Logic-in-memory architecture based on spintronic memories shows fascinating prospects in neural networks (NNs) for its high energy efficiency and good endurance. In this work, we leveraged two magnetic tunnel junctions (MTJs), which are driven by the interplay of field-free spin orbit torque (SOT) and spin transfer torque (STT) effects, to achieve a novel statefullogic-in-memory paradigm for ternary multiplication operations. Based on this paradigm, we further proposed a highly parallel array structure to serve for ternary neural networks (TNNs). Our results demonstrate the advantage of our design in power consumption compared with CPU, GPU and other state-of-the-art works.