The capability of emulating neural functionalities efficiently in hardware is crucial for building neuromorphic computing systems. While various types of neuro-mimetic devices have been investigated, it remains challenging to provide a compact device that can emulate spiking neurons. In this work, we propose a non-volatile spin-based device for efficiently emulating a leaky integrate-and-fire neuron. By incorporating an exchange-coupled composite free layer in spin-orbit torque magnetic tunnel junctions, multi-domain magnetization switching dynamics is exploited to realize gradual accumulation of membrane potential for a leaky integrate-and-fire neuron with compact footprints. The proposed device offers significantly improved scalability compared with previously proposed spin-based neuro-mimetic implementations while exhibiting high energy efficiency and good controllability. Moreover, the proposed neuron device exhibits a varying leak constant and a varying membrane resistance that are both dependent on the magnitude of the membrane potential. Interestingly, we demonstrate that such device-inspired dynamic behaviors can be incorporated to construct more robust spiking neural network models, and find improved resiliency against various types of noise injection scenarios. The proposed spintronic neuro-mimetic devices may potentially open up exciting opportunities for the development of efficient and robust neuro-inspired computational hardware.