Spintronic devices based on domain wall (DW) motion through ferromagnetic nanowire tracks have received great interest as components of neuromorphic information processing systems. Prior proposals for spintronic artificial neurons required external stimuli to perform the leaking functionality, one of the three fundamental functions of a leaky integrate-and-fire (LIF) neuron. The use of this external magnetic field or electrical current stimulus results in either a decrease in energy efficiency or an increase in fabrication complexity. Here, we modify the shape of previously demonstrated three-terminal magnetic tunnel junction neurons to perform the leaking operation without any external stimuli. The trapezoidal structure causes a shape-based DW drift, thus intrinsically providing the leaking functionality with no hardware cost. This LIF neuron, thus, promises to advance the development of spintronic neural network crossbar arrays.