Role of Electronic Structure in the Martensitic Phase Transition of ${\mathrm{Ni}}_2{\mathrm{Mn}}_{1+x}{\mathrm{Sn}}_{1-x}$ Studied by Hard-X-Ray Photoelectron Spectroscopy and Ab Initio Calculation

We have revealed the underlying mechanism of the martensitic phase transition (MPT) in a new class of ferromagnetic shape memory alloys, ${\mathrm{Ni}}_2{\mathrm{Mn}}_{1+x}{\mathrm{Sn}}_{1-x}$, by the combination of bulk-sensitive hard-x-ray photoelectron spectroscopy and a first-principles density-functional calculation. The Ni $3d$ $e_g$ state in the cubic phase systematically shifts towards the Fermi energy with an increase in the number of Mn atoms substituted in the Sn sites. An abrupt decrease of the intensity of the Ni $3d$ $e_g$ states upon MPT for $x=0.36–0.42$ has been observed in the vicinity of the Fermi level. The energy shift of the Ni $3d$ minority-spin $e_g$ state in the cubic phase originates from hybridization with the antiferromagnetically coupled Mn in the Sn site. Below the MPT temperature, the Ni $3d$ state splits into two levels located below and above the Fermi energy in order to achieve an energetically stable state.

Figure 1

(a)–(d) Valence-band spectra of ${\mathrm{Ni}}_2{\mathrm{Mn}}_{1+x}{\mathrm{Sn}}_{1-x}$ with $x=0.42$, 0.36, 0.12, and 0.00, acquired by hard-x-ray photoelectron spectroscopy ($hv=5956.5\mathrm{eV}$) at several temperatures. The Fermi energy is taken as the origin of binding energy.

Figure 2

(a) Valence-band spectra of ${\mathrm{Ni}}_2{\mathrm{Mn}}_{1+x}{\mathrm{Sn}}_{1-x}$ with various $x$’s in cubic Heusler $L{2}_1$ phase (300 K). (b) The simulated spin-integrated x-ray photoelectron spectra.

Figure 3

(a) The total density of states (DOS) near $E_F$, in the cubic (austenite) phase of ${\mathrm{Ni}}_2{\mathrm{Mn}}_{1+x}{\mathrm{Sn}}_{1-x}$ for $x=0$ , 0.25, and 0.5, respectively. The DOS in the tetragonal phase ($c/a=1.31$) for $x=0.5$ is also shown for comparison. (b) The total energy difference (per formula unit) relative to the cubic phase as a function of the axial ratio, $c/a$, in the tetragonal structure calculated for ${\mathrm{Ni}}_2{\mathrm{Mn}}_{1+x}{\mathrm{Sn}}_{1-x}$ with $x=0$, 0.25, and 0.5, respectively.