We study the critical energy dissipation in an atomic superfluid gas with two symmetric spin components by an oscillating magnetic obstacle. Above a certain critical oscillation frequency, spin-wave excitations are generated by the magnetic obstacle, demonstrating the spin superfluid behavior of the system. When the obstacle is strong enough to cause density perturbations via local saturation of spin polarization, half-quantum vortices (HQVs) are created for higher oscillation frequencies, which reveals the characteristic evolution of critical dissipative dynamics from spin-wave emission to HQV shedding. Critical HQV shedding is further investigated using a pulsed linear motion of the obstacle, and we identify two critical velocities to create HQVs with different core magnetization.
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