Spiking neural networks encode information in spike timing and offer a pathway toward energy efficient artificial intelligence. However, a key challenge in spiking neural networks is realizing nonlinear and expressive computation in compact, energy-efficient hardware without relying on additional circuit complexity. In this work, we examine nonlinear computation in a CMOS+X spiking neuron implemented with a magnetic tunnel junction connected in series with an NMOS transistor. Circuit simulations of a multilayer network solving the XOR classification problem show that three intrinsic neuronal properties enable nonlinear behavior: threshold activation, response latency, and absolute refraction. Threshold activation determines which neurons participate in computation, response latency shifts spike timing, and absolute refraction suppresses subsequent spikes. These results show that magnetization dynamics of MTJ devices can support nonlinear computation in compact neuromorphic hardware.