Pressure-induced structural phase transition in the ferromagnetic Heusler alloy ${\mathrm{Ni}}_2\mathrm{MnGa}$

The effect of pressure on the crystal structure of ${\mathrm{Ni}}_2\mathrm{MnGa}$ was investigated up to 41 GPa using in situ angle-dispersive x-ray diffraction with synchrotron radiation, an imaging plate detector, and a diamond anvil cell. A pressure-induced transition from a cubic $L{2}_1$ structure (space group $\mathit{Fm}\overline{3} m$) to a 10-layer modulated monoclinic structure ($C2/m$) with a distortion of $\beta \sim {92}^{\circ }$ occurred at a pressure of 19.1 GPa or lower. The volume change at the martensitic transition is a minute value of about $-0.1\%$. The bulk modulus for the low-pressure phase is 147(2) GPa, consistent with previous studies. In contrast, the bulk modulus for the high-pressure phase is 229(4) GPa, significantly higher than the former bulk modulus. Initial permeability measurements of the ${\mathrm{Ni}}_2\mathrm{MnGa}$ were also conducted at various pressures up to 1 GPa. The pressure dependencies of the Curie temperature, premartensitic, and martensitic transition temperatures are discussed in detail.

Figure 1

(a) Rietveld refinement of the RT XRPD pattern for ${\mathrm{Ni}}_2\mathrm{MnGa}$ at ambient pressure. The experimental data, fitted curve, and the residue are shown by the cross (black), continuous line (red), and bottom-most plot (blue), respectively. The tick marks (green) represent the Bragg peak positions. The final fit resulted in reliability factors of $R_{\mathrm{wp}}=3.22\%, R_{\mathrm{p}}=2.21\%$, and $R_{\mathrm{B}}=4.79\%$.

Figure 2

The RT XRPD patterns of ${\mathrm{Ni}}_2\mathrm{MnGa}$ at position A under various pressures. The inset provides an enlarged scale view of the pattern around the main peak at 23.9 GPa.

Figure 3

The RT XRPD patterns of ${\mathrm{Ni}}_2\mathrm{MnGa}$ near the 220 main peak at position B under pressure at 17.0, 19.1, and 19.7 GPa.

Figure 4

(a) The experimental x-ray powder diffraction pattern of ${\mathrm{Ni}}_2\mathrm{MnGa}$ under a pressure of 30.2 GPa at RT. The down arrows indicate the diffraction line of interest mentioned in the text. (b) The calculated x-ray powder diffraction pattern of ${\mathrm{Ni}}_2\mathrm{MnGa}$ with the 10M modulated structure (S.G.: $C2/m$). (c) The calculated x-ray powder diffraction pattern of ${\mathrm{Ni}}_2\mathrm{MnGa}$ with the 14M modulated structure (S.G.: $C2/m$).

Figure 5

Pressure dependencies of the lattice parameters for ${\mathrm{Ni}}_2\mathrm{MnGa}$: (a) the axial lengths of $a_{\mathrm{c}}$ in the LPA cubic cell, and of $a_{\mathrm{m}}, b_{\mathrm{m}}, c_{\mathrm{m}}$ in the HPM monoclinic cell; and (b) the angle $\beta$ between the $a_{\mathrm{m}}$ and $c_{\mathrm{m}}$ axes. The solid red line denotes the result of a least-squares fit. The dashed line denotes the transition pressure. The error bars are covered by the symbols.

Figure 6

Pressure dependencies of the axial ratios for ${\mathrm{Ni}}_2\mathrm{MnGa}$: (a) the ratio of $c_{\mathrm{m}}/5a_{\mathrm{m}}$ and (b) the ratio of $b_{\mathrm{m}}/\sqrt{2}{a}_{\mathrm{m}}$ in the HPM monoclinic cell. The solid red lines denote the results of a least-squares fit. The dashed line denotes the transition pressure. The error bars are covered by the symbols.

Figure 7

Pressure dependencies of the interatomic distances $d_{\mathrm{c}}$(Mn1-M1), $d_{\mathrm{m}}$(Mn1-M1), and $d_{\mathrm{m}}$(Mn2-Mn2) for ${\mathrm{Ni}}_2\mathrm{MnGa}$. Here, $d_{\mathrm{c}}$ and $d_{\mathrm{m}}$ denote interatomic distances for the cubic A and monoclinic M phases, respectively. In the A phase, Mn1 denotes the Mn ion at the Wyckoff $4a$ site in the $L{2}_1$ structure. In the M phase, Mn1 and Mn2 denote the sites listed in Table 1. The dashed line denotes the transition pressure. The error bars are covered by the symbols.

Figure 8

Pressure dependence of the volume for ${\mathrm{Ni}}_2\mathrm{MnGa}$. Here, $V_{\mathrm{c}}$ is the volume of a cubic cell in the austenite phase and $V_{\mathrm{m}}$ is the volume of a monoclinic cell in the martensite phase. The volume of the high-pressure 10M-monoclinic structure, $V_{\mathrm{m}}$, is scaled to $2/5V_{\mathrm{m}}$ for comparison with $V\mathrm{c}$. (The number of formula units in each unit cell, $Z$, is equal to 4.) Solid lines represent the fitting functions of the Murnaghan EOS applied to the experimental volumes of both phases. The error bars are covered by the symbols.

Figure 9

The initial permeability $\mu$ versus temperature curves for ${\mathrm{Ni}}_2\mathrm{MnGa}$ at various pressures. The blue and red solid lines denote the data obtained during the cooling and heating processes, respectively.

Figure 10

The pressure dependencies of the Curie temperature $T_{\mathrm{C}}$, the martensitic transition temperature $T_{\mathrm{M}}$, and the premartensitic transition temperature $T_{\mathrm{PM}}$ for ${\mathrm{Ni}}_2\mathrm{MnGa}$. The solid lines denote the results of least-squares fits for each specific temperature.