Ordering tendencies and electronic properties in quaternary Heusler derivatives

The phase stabilities and ordering tendencies in the quaternary full-Heusler alloys NiCoMnAl and NiCoMnGa have been investigated by in situ neutron diffraction, calorimetry, and magnetization measurements. NiCoMnGa was found to adopt the $\mathrm{L}{2}_1$ structure, with distinct Mn and Ga sublattices but a common Ni-Co sublattice. A second-order phase transition to the $\mathrm{B}2$ phase with disorder also between Mn and Ga was observed at $1160\text{K}$. In contrast, in NiCoMnAl slow cooling or low-temperature annealing treatments are required to induce incipient $\mathrm{L}{2}_1$ ordering, otherwise the system displays only $\mathrm{B}2$ order. Linked to $\mathrm{L}{2}_1$ ordering, a drastic increase in the magnetic transition temperature was observed in NiCoMnAl, while annealing affected the magnetic behavior of NiCoMnGa only weakly due to the low degree of quenched-in disorder. First principles calculations were employed to study the thermodynamics as well as order-dependent electronic properties of both compounds. It was found that a near half-metallic pseudogap emerges in the minority spin channel only for the completely ordered Y structure. However, this structure is energetically unstable compared to a tetragonal structure with alternating layers of Ni and Co, which is predicted to be the low-temperature ground state. The experimental inaccessibility of the totally ordered structures is explained by kinetic limitations due to the low ordering energies.

Figure 1

Illustration of the ordered structures of NiCoMnZ considered here. Starting with $\mathrm{B}2$ (NiCo)(MnZ), NaCl-type ordering on either sublattice leads to $\mathrm{L}{2}_1$ structure of (NiCo)MnZ or NiCo(MnZ) type, and ordering on both sublattices to the Y structure. Those four structures have cubic symmetry. Ordering of the Ni and Co atoms in $\mathrm{L}{2}_1$ (NiCo)MnZ into alternating columns or planes gives the tetragonal ${\mathrm{T}}^{\text{c}}$ and ${\mathrm{T}}^{\text{p}}$ structures, respectively.

Figure 2

Field-dependent magnetization of NiCoMnAl in different annealing conditions measured at $293\text{K}$ and $77\text{K}$.

Figure 3

Temperature-dependent magnetization of NiCoMnGa and NiCoMnAl in different annealing conditions at an external magnetic field of $500\text{Oe}$. Depicted in red and blue are the heating and cooling curves, while the markers represent the magnetic transition temperatures determined as given in the text.

Figure 4

DSC measurements of annealed NiCoMnGa and NiCoMnAl. DSC curves have been recorded on heating with a rate of $10\mathrm{K}/\min$.

Figure 5

Waterfall plots of the temperature-dependent neutron powder diffraction patterns of NiCoMnGa (above) and NiCoMnAl (below) on heating and cooling with rates of approximately $2\mathrm{K}/\min$. Before the measurement, samples were solution annealed at $1273\text{K}$ and quenched in room temperature water. The unlabelled peaks with pronouncedly lower thermal expansion are due to the Nb sample cans.

Figure 6

Middle panel: Temperature-dependent lattice constants of NiCoMnGa and NiCoMnAl on heating and cooling starting with samples quenched from $1273\text{K}$. Upper and lower panels depict the temperature-dependent thermal expansion coefficients $\alpha =\frac{1}{a}\frac{\mathrm{d}a}{\mathrm{d}T}$.

Figure 7

Structure factors of the $\mathrm{B}2$ (red) and $\mathrm{L}{2}_1$ (blue) peak families as a function of temperature on heating and cooling as determined by in situ neutron diffraction for both systems. Theoretical values for different ordered structures are given as horizontal lines.

Figure 8

Comparison of the total energies of the various structures of ferromagnetic NiCoMnAl and NiCoMnGa obtained from density functional theory. The inner levels (blue) refer to fully relaxed structures (positions and lattice constants), whereas in the outer columns (red) only the lattice constants were relaxed and the ions remain on the ideal (symmetric) positions with bcc coordination. The energies are specified relative to a mixture of the ferromagnetic ground state structures of ternary ferromagnetic ${\mathrm{Co}}_2\mathrm{MnZ}$ and ${\mathrm{Ni}}_2\mathrm{MnZ}$. Thus negative energies denote structures which are inherently stable against demixing, whereas the others require to be stabilized by mixing entropy.

Figure 9

Spin-polarized electronic density of states (DOS) in ferromagnetic NiCoMnGa for the distinct ordered structures.