  Neutron scattering has been used to study the nature of the ferromagnetic
transition in single crystals of La_0.7Ca_0.3MnO_3 and La_0.8Ca_0.2MnO_3, and
polycrystalline samples of La_0.67Ca_0.33MnO_3 and La_5/8Ca_3/8MnO_3 where the
naturally occurring O-16 can be replaced with the O-18 isotope. Small angle
neutron scattering on the x=0.3 single crystal reveals a discontinuous change
in the scattering at the Curie temperature for wave vectors below ~0.065 A^-1.
Strong relaxation effects are observed for this domain scattering, for the
magnetic order parameter, and for the quasielastic scattering, demonstrating
that the transition is not continuous in nature. There is a large oxygen
isotope effect observed for the T_C in the polycrystalline samples. For the
optimally doped x=3/8 sample we observed T_C(O-16)=266.5 K and T_C(O-18)=261.5
K at 90% O-18 substitution. The temperature dependence of the spin-wave
stiffness is found to be identical for the two samples despite changes in T_C.
Hence, T_C is not solely determined by the magnetic subsystem, but instead the
ferromagnetic phase is truncated by the formation of polarons which cause an
abrupt transition to the paramagnetic, insulating state. Application of
uniaxial stress in the x=0.3 single crystal sharply enhances the polaron
scattering at room temperature. Measurements of the phonon density-of-states
show only modest differences above and below T_C and between the two different
isotopic samples.
