Pressure dependence of the Curie temperature in ${\mathrm{Ni}}_2\mathrm{MnSn}$ Heusler alloy: A first-principles study

The pressure dependence of electronic structure, exchange interactions, and Curie temperature in the ferromagnetic Heusler alloy ${\mathrm{Ni}}_2\mathrm{MnSn}$ has been studied theoretically within the framework of the density-functional theory. The calculation of the exchange parameters is based on the frozen-magnon approach. The Curie temperature $T_c$ is calculated within the mean-field approximation by solving the matrix equation for a multisublattice system. In agrement with experiment the Curie temperature increased from 362 K at ambient pressure to 396 K at 12 GPa. Extending the variation of the lattice parameter beyond the range studied experimentally, we obtained nonmonotonic pressure dependence of the Curie temperature and metamagnetic transition. We relate the theoretical dependence of $T_c$ on the lattice constant to the corresponding dependence predicted by the empirical interaction curve. The Mn-Ni atomic interchange observed experimentally is simulated to study its influence on the Curie temperature.

Figure 1

Schematic representation of the $L{2}_1$ structure adapted by the full Heusler alloys. The lattice consists of four interpenetrating fcc sublattices with the positions (0,0,0) and $(1∕2,1∕2,1∕2)$ for the Ni and $(1∕4,1∕4,1∕4)$ and $(3∕4,3∕4,3∕4)$ for the Mn and Sn, respectively.

Figure 2

Upper panel: Spin projected density of states of ${\mathrm{Ni}}_2\mathrm{MnSn}$ for ambient pressure and applied pressure of 16 GPa. Lower panel: The same for the case of Mn-Ni atomic interchange.

Figure 3

Pressure dependence of magnetic moments in ${\mathrm{Ni}}_2\mathrm{MnSn}$.

Figure 4

(a) Upper panel: Interatomic exchange parameters of ${\mathrm{Ni}}_2\mathrm{MnSn}$ for ambient pressure and applied pressure of 16 GPa. Lower panel: The same for the case of Mn-Ni atomic interchange. Zero-pressure comparison of both Mn-Mn $(+)$ and Mn-Ni (★) exchange parameters with those of Ref. 28 is also shown. (b) Pressure variation of the Curie temperature with increasing number of coordination spheres with and without Mn-Ni atomic interchange.

Figure 5

Pressure dependence of the first four nearest-neighbor Mn-Mn exchange parameters and two Mn-Ni exchange parameters.

Figure 6

Mn and total magnetic moments as a function of the Mn-Mn distance. Upper inset shows the variation of induced Ni moment with Mn-Mn distance. Lower inset shows $E_{tot}$ as a function of Mn magnetic moment for selected Mn-Mn interatomic distances. Arrows indicate the energy minima.

Figure 7

The first four nearest-neighbor Mn-Mn exchange interactions in ${\mathrm{Ni}}_2\mathrm{MnSn}$ as a function of Mn-Mn interatomic distance. The ellipses show the region of the metamagnetic transition.

Figure 8

Schematic representation of Kanomata et al.’s empirical interaction curve and the calculated Curie temperature as a function of the interatomic Mn-Mn distance in ${\mathrm{Ni}}_2\mathrm{MnSn}$. Inset shows pressure variation of $T_c$ in the low-pressure region. Small rectangles present the Curie temperatures of the corresponding compounds at ambient pressure. The attached arrows show the sign of $d{T}_c∕dP$. The experimental information is taken from Ref. 40.