We have examined the transition from nonmagnetic to ferromagnetic behavior for elemental bcc vanadium, chromium, manganese, and iron by analyzing self-consistent parameter-free total-energy band-structure calculations in the local-spin-density approximation utilizing a fixed-spin-moment procedure. All systems are found to exhibit singular behavior and to undergo complex transitions as a function of volume. For each system, we find a set of critical Wigner-Seitz radii rWS defining the onset of magnetic behavior and the end of nonmagnetic behavior. Vanadium and manganese exhibit composite (second-order and first-order) transitions with nonmagnetic low-spin and high-spin magnetic behavior. Chromium undergoes a first-order transition from nonmagnetic to magnetic behavior at expanded volumes, and iron undergoes a second-order transition and becomes nonmagnetic at reduced volumes. © 1988 The American Physical Society.