  First order phase transitions, where one phase replaces another by virtue of
a simple crossing of free energies, are best known between solids, liquids and
vapours, but they also occur in a wide range of other contexts, including even
elemental magnets. The key challenges are to establish whether a phase
transition is indeed first order, and then to determine how the new phase
emerges because this will determine thermodynamic and electronic properties.
Here we meet both challenges for the spin reorientation transition in the
topological metallic ferromagnet Fe3Sn2. Our magnetometry and variable
temperature magnetic force microscopy experiments reveal that, analogous to the
liquid-gas transition in the temperature-pressure plane, this transition is
centred on a first order line terminating in a critical end point in the
field-temperature plane. We directly image the nucleation and growth associated
with the transition and show that the new phase emerges at the most convoluted
magnetic domain walls for the high temperature phase and then moves to self
organize at the domain centres of the high temperature phase. The dense domain
patterns and phase coexistence imply a complex inhomogeneous electronic
structure, which will yield anomalous contributions to the magnetic field- and
temperature-dependent electrical conductivity.
