Premartensite to martensite transition and its implications for the origin of modulation in $\mathrm{N}{\mathrm{i}}_2\mathrm{MnGa}$ ferromagnetic shape-memory alloy

We present results of a temperature-dependent high-resolution synchrotron x-ray powder diffraction study of sequence of phase transitions in $\mathrm{N}{\mathrm{i}}_2\mathrm{MnGa}$. Our results show that the incommensurate martensite phase results from the incommensurate premartensite phase and not from the austenite phase assumed in the adaptive phase model. The premartensite phase transforms to the martensite phase through a first order phase transition with coexistence of the two phases in a broad temperature interval $(\sim 40\mathrm{K})$, discontinuous change in the unit cell volume as also in the modulation wave vector across the transition temperature, and considerable thermal hysteresis in the characteristic transition temperatures. The temperature variation of the modulation wave vector $\mathbf{q}$ shows smooth analytic behavior with no evidence for any devilish plateau corresponding to an intermediate or ground state commensurate lock-in phase. The existence of the incommensurate 7M-like modulated structure down to 5 K suggests that the incommensurate 7M-like modulation is the ground state of $\mathrm{N}{\mathrm{i}}_2\mathrm{MnGa}$ and not the Bain distorted tetragonal $\mathrm{L}{1}_0$ phase or any other lock-in phase with a commensurate modulation. These findings can be explained within the framework of the soft phonon model.

Figure 1

Low field (at 100 Oe) magnetization as a function of temperature in cooling and heating cycles. Inset: Expanded view of the austenite to premartensite to martensite (during cooling and martensite to premartensite to austenite (during heating) transitions over the 200–320 K range.

Figure 2

Evolution of SXRPD patterns of $\mathrm{N}{\mathrm{i}}_2\mathrm{MnGa}$ as a function of temperature during the cooling cycle. “C,” “P,” and “M” represent the Bragg peaks due to the cubic, premartensite, and martensite phases, respectively. Inset in (a) shows the Bragg reflections on an expanded scale.

Figure 3

Rietveld fits for the SXRPD patterns of $\mathrm{N}{\mathrm{i}}_2\mathrm{MnGa}$ at (a) 298 K (cubic austenite phase), (b) 228 K (premartensite phase), and (c) 108 K (martensite phase). The experimental data, fitted curve, and the residue are shown by circles (black), continuous line (red), and bottom-most plot (green), respectively. The tick marks (blue) represent the Bragg peak positions. The insets show the fit for the main peak region on an expanded scale. Arrows in (b) and (c) represent satellite reflections in the premartensite (P) and martensite phases (M), respectively.

Figure 4

Rietveld fits for the SXRPD patterns of $\mathrm{N}{\mathrm{i}}_2\mathrm{MnGa}$ at 218 K with (a) 3M-like incommensurate premartensite structure, (b) combination of cubic and 3M-like incommensurate premartensite structure, (c) combination of cubic and 7M-like incommensurate martensite structure, and (d) combination of 3M-like incommensurate premartensite and 7M-like incommensurate martensite structure. The experimental data, fitted curve, and the residue are shown by circles (black), continuous line (red), and bottom-most plot (green), respectively. The tick marks (blue) represent the Bragg peak positions. The insets show the fit for the satellite reflections corresponding to the premartensite (P) and martensite (M) phases.

Figure 5

Evolution of SXRPD patterns of $\mathrm{N}{\mathrm{i}}_2\mathrm{MnGa}$ as a function of temperature during the heating cycle. “C,” “P,” and “M” represent the Bragg peaks due to the cubic, premartensite, and martensite phases, respectively. Inset (a) shows the Bragg reflections on an expanded scale.

Figure 6

(a) Variation of weight fraction of the premartensite (PM) and martensite phases (M), as obtained by Rietveld refinements, with temperature during cooling and heating cycles. (b) Temperature variation of $a,b,c$, in the austenite (C), 3M-like premartensite (PM) and the 7M-like martensite (M) phase regions for the cooling cycle. The volume of cubic phase is scaled by ½ for comparison.

Figure 7

Variation of modulation vector $\left(\mathit{q}\right)$ as a function of temperature obtained from superspace Rietveld refinements during cooling. The modulation wave vector obtained from neutron diffraction data at 5 K is also shown in red. Dashed line shows discontinuous jump in $\mathit{q}$ at the transition temperature. $\mathit{q}\text{−}T$ is nonlinear as $\mathit{q}$ behaves like an order parameter that changes discontinuously at a first order phase transition.