Step Stone Effect: A sp anti-bonding Mediated Long-Range Ferromagnetism in Cr-doped Carrier-Free Bi2Te3

Despite the recent success in the realization of the quantum anomalous Hall effect, the underlying physical mechanism of the long range Ferromagnetism is still unclear. Based on our density functional theory calculations, we discovered an intriguing long-range ferromagnetic order in Cr-doped, carrier-free Bi2Te3, with the separation between dopants more than 8 {\AA}. We found that this magnetic coupling is facilitated by an anti-bonding state originated from the lone pair of a Te 5p state and a Bi 6s state, despite this anti-bonding state lies below the valence band maximum. Such a state serves as a hidden step stone merged in the electron sea and mediates the long-range magnetic order. An effective electron hopping model is proposed to explain this mechanism. This novel mechanism sheds light on the understanding of long-range ferromagnetism in insulators and may lead to the realization of the long-range magnetic order in dilute magnetic semiconductors.