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Compute-in-memory (CIM) based on emerging nonvolatile memory (eNVM) is an effective way to deploy neural networks to low-power edge devices for both storage and computation. NVMs such as ReRAM have been widely used in CIM. Meanwhile, MRAM has higher read and write cycles, lower device and cycle variation and a lower bit error rate, making it equally attractive for storage. However, the high read current and low on/off ratio result in large energy consumption in MRAM read limiting its large-scale application in CIM. The spiking neural network (SNN) represents the information as sparse spike sequences and facilitates hardware to achieve low-power computing by taking advantage of its spatial-temporal sparsity. To further increase the input sparsity of SNN and reduce the read energy consumption, this paper proposes ADC-free, dual-spike (DS) -CIM macro, a spiking MRAM CIM macro driven by asynchronous dual spikes. Compared to the conventional rate coding, our dual-spike coding method uses only 2 spikes to encode the information without losing accuracy. Moreover, the event-driven feature allows the macro to have sub-nW static power consumption. Our DS-CIM macro achieves comparable or higher accuracy while maintaining very low energy consumption. Specifically, it achieves accuracies of 96.99%, 82.87%, 90.00%, and 85.97% for digit classification, image classification, gesture recognition, and action recognition tasks, with energy consumption of only 8.07nJ, 71.26nJ, 729.3nJ, and 369.82nJ, respectively. These results emphasize the significance of DS-CIM and provide ideas for low-power inference on edge devices.