  Diluted magnetic semiconductors possessing intrinsic static magnetism at high
temperatures represent a promising class of multifunctional materials with high
application potential in spintronics and magneto-optics. In the hexagonal
Fe-doped diluted magnetic oxide, 6H-BaTiO$_{3-\delta}$, room-temperature
ferromagnetism has been previously reported. Ferromagnetism is broadly accepted
as an intrinsic property of this material, despite its unusual dependence on
doping concentration and processing conditions. However, the here reported
combination of bulk magnetization and complementary in-depth local-probe
electron spin resonance and muon spin relaxation measurements, challenges this
conjecture. While a ferromagnetic transition occurs around 700 K, it does so
only in additionally annealed samples and is accompanied by an extremely small
average value of the ordered magnetic moment. Furthermore, several additional
magnetic instabilities are detected at lower temperatures. These coincide with
electronic instabilities of the Fe-doped 3C-BaTiO$_{3-\delta}$ pseudocubic
polymorph. Moreover, the distribution of iron dopants with frozen magnetic
moments is found to be non-uniform. Our results demonstrate that the intricate
static magnetism of the hexagonal phase is not intrinsic, but rather stems from
sparse strain-induced pseudocubic regions. We point out the vital role of
internal strain in establishing defect ferromagnetism in systems with competing
structural phases.
