Magnetic order and surface state gap in ${\left({\mathrm{Sb}}_{0.95}{\mathrm{Cr}}_{0.05}\right)}_2 {\mathrm{Te}}_3$

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 $H_{\mathrm{int}}\left(T\right)=H_{\mathrm{int}}\left(0\right){[1-T/T_C]}^{\beta }$ with ordering temperature $T_C\approx 6.1$ K and critical exponent $\beta \approx 0.22$. 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 ${\mathrm{Sb}}_2{\mathrm{Te}}_3$.

Figure 1

(a) X-ray powder diffraction patterns (symbols) with Rietveld refinement (solid curves) of diffraction pattern and (b) diffraction pattern of the single crystal along the planes parallel to the (003) at 300 K. TEM image of (c) a portion of a particle and the planes identified as (015) in (d). The (e) SAD pattern with the assigned Miller indices. The core-level XPS of (f) Sb, (g) Cr, and (h) Te with the fitted continuous curves and backgrounds.

Figure 2

The (a) ${\rho }_{xx}$ with $T$ at selected $H$, (b) MR(%) with $H$ at selected $T$, and (c) MR(%) with scaled $H/{\rho }_0$ for different $T$, for the $\parallel$ component. (d) MR(%) with $H$ at selected $T$ for the $\perp$ component.

Figure 3

(a) Hall resistivity ${\rho }_{yx}$ with $H$ at selected $T$. (b) Example of the global fitting of thermal variation of conductivities using Eqs. (1) and (2) at 2.4 K. The $T$ variations of (c) $n_e$ and $n_h$, and (d) ${\mu }_e$ and ${\mu }_h$.

Figure 4

Magnetic hysteresis loop at selected temperatures for the (a) $\parallel$ and (c) $\perp$ components, showing the dHvA effects. The oscillatory component ($\mathrm{\Delta }M$) with $1/H$ at selected $T$ for the (b) $\parallel$ and (d) $\perp$ components. Inset depicts the amplitude of FFT component with frequency ($F_{\text{dHvA}}$), showing a peak around 550 and 660 kOe for the $\parallel$ and $\perp$ component, respectively.

Figure 5

Amplitude of the oscillatory component with temperature ($T$) for the (a) $\parallel$ and (b) $\perp$ components. The plot of $ln[\mathrm{\Delta }M{H}^{1/2}sinh\left(\zeta \right)]$, where $\zeta =2{\pi }^2{k}_B{m}^{*}{T}_D/\hslash eH$, with $1/H$ for the (c) $\parallel$ and (d) $\perp$ components. The continuous curves are LK fit in (a)–(d). Landau-level fan diagram with the plot of $n$ with $1/H$ for the (e) $\parallel$ and (f) $\perp$ components. (g) Schematic diagram of a gapped surface state with the possible Fermi energy level. (h) Experimental band structure along the $M\mathrm{\Gamma }M$ symmetry direction at 70 K, as obtained from ARPES. Topological surface state (TSS) is indicated by an arrow.

Figure 6

Muon asymmetry data $A\left(t\right)$ with time ($t$) at selected temperature ($T$) in the range of (a) 2 $\le T\le$ 10 K, (c) 12.5 K, (d) 37.5 K. Inset of (a) amplifies the damped oscillation component further in the low-$t$ region. (b) The internal magnetic field ($H_{\mathrm{int}}$) with $T$. The continuous curves show the fit. (e) Spin-lattice relaxation rate ($\lambda$) with $T$. (f) The log-log plot of $\lambda$ versus ($T/T_C-1$). Straight line shows the fit, as described in the text.