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The stability of magnetic states is essential for potential spintronic applications. Here we report on the thermal stability of magnetic states of monovacancy graphene using  ab initio  molecular dynamics simulations. At room temperature, thermal fluctuations of the graphene lattice induce a rapid magnetic switching between two states with a high and low magnetic moment, indicating that due to the instability of the atomic structure of the vacancy, the associated magnetic moment is thermodynamically unstable. Lowering the temperature can significantly reduce the rate of the switching process and enhance the resident time on the high magnetic state. It stabilizes in the high magnetic state at as low as 30 K. Analyzing the atomic trajectories and the instant electronic structures confirms that these two magnetic states in MD simulations correspond to the magnetic and nonmagnetic states reported in the literatures. Such fluctuations of local magnetic moments are associated with the vertical displacement of the carbon atoms with the unsaturated dangling bond. This study reveals the dynamical correlation between atomic movement and the magnetic switching, and a comprehensive picture of vacancy magnetism in graphene. It has implications in graphene based spintronic devices.

Thermodynamic stability of magnetic states of monovacancy in graphene revealed by ab initio molecular dynamics simulations