Lattice dynamics and phonon softening in $\mathrm{Ni}\text{−}\mathrm{Mn}\text{−}\mathrm{Al}$ Heusler alloys

Inelastic and elastic neutron scattering have been used to study a single crystal of the ${\mathrm{Ni}}_{54}{\mathrm{Mn}}_{23}{\mathrm{Al}}_{23}$ Heusler alloy over a broad temperature range. The paper reports the experimental determination of the low-lying phonon dispersion curves for this alloy system. We find that the frequencies of the ${\mathrm{TA}}_2$ modes are relatively low. This branch exhibits an anomaly (dip) at a wave number ${\xi }_0=1∕3\approx 0.33$, which softens with decreasing temperature. Associated with this anomalous dip at ${\xi }_0$, an elastic central peak scattering is also present. We have also observed satellites due to the magnetic ordering.

Figure 1

Acoustic phonon dispersion curves along the high-symmetry directions $\left[\xi \xi \xi \right]$, $\left[\xi \xi 0\right]$, and $\left[\xi 00\right]$, measured at room temperature. Note the change of the horizontal scale corresponding to the branch measured along the high-symmetry direction $\left[\xi 00\right]$. Solid lines are guides to the eye.

Figure 2

Temperature dependence of the partial acoustic dispersion curves. (a) Temperature dependence of the anomaly in the ${\mathrm{TA}}_2\left[\xi \xi 0\right]$ branch. (b) Temperature dependence of the longitudinal L[$\xi \xi 0$] and transverse T[$\xi 00$]. Whereas the wiggle at ${\xi }_0\approx 0.33$ in the ${\mathrm{TA}}_2\left[\xi \xi 0\right]$ branch deepens with decreasing temperature, the other measured branches do not change significantly. Solid lines are guides to the eye.

Figure 3

Temperature dependence of the energy squared of the ${\mathrm{TA}}_2\left[\xi \xi 0\right]$ ${\xi }_0=0.33$ phonon. Data from related systems ${\mathrm{Ni}}_2\mathrm{MnGa}$ and ${\mathrm{Ni}}_{62.5}{\mathrm{Al}}_{37.5}$ are also shown for comparison. $T_I$ represents the premartensitic transformation temperature. The data for the latter systems were taken from Refs. 5, 29 for ${\mathrm{Ni}}_2\mathrm{MnGa}$ and ${\mathrm{Ni}}_{62.5}{\mathrm{Al}}_{37.5}$, respectively.

Figure 4

Temperature dependence of the elastic scattering along the $\left[\overline{\xi }\xi 0\right]$ direction starting from the (020) reflection. (a) Satellite due to the conical antiferromagnetic order. (b) Central peak associated with the anomalous dip at ${\xi }_0$ in the acoustic ${\mathrm{TA}}_2\left[\xi \xi 0\right]$ phonon branch. Temperatures from top to bottom are 12, 50, 75, 100, 150, 175, 200, 225, 250, 275, 300, 330, and $350\mathrm{K}$. Solid lines are guides to the eye.

Figure 5

Temperature dependence of the elastic scattering along the [$\overline{\xi }\xi 0$] direction starting from the (220) reflection. Temperatures from top to bottom are 12, 50, 75, 100, 150, 175, 200, 225, 250, 275, 300, 330, and $350\mathrm{K}$. Solid lines are guides to the eye.

Figure 6

Temperature dependence of (a) normalized maximum intensity, and (b) width (FWHM) of the elastic satellites reported. Symbols $엯$, $▴$, and $\nabla$ represent the $[-0.1,2.1,0]$, $[1.82,2.18,0]$, and $[-0.33,2.33,0]$ satellites, respectively. The width of the (020) Bragg reflection $(∎)$ is also shown in order to compare the widths of the satellites to the fundamental reflections. None of the widths of the Bragg peaks measured were instrumentally limited.