Spin dynamics and magnetic interactions of Mn dopants in the topological insulator ${\mathrm{Bi}}_2{\mathrm{Te}}_3$

The magnetic and electronic properties of the magnetically doped topological insulator ${\mathrm{Bi}}_{2-x}{\mathrm{Mn}}_x{\mathrm{Te}}_3$ were studied using electron-spin resonance (ESR) and measurements of static magnetization and electrical transport. The investigated high-quality single crystals of ${\mathrm{Bi}}_{2-x}{\mathrm{Mn}}_x{\mathrm{Te}}_3$ show a ferromagnetic phase transition for $x\ge 0.04$ at $T_{\mathrm{C}}\approx 12$ K. The Hall measurements reveal a $p$-type finite charge-carrier density. Measurements of the temperature dependence of the ESR signal of Mn dopants for different orientations of the external magnetic field give evidence that the localized Mn moments interact with the mobile charge carriers leading to Ruderman-Kittel-Kasuya-Yosida-type ferromagnetic coupling between the Mn spins of order 2–3 meV. Furthermore, ESR reveals a low-dimensional character of magnetic correlations that persist far above the ferromagnetic ordering temperature.

Figure 1

Temperature dependence of (a) the static magnetization $M\left(T\right)$ and (b) the inverse magnetic susceptibility $\chi {\left(T\right)}^{-1}$ of ${\mathrm{Bi}}_{2-x}{\mathrm{Mn}}_x{\mathrm{Te}}_3$, measured in a weak external field $H$ for various doping concentrations $x$. The external magnetic field ${\mu }_{0}H=0.1$ T was applied perpendicular to the crystallographic $c$ axis. The solid lines correspond to Curie-Weiss fit functions of the linear high-temperature regime ${(\chi -{\chi }_0)}^{-1}=(T-{\theta }_{\mathrm{CW}})/C$ (see Sec. 3a).

Figure 2

Temperature dependence of the resistivity parallel to the charge current ${\rho }_{xx}\left(T\right)$ of ${\mathrm{Bi}}_{2-x}{\mathrm{Mn}}_x{\mathrm{Te}}_3$ for various doping concentrations $x$. The inset shows the enlarged low-temperature regime for $x=0.09$.

Figure 3

Magnetic-field dependence of the Hall resistivity ${\rho }_{xy}\left(H\right)$ of ${\mathrm{Bi}}_{2-x}{\mathrm{Mn}}_x{\mathrm{Te}}_3$ for $x=0.07$ at various temperatures. Measurements were performed in the $ab$ basal plane; the external field $H$ was applied normal to this plane ($\parallel c$ axis).

Figure 4

Temperature dependence of the charge-carrier density $p_{\mathrm{Hall}}\left(T\right)$ of ${\mathrm{Bi}}_{2-x}{\mathrm{Mn}}_x{\mathrm{Te}}_3$ for various $x$. The values were obtained from the Hall resistivity in the high-field region ${\mu }_{0}H\ge 11$ T (see the text).

Figure 5

ESR spectra of the ${\mathrm{Bi}}_{2-x}{\mathrm{Mn}}_x{\mathrm{Te}}_3$ sample with the highest doping level $x=0.09$ for various temperatures. The external magnetic field $H$ was applied parallel to the crystallographic $c$ axis.

Figure 6

Temperature dependence of the resonance field $H_{\mathrm{res}}\left(T\right)$ (a) and the linewidth $\mathrm{\Delta }H\left(T\right)$ (b) of ${\mathrm{Bi}}_{2-x}{\mathrm{Mn}}_x{\mathrm{Te}}_3$ with $x=0.09$. The external magnetic field $H$ is applied parallel and perpendicular to the crystallographic $c$ axis. The vertical dashed line marks the transition temperature $T_{\mathrm{C}}$. The horizontal dashed lines in (a) denote the averaged values of the resonance field in the range $T=50$–80 K with the corresponding values of $g$. The solid lines in (b) are fits according to Eq. (4).

Figure 7

Temperature dependence of the linewidth $\mathrm{\Delta }H\left(T\right)$ of ${\mathrm{Bi}}_{2-x}{\mathrm{Mn}}_x{\mathrm{Te}}_3$ for various doping concentrations $x$. The external magnetic field $H$ was applied perpendicular to the crystallographic $c$ axis. The solid lines are linear fits for $T\ge 25$ K.

Figure 8

Angular dependence of the linewidth $\mathrm{\Delta }H\left(\theta \right)$ of ${\mathrm{Bi}}_{2-x}{\mathrm{Mn}}_x{\mathrm{Te}}_3$ for $x=0.09$. $\theta$ is the angle between the external magnetic field $H$ and the crystallographic $c$ axis. The lines correspond to fits of the data (see the text).