Many recent studies have focused on Processing-in-memory (PIM) architectures for neural networks to resolve the memory bottleneck problem. Especially, an increased interest in Spin Orbit Torque (SOT)-MRAMs has emerged due to its low latency, high energy efficiency, and non-volatility. However, the previous work added extra computing circuits to support complicated computations, which results in large energy overheads. In this work, we propose a new PIM architecture with relatively small peripheral circuit, which produces the highest energy efficiency for processing a Long Short Term Memory (LSTM) among the PIM architectures. We improve the efficiency with a new computing method for logical operations, which exploits characteristics of SOT-MRAMs. We reduce the number of word lines (WLs) activated concurrently to one from two in the previous works. As a result, the energy for driving WLs is saved, and the sensing current for computation is reduced. Moreover, we propose efficient methods for additions, multiplications and non-linear activation functions in memory to process an LSTM. Accordingly, we achieve 1.26x energy efficiency with the proposed computing method for logical operations compared to the previous study based on SOT-MRAMs and up to 5.54x energy efficiency over the previous PIM architectures based on other memories.