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

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