We demonstrate remarkably strong nonlinear terahertz (THz) effects in an intrinsic GaAs wafer patterned with a nanometer-width slot antenna array. The antenna near-field reaches 20 MV/cm due to the huge field enhancement in the plasmonic nano-structure (field enhancement factor, alpha congruent to 50). The THz fields are strong enough to generate high density free carriers (N-e > 10(17) cm(-3)) via interband excitations associated with impact ionizations and thus to induce large absorption of the THz radiation (>35%). The nonlinear THz interactions take place in the confined region of nanometer-scale layer adjacent to the antenna.