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Carrier-independent ferromagnetism of chromium doped topological insulator$Bi_xSb_{2-x}Te_3$ thin films,which cannot be explained by current theory ofdilute magnetic semiconductor, has been reported recently. To study if it isrelated to the distinctive surface state of topological insulator, we studiedthe 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 measurementsby Arrott plots, is found to be proportional to $p^{1/3}$, where p is the holedensity. This fact supports a scenario of RKKY interaction with mean-fieldapproximation. This carrier density dependent nature enables tuning andcontrolling of the magnetic properties by applying a gate voltage in the futurescience researches and spintronics applications.

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