Temperature and magnetic-field dependence of the elastic constants of Ni-Mn-Al magnetic Heusler alloys

We report on measurements of the adiabatic second-order elastic constants of the off-stoichiometric ${\mathrm{Ni}}_{54}{\mathrm{Mn}}_{23}{\mathrm{Al}}_{23}$ single-crystalline Heusler alloy. The variation in the temperature dependence of the elastic constants has been investigated across the magnetic transition and over a broad temperature range. Anomalies in the temperature behavior of the elastic constants have been found in the vicinity of the magnetic phase transition. Measurements under applied magnetic field, both isothermal and variable temperature, show that the value of the elastic constants depends on magnetic order, thus giving evidence for magnetoelastic coupling in this alloy system.

Figure 1

Temperature dependence of the elastic moduli (a) $C_L$, (b) $C_{44}$, and (c) $C_{11}$. Cooling and heating runs are represented by open and solid symbols, respectively. The dashed lines show the expected behavior for a Debye solid. (d) shows the values of the bulk modulus $\left(B\right)$ and the shear elastic constant $\left(C^{\prime }\right)$ calculated from the complete set of elastic constants measured (solid lines). The values of $C^{\prime }$ measured from the thinner sample are also shown for comparison.

Figure 2

(Color online) (a) ZFC, FC, and FH $M\left(T\right)$ in a field of $H=50\mathrm{Oe}$ applied along the [001] crystallographic direction. (b) Magnetization versus field at several temperatures above and below the magnetic transition. Prior to each $M\left(H\right)$ measurement, the samples were prepared in the ZFC state by bringing them above $380\mathrm{K}$. Solid lines are guides to the eye.

Figure 3

(Color online) Magnetization versus field curves for small fields along three crystallographic directions (a) [001], (b) [110], and (c) $\left[1\overline{1}0\right]$ at selected temperatures. The dashed lines in (a) represent the linear behavior extrapolated at small and high fields at $5\mathrm{K}$. The inset shows the deviation of the magnetization from the linear behavior corresponding to the small-field region.

Figure 4

(Color online) Temperature dependence of the elastic constants measured while cooling across the magnetic transition under magnetic field $H=5\mathrm{kOe}$ (a) $C_L$, (b) $C_{44}$, and (c) $C_{11}$. Circles represent the values without applied magnetic field. Square, triangle, and diamond symbols represent measurements obtained with the magnetic field applied along the $\left[1\overline{1}0\right]$, [001], and [110] directions, respectively.

Figure 5

(Color online) Magnetic-field dependence of the relative change of the elastic constants with respect to the value at zero field at $T=263\mathrm{K}$. Square, triangle, and diamond symbols represent measurements obtained with the magnetic field applied along the $\left[1\overline{1}0\right]$, [001], and [110] directions, respectively.