Magnetic order and surface state gap in (Sb0.95Cr0.05)2 Te3

Magnetic 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 (${\mathrm{Sb}}_0.95{\mathrm{Cr}}_0.05{)}₂{\mathrm{Te}}₃$ 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 (${H}_{\mathrm{int}}$), which follows ${H}_{\mathrm{int}}(T)={H}_{\mathrm{int}}(0){[1\ensuremath{-}T/{T}_C]}^{\ensuremath{\beta}}$ with ordering temperature ${T}_C\ensuremath{\approx}6.1$ K and critical exponent $\ensuremath{\beta}\ensuremath{\approx}0.22$. The critical exponent is close to the two-dimensional 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 ${\mathrm{Sb}}₂{\mathrm{Te}}₃$.