathrm{i}}_{0.2}\mathrm{S}{\mathrm{b}}_{0.8}\right)}_2\mathrm{T}{\mathrm{e}}_3$ (111) buffer film (b), and $12-\mathrm{DL}\mathrm{S}{\mathrm{n}}_{0.9}\mathrm{C}{\mathrm{r}}_{0.1}\mathrm{Te}$ (111) film (c). (d) XRD image of $48-\mathrm{DL}\mathrm{S}{\mathrm{n}}_{0.9}\mathrm{C}{\mathrm{r}}_{0.1}\mathrm{Te}$ (111) film. (e) The ϕ-scan result of $12-\mathrm{DL}\mathrm{S}{\mathrm{n}}_{0.9}\mathrm{C}{\mathrm{r}}_{0.1}\mathrm{Te}$ (111) film. (f) High-resolution cross-sectional STEM image of $12-\mathrm{DL}\mathrm{S}{\mathrm{n}}_{0.9}\mathrm{C}{\mathrm{r}}_{0.1}\mathrm{Te}$ (111) film. (g) Corresponding EDS mapping of the Cr element in $12-\mathrm{DL}\mathrm{S}{\mathrm{n}}_{0.9}\mathrm{C}{\mathrm{r}}_{0.1}\mathrm{Te}$ (111) film.

Figure 3

Transport properties of 12-DL undoped SnTe (111) film. (a) Temperature dependence of the sheet longitudinal resistance $\left({\rho }_{xx}\right)$ of 12-DL SnTe (111) film. Inset: The normalized ${\rho }_{xx}/{\rho }_{xx,min}$ shows an upturn with decreasing $T$ when $T<5\mathrm{K}$. (b) Angle dependence of the normalized magnetoresistance $MR={\rho }_{xx}\left(H\right)/{\rho }_{xx}\left(0\right)$ of 12-DL SnTe(111) film measured at $T=2\mathrm{K}$. (c) Hall trace of 12-DL SnTe (111) film measured at $T=2\mathrm{K}$. (d) Temperature dependence of carrier density $n_{2\mathrm{D}}$ (red) and carrier mobility μ (blue) of 12-DL SnTe (111) film.

Figure 4

Transport properties of 12-DL Cr-doped SnTe (111) film. (a) Temperature dependence of the ${\rho }_{xx}$ of $12-\mathrm{DL}\mathrm{S}{\mathrm{n}}_{0.9}\mathrm{C}{\mathrm{r}}_{0.1}\mathrm{Te}$ (111) film. Inset: temperature dependence of ${\rho }_{xx}$ of $12-\mathrm{DL}\mathrm{S}{\mathrm{n}}_{0.9}\mathrm{C}{\mathrm{r}}_{0.1}\mathrm{Te}$ (111) film plotted in a semilog scale. ${\rho }_{xx}$ diverges much faster than $\text{log}T$ at low temperatures. (b), (c) The ${\mu }_{0}H$ dependence of the normalized ${\rho }_{xx}$ and the ${\rho }_{yx}$ of the $12-\mathrm{DL}\mathrm{S}{\mathrm{n}}_{0.9}\mathrm{C}{\mathrm{r}}_{0.1}\mathrm{Te}$ (111) film measured at different temperatures.

Figure 5

Anomalous Hall resistance of 12-DL Cr-doped SnTe (111) film. (a) Temperature dependence of the anomalous Hall resistance $\left({\rho }_{\mathrm{AH}}\right)$ of $12-\mathrm{DL}\mathrm{S}{\mathrm{n}}_{0.9}\mathrm{C}{\mathrm{r}}_{0.1}\mathrm{Te}$ (111) film. Inset: the Arrott plot of $12-\mathrm{DL}\mathrm{S}{\mathrm{n}}_{0.9}\mathrm{C}{\mathrm{r}}_{0.1}\mathrm{Te}$ (111) film, showing its $T_{\mathrm{C}}$ is ∼110 K. (b) Schematics of the gapped surface states at $\overline{\mathrm{\Gamma }}$ and $\overline{M}$ points in Cr-doped SnTe (111) films when the chemical potential is near the charge-neutral point. The binding-energy difference of the Zeeman gaps at $\overline{\mathrm{\Gamma }}$ and $\overline{M}$ might be reduced by tuning thickness and/or composition of the films, and the chemical potential can be tuned into all four Zeeman gaps.