First-principles investigation of structural and magnetic disorder in CuNiMnAl and CuNiMnSn Heusler alloys

Two quaternary Heusler alloys, equiatomic CuNiMnAl and CuNiMnSn, are studied using density functional theory to understand their tendency for atomic disorder on the lattice and the magnetic effects of disorder. Disordered structures with antisite defects of atoms of the same and different sublattices are considered, with the level of atomic disorder ranging from 3% to 25%. Formation energies and magnetic moments are calculated relative to the ordered ground state and combined with a simple thermodynamical model to estimate temperature effects. We predict the relative levels of disordering in the two equiatomic alloys with good correlation to experimental x-ray diffraction results. The effect of swaps involving Mn is also discussed.

Figure 1

XRD traces for CuNiMnAl and CuNiMnSn heat-treated alloys. Powder XRD was performed using the PANalytical Xpert Multipurpose X-ray Diffraction System using a Cu $K\alpha$ radiation source. Samples were prepared using a ring mill. Both scans were performed using identical machine settings. Additionally, longer scans were performed on the CuNiMnAl sample which did not reveal additional reflections. Adapted from Ref. [15].

Figure 2

A 128-atom quaternary Heusler cell with (a) ordered structure and (b) 25% of the Cu and Mn atoms swapped. Visualization created using the vesta software package [25].

Figure 3

Energy difference per atom between the ordered ground-state structure and the disordered structures for the average of three SQSs for (a) CuNiMnAl and (b) CuNiMnSn, and magnetic moment per atom of the ordered ground state and the disordered structures for (c) CuNiMnAl and (d) CuNiMnSn. Swaps of elements across the same sublattice are represented by solid symbols and solid lines, and swaps of elements across different sublattices are represented by open symbols and dashed lines.

Figure 4

Temperature vs disordering level for the average of three SQSs for (a) CuNiMnAl and (b) CuNiMnSn. The legends are the same as those of Figs. 3 and 3.

Figure 5

Predicted magnetic moment per atom vs temperature using the average of three SQSs for CuNiMnAl and CuNiMnSn. Each point here corresponds to a temperature where an additional disordered structure is predicted to become energetically accessible

Figure 6

Spin-resolved density of states for (a) ordered CuNiMnAl, (b) ordered CuNiMnSn, (c) disordered CuNiMnAl 25% Cu-Ni, and (d) disordered CuNiMnAl 25% Cu-Mn. In (d) Mn1 refers to a normal site Mn atom while Mn2 refers to an antisite Mn atom. The $x$ axis is the energy relative to the Fermi level.

Figure 7

(a) Site on the lattice of a Mn atom defect is outlined. (b) Isosurface of the difference in spin-up and spin-down charge density at the location of the Mn atom usually occupied by Cu in CuNiMnAl. The isosurface value is 0.097 $e^{-}$/Å${}^3$. The center Mn has a localized spin-down charge density that contributes to a reduced overall magnetic moment in the disordered structure. Visualization created using the vesta software package [25].