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 determ
ination 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 $<1bar{1}0>$ directions. Additionally, we measured low-lying phonon dispersion branches and elastic constants in applied magnetic fields aimed to characterize the magnetoelastic coupling.
We report magnetization and differential thermal analysis measurements as a function of pressure accross the martensitic transition in magnetically superelastic Ni-Mn-In alloys. It is found that the properties of the martensitic transformation are si
gnificantly affected by the application of pressure. All transition temperatures shift to higher values with increasing pressure. The largest rate of temperature shift with pressure has been found for Ni$_{50}$Mn$_{34}$In$_{16}$ as a consequence of its small entropy change at the transition. Such a strong pressure dependence of the transition temperature opens up the possibility of inducing the martensitic transition by applying relatively low hydrostatic pressures.
We report on measurements of the adiabatic temperature change in the inverse magnetocaloric Ni$_{50}$Mn$_{34}$In$_{16}$ alloy. It is shown that this alloy heats up with the application of a magnetic field around the Curie point due to the conventiona
l magnetocaloric effect. In contrast, the inverse magnetocaloric effect associated with the martensitic transition results in the unusual decrease of temperature by adiabatic magnetization. We also provide magnetization and specific heat data which enable to compare the measured temperature changes to the values indirectly computed from thermodynamic relationships. Good agreement is obtained for the conventional effect at the second-order paramagnetic-ferromagnetic phase transition. However, at the first order structural transition the measured values at high fields are lower than the computed ones. Irreversible thermodynamics arguments are given to show that such a discrepancy is due to the irreversibility of the first-order martensitic transition.
