Magnetic order and surface state gap in Cr doped Sb₂Te₃

The transition element doping in topological insulators, which breaks the time-reversal symmetry, gives

rise to the diverse range of exotic consequences, though proper understanding of the magnetic order has rarely

been attempted by using any microscopic experiments. We report the occurrence of the magnetic order in Cr

Sb₂Te₃ using the muon spin relaxation studies. The asymmetry curve at low temperature (T) shows

an evidence of a damped oscillation, providing a clue about the internal magnetic field (H_int ), which follows

H_int (T ) = H_int (0)[1 − T/T_C]^β with ordering temperature T_C ≈ 6.1 K and critical exponent β ≈ 0.22. The critical

exponent is close to the 2D XY-type interaction. The magnetization curves at low T exhibit a

ferromagnetic behavior at low field (H) and the de Haas–van Alphen (dHvA) effect at high H. The analysis

of the dHvA oscillation proposes the charge carrier that acts like a massive Dirac fermion. The Berry phase,

as obtained from the Landau-level fan diagram, suggests a surface state gap at the Dirac point. The complex

electronic structure is discussed by correlating the magnetic order attributed to the Cr doping in Sb₂Te₃.