Electronic structure and lattice dynamics of the magnetic shape-memory alloy ${\text{Co}}_2\text{NiGa}$

In addition to the prototypical Ni-Mn-based Heusler alloys, the Co-Ni-Ga systems have recently been suggested as another prospective materials class for magnetic shape-memory applications. We provide a characterization of the dynamical properties of this material and their relation to the electronic structure within a combined experimental and theoretical approach. This relies on inelastic neutron scattering to obtain the phonon dispersion while first-principles calculations provide the link between dynamical properties and electronic structure. In contrast to ${\text{Ni}}_2\text{MnGa}$, where the softening of the ${\text{TA}}_2$ phonon branch is related to Fermi-surface nesting, our results reveal that the respective anomalies are absent in Co-Ni-Ga, in the phonon dispersions as well as in the electronic structure.

Figure 1

(Color online) The Ga-Co-Ni phase diagram showing the martensitic phase at room temperature with the isothermal room-temperature martensite start temperature $M_{\text{s}}\left(T_{\text{R}}\right)$ represented in the isothermal section of $1000°\text{C}$, constructed from the data in Ref. 35. The isothermal section shows the equilibrium fcc- and bcc-like phases, $\gamma$ (A1), ${\gamma }^{\prime }$ $\left(\text{L}{1}_2\right)$, and $\beta$ (B2), respectively, as well as the two-phase field $\gamma +\beta$ region. Tetragonal ${\beta }^{\prime }$ $\left(\text{L}{1}_0\right)$ corresponds to the martensitic structure. The extrapolated B2 phases (dashed triangles) show the favorable overlapping $\beta$ regions at $0°\text{C}$ for the formation of magnetic-shape-memory (MSM) $\text{L}{2}_1$-like Heusler structures (Ref. 36). The yellow dot marks the perfect $\text{L}{2}_1$ ${\text{Co}}_2\text{NiGa}$ compound on the dashed line of constant $e/a=7.75$. The second dashed line of constant $e/a=7.42$ goes through the white square corresponding to completely disordered $\beta$-phase ${\text{Co}}_{48}{\text{Ni}}_{22}{\text{Ga}}_{30}$ $\left({\text{Co}}_{1.92}{\text{Ni}}_{0.88}{\text{Ga}}_{1.2}\right)$ for which the phonon dispersions were measured by neutron-scattering experiment at room temperature. First-principles phonon calculations were done for $\text{L}{2}_1$ ${\text{Co}}_2\text{NiGa}$, ${\text{Co}}_8{\text{Ni}}_3{\text{Ga}}_5$ $\left({\text{Co}}_2{\text{Ni}}_{0.75}{\text{Ga}}_{1.25}\right)$, and ${\text{Co}}_7{\text{Ni}}_4{\text{Ga}}_5$ $\left({\text{Co}}_{1.75}{\text{NiGa}}_{1.25}\right)$, the latter are represented by white circles. The regions with Curie temperatures $T_c$ larger or smaller than the martensite transformation temperatures $M_{\text{s}}$ are separated by the thick blue line (constructed from the data in Ref. 11).

Figure 2

(Color online) Schematic view of the (a) conventional Heusler structure $\left(\text{L}{2}_1\right)$ with the Co atoms (bright yellow) occupying the corners, center, and faces of the simulation cell while the Ga atoms (black) and Ni atoms (medium green) occupy the other rocksalt sublattice and (b) the inverse structure of the stoichiometric composition. Some of the supercells with Ga excess are also plotted. The cell in (c) belongs to the Heusler structure of ${\text{Co}}_8{\text{Ni}}_3{\text{Ga}}_5$ $\left({\text{Co}}_2{\text{Ni}}_{0.75}{\text{Ga}}_{1.25}\right)$ where one Ni atom of the stoichiometric compound has been replaced by Ga. The cell in (d) belongs to the inverse Heusler structure of the ${\text{Co}}_7{\text{Ni}}_4{\text{Ga}}_8$ $\left({\text{Co}}_{1.75}{\text{NiGa}}_{1.25}\right)$ compound where one Co atom has been replaced by Ga.

Figure 3

Total-energy dependence under the variation in $c/a$ from ab initio calculations for different compositions and conventional ($\text{L}{2}_1$ like) and inverse crystal structures.

Figure 4

(Color online) The measured dispersion curve of the $\left[\xi \xi 0\right]{\text{-TA}}_2$ phonon branch in ${\text{Co}}_{1.92}{\text{Ni}}_{0.88}{\text{Ga}}_{1.2}$ at several temperatures. The data for stoichiometric ${\text{Ni}}_2\text{MnGa}$ was taken from Ref. 16.

Figure 5

(Color) Computed phonon-dispersion curves for the conventional Heusler structures of ${\text{Ni}}_2\text{MnGa}$, ${\text{Co}}_2\text{NiGa}$, and ${\text{Co}}_8{\text{Ni}}_3{\text{Ga}}_5$ $\left({\text{Co}}_2{\text{Ni}}_{0.75}{\text{Ga}}_{1.25}\right)$ and the inverse Heusler structure of ${\text{Co}}_8{\text{Ni}}_3{\text{Ga}}_5$ $\left({\text{Co}}_2{\text{Ni}}_{0.75}{\text{Ga}}_{1.25}\right)$ along the [110] direction. The contributions of the different elements are represented through a color scheme which is obtained from the eigenvectors belonging to the respective dynamical matrix. The squares denote the results of the measurements for the ${\text{Co}}_{48}{\text{Ni}}_{22}{\text{Ga}}_{30}$ $\left({\text{Co}}_{1.92}{\text{Ni}}_{0.88}{\text{Ga}}_{1.2}\right)$ sample.

Figure 6

(Color online) Fermi surfaces of (a) ${\text{Ni}}_2\text{MnGa}$ (upper left, adapted from Ref. 24) and [(b)–(d)] ${\text{Co}}_2\text{NiGa}$ for different valence-electron concentrations $e/a$ in a repetitive scheme of the Brillouin zone. The $\Gamma$ point can be found in the center of the displayed cubes as well as in each corner of the cubes. Different colors denote different bands crossing $E_{\text{F}}$. The Fermi surfaces of the Co-Ni-Ga systems all refer to the same color scheme. Here, only the Fermi surfaces corresponding to the minority-spin channels are plotted.

Figure 7

(Color online) Partial and total densities of states of ${\text{Co}}_2\text{NiGa}$ for the full Heusler structure at (a) $c/a=1$ and (b) $c/a=1.41$, (c) the inverse Heusler structure in the cubic state and (d) ${\text{Co}}_8{\text{Ni}}_3{\text{Ga}}_5$ $\left({\text{Co}}_2{\text{Ni}}_{0.75}{\text{Ga}}_{1.25}\right)$ in the full Heusler structure.