Ferroelectric domain nucleation and growth in multiferroic BiFeO_3 is studied on a single-domain level by using piezoresponse force spectroscopy. Variation of local electromechanical response with dc tip bias is used to determine the size of the domain formed below the conductive scanning probe tip. The domain parameters are calculated self-consistently from the decoupled Green function theory by using tip geometry determined from the domain wall profile. The critical parameters of the nucleating domain and the activation energy for nucleation are determined. The switching mechanism is modeled by using the phase-field method, and comparison with experimental results shows that the nucleation biases are within a factor of ～ 2 of the intrinsic thermodynamic limit. The role of atomic-scale defects and long-range elastic fields on nucleation bias lowering is discussed. These measurements open a pathway for quantitative studies of the role of a single defect on kinetics and thermodynamics of first order bias-induced phase transitions and electrochemical reactions.
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