  Neutron scattering and ultrasonic methods have been used to study the lattice
dynamics of two single crystals of Ni-Mn-In Heusler alloys close to
Ni$_{50}$Mn$_{34}$In$_{16}$ magnetic superelastic composition. The paper
reports the experimental determination of the low-lying phonon dispersion
curves and the elastic constants for this alloy system. We found that the
frequencies of the TA$_{2}$ branch are relatively low and it exhibits a small
dip anomaly at a wave number $\xi_{0} \approx 1/3$, which softens with
decreasing temperature. Associated with the softening of this phonon, we also
observed the softening of the shear elastic constant $C'=(C_{11}-C_{12})/2$.
Both temperature softenings are typical for bcc based solids which undergo
martensitic transformations and reflect the dynamical instability of the cubic
lattice against shearing of $\{110\}$ planes along $<1\bar{1}0>$ directions.
Additionally, we measured low-lying phonon dispersion branches and elastic
constants in applied magnetic fields aimed to characterize the magnetoelastic
coupling.
