Influence of an Anomalous Temperature Dependence of the Phase Coherence Length on the Conductivity of Magnetic Topological Insulators

Magnetotransport constitutes a useful probe to understand the interplay between electronic band topology and magnetism in spintronic devices. A recent theory of Lu and Shen [Phys. Rev. Lett. 112, 146601 (2014)] on magnetically doped topological insulators predicts that quantum corrections $\mathrm{\Delta }\kappa$ to the temperature dependence of conductivity can change sign across the Curie transition. This phenomenon has been attributed to a suppression of the Berry phase of the topological surface states at the Fermi level, caused by a magnetic energy gap. Here, we demonstrate experimentally that $\mathrm{\Delta }\kappa$ can reverse its sign even when the Berry phase at the Fermi level remains unchanged. The contradictory behavior to theory predictions is resolved by extending the model by Lu and Shen to a nonmonotonic temperature scaling of the inelastic scattering length showing a turning point at the Curie transition.

Figure 1

(a) Hall bar measurement geometry. (b) Temperature dependence of the electrical resistivity ${\rho }_{xx}$ in zero magnetic field for $x_{\text{Mn}}=0\%$, 4%, and 8% at $t=(40\pm 5)\mathrm{nm}$. (c)–(e) Normalized transversal resistance after subtraction of ordinary Hall effect contributions.

Figure 2

Magnetic field dependence ${\sigma }_{xx}(B)$ for different temperatures (a) $x_{\text{Mn}}=0$, (b) 4%, and (c) 8%. The solid lines represent fits using Eq. (1). Respective $\beta B^2$ contributions at $T=2\mathrm{K}$ are also plotted (dashed lines).

Figure 3

Temperature dependence (a) $\alpha (T)$ and (b) $l_{\mathrm{\Phi }}(T)$ for different $x_{\text{Mn}}$. Values were derived from the low-field data ($B\le 1\mathrm{T}$) with $\beta =0$. $l_{\mathrm{\Phi }}$ is fitted assuming $l_{\mathrm{\Phi }}\propto T^{-p/2}$ for $T>T_C$ ($p>0$, solid lines) and $T<T_C$ ($p<0$, dashed lines).

Figure 4

(a)–(c) Temperature dependence of ${\sigma }_{xx}$ in various magnetic fields on a logarithmic scale for $x_{\text{Mn}}=0$, 4%, and 8%, respectively. Solid lines are linear fits at $T<T_{\mathrm{E}}$. For 4 and 8% Mn samples, $T_C$ is indicated by a dashed vertical line. (d)–(f): The magnetic field dependence of the slopes $\kappa$ obtained from the linear fits in (a)–(c).

Figure 5

(a) and (b): ARPES for $x_{\text{Mn}}=0$ and 7% measured at $h\nu =18\mathrm{eV}$ and $T=100\mathrm{K}$ after the second derivative processing [44].