Neurons are crucial components of neural networks, but implementing biologically accurate neuron models in hardware is challenging due to their nonlinearity and time variance. This paper introduces the SC-IZ neuron model, a low-cost digital implementation of the Izhikevich neuron model designed for large-scale neuromorphic systems using stochastic computing (SC). Simulation results show that SC-IZ can reproduce the behaviors of the original Izhikevich neuron. The model is synthesized and implemented on an FPGA. Comparative analysis shows improved hardware efficiency; reduced resource utilization, which is a 56.25% reduction in slices, 57.61% reduction in Look-Up Table (LUT) usage, and a 58.80% reduction in Flip-Flop (FF) utilization; and a higher operating frequency compared to state-of-the-art Izhikevich implementation.