  We extend the solid-state nudged elastic band method to handle a
non-conserved order parameter - in particular, magnetization, that couples to
volume and leads to many observed effects in magnetic systems. We apply this
formalism to the well-studied magneto-volume collapse during the
pressure-induced transformation in iron - from ferromagnetic body-centered
cubic (bcc) austenite to hexagonal close-packed (hcp) martensite. We find a
bcc-hcp equilibrium coexistence pressure of 8.4 GPa, with the transition-state
enthalpy of 156 meV/Fe at this pressure. A discontinuity in magnetization and
coherent stress occurs at the transition state, which has a form of a cusp on
the potential-energy surface (yet all the atomic and cell degrees of freedom
are continuous); the calculated pressure jump of 25 GPa is related to the
observed 25 GPa spread in measured coexistence pressures arising from
martensitic and coherency stresses in samples. Our results agree with
experiments, but necessarily differ from those arising from drag and restricted
parametrization methods having improperly constrained or uncontrolled degrees
of freedom.
