Strain and order-parameter coupling in Ni-Mn-Ga Heusler alloys from resonant ultrasound spectroscopy

Resonant ultrasound spectroscopy and magnetic susceptibility experiments have been used to characterize strain coupling phenomena associated with structural and magnetic properties of the shape-memory Heusler alloy series ${\mathrm{Ni}}_{50+x}{\mathrm{Mn}}_{25-x}{\mathrm{Ga}}_{25}$ ($x=0$, 2.5, 5.0, and 7.5). All samples exhibit a martensitic transformation at temperature $T_M$ and ferromagnetic ordering at temperature $T_C$, while the pure end member ($x=0$) also has a premartensitic transition at $T_{PM}$, giving four different scenarios: $T_C>T_{PM}>T_M,T_C>T_M$ without premartensitic transition, $T_C\approx T_M$, and $T_C<T_M$. Fundamental differences in elastic properties, i.e., stiffening versus softening, are explained in terms of coupling of shear strains with three discrete order parameters relating to magnetic ordering, a soft mode, and the electronic instability responsible for the large strains typical of martensitic transitions. Linear-quadratic or biquadratic coupling between these order parameters, either directly or indirectly via the common strains, is then used to explain the stabilities of the different structures. Acoustic losses are attributed to critical slowing down at the premartensite transition, to the mobility of interphases between coexisting phases at the martensitic transition, and to mobility of some aspect of the twin walls under applied stress down to the lowest temperatures at which measurements were made.

Figure 1

Schematic phase diagram for the Ni-rich end of the system ${\mathrm{Ni}}_{50+x}{\mathrm{Mn}}_{25-x}{\mathrm{Ga}}_{25}$ (following Refs. [15, 16, 17, 18]). The boundary between stability fields of $5M/7M$ martensites and the nonmodulated $I4/mmm$ structure has not yet been determined. Ferromagnetic structures become stable below the blue line ($T_C$) and martensitic structures become stable below the red line ($T_M$). The green line is $T_{PM}$, which marks the transition from the ferromagnetic austenite structure to the premartensite $3M$ structure.

Figure 2

Segments of RUS spectra for ${\mathrm{Ni}}_{50}{\mathrm{Mn}}_{25}{\mathrm{Ga}}_{25}$. The ordinate is the amplitude of the RUS spectra in arbitrary units. Each spectrum has been offset in proportion to the temperature at which it was collected. Accordingly, the axis is labeled as temperature. Blue traces are spectra collected during cooling and red traces are spectra collected during heating.

Figure 3

Temperature dependence $f^2$ (left axis) and magnetic susceptibility $M/H$ (right axis) for the series ${\mathrm{Ni}}_{50+x}{\mathrm{Mn}}_{25-x}{\mathrm{Ga}}_{25}$ with (a) $x=0$, (b) 2.5, (c) 5.0, and (d) 7.5. Blue triangles (lines) indicate data recorded on cooling and red circles (lines) on heating. Inset of (b) and (d) show the martensitic transition in detail. Magnetization measurements were performed at 200 Oe.

Figure 4

Temperature dependence of acoustic loss for the samples ${\mathrm{Ni}}_{50+x}{\mathrm{Mn}}_{25-x}{\mathrm{Ga}}_{25}$ with (a) $x=0$, (b) $x=2.5$, (c) $x=5.0$, and (d) $x=7.5$. Resonant peaks in the primary spectra remain broad and weak at $T<T_M$, in comparison with those at $T>T_M$. Blue triangles indicate data recorded on cooling and red circles on heating.

Figure 5

Variations of the change in $f^2\left(T\right),\mathrm{\Delta }{f}^2\left(T\right)$, with respect to a linear baseline fit to data in Fig. 3 at $T>T_C$ for $x=0$ and 2.5. $\mathrm{\Delta }{f}^2\left(T\right)$ is expected to scale with the square of the ferromagnetic order parameter, but its magnitude clearly reduces with increasing $x$.