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

The magnetic and electronic properties of the magnetically doped topological insulator Bi$_{\rm 2-x}$Mn$_{\rm x}$Te$_3$ were studied using electron spin resonance (ESR) and measurements of static magnetization and electrical transport. The investigated high quality single crystals of Bi$_{\rm 2-x}$Mn$_{\rm x}$Te$_3$ show a ferromagnetic phase transition for $x\geq 0.04$ at $T_{C}\approx 12$ 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 a 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.