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Carrier dependent ferromagnetism in chromium doped topological insulator $Cr_{0.2}Bi_xSb_{1.8-x}Te_3$

Carrier-independent ferromagnetism of chromium doped topological insulator $Bi_xSb_{2-x}Te_3$ thin films,which cannot be explained by current theory of dilute magnetic semiconductor, has been reported recently. To study if it is related to the distinctive surface state of topological insulator, we studied the structural, magnetic and transport characters of $Cr_{0.2}Bi_xSb_{1.8-x}Te_3$ single crystals. The Curie temperature $T_c$, which is determined from magnetization and anomalous Hall effect measurements by Arrott plots, is found to be proportional to $p^{1/3}$, where p is the hole density. This fact supports a scenario of RKKY interaction with mean-field approximation. This carrier density dependent nature enables tuning and controlling of the magnetic properties by applying a gate voltage in the future science researches and spintronics applications.