Disorder-induced cubic phase in Fe${}_{2}$-based Heusler alloys

Disorder-induced cubic phase in Fe $_{2}$ -based Heusler alloys

Janos Kiss, Stanislav Chadov, Gerhard H. Fecher, and Claudia Felser

Phys. Rev. B 87, 224403 – Published 10 June 2013

Abstract

Based on the first-principles electronic structure calculations, we analyze the chemical and magnetic mechanisms stabilizing the cubic phase in Fe $_{2}$ -based Heusler materials, which were predicted to be tetragonal when being chemically ordered. In agreement with recent experimental data, we found that these compounds crystallize within the so-called “inverted” cubic Heusler structure perturbed by a certain portion of the intrinsic chemical disorder. Understanding of these mechanisms is a necessary step to guide the successful future synthesis of the stable Fe $_{2}$ -based tetragonal phases, which are promising candidates for the rare-earth-free permanent magnets.

Received 4 February 2013

DOI:https://doi.org/10.1103/PhysRevB.87.224403

Authors & Affiliations

Janos Kiss, Stanislav Chadov, Gerhard H. Fecher^*, and Claudia Felser

Max-Planck-Institut für Chemische Physik fester Stoffe, Nöthnitzer Strasse 40, 01187 Dresden, Germany

^*gerhard.fecher@cpfs.mpg.de

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Vol. 87, Iss. 22 — 1 June 2013

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Figure 1
The cubic unit cell of point-symmetry group 216 together with its schematic graphical diagram and the corresponding written notation. The high-symmetric Wyckoff positions $4 a$ , $4 b$ , $4 c$ , and $4 d$ are distinguished by different colors.Reuse & Permissions
Figure 2
Total energy of the Fe $_{2}$ CuGa Heusler alloy calculated as a function of the $c / a$ ratio for various distributions of Fe and Cu (indicated by the boxlike diagram; green, yellow, and white colored areas correspond to the Fe, Cu, and Ga occupations, respectively). (a) Thick black and red curves correspond to CuGa/FeFe (regular) and FeGa/CuFe (inverted) configurations, respectively. The thin violet line shows the intermediate [Cu $_{0.5}$ Fe $_{0.5}$ ]Ga/[Cu $_{0.5}$ Fe $_{0.5}$ ]Fe case between regular and inverted configurations. The absolute energy minimum of the regular (CuGa/FeFe) tetragonal phase is taken as a reference. (b) Solid red curve represents the same inverted configuration as in (a), whereas the solid blue line shows the most stable configuration: FeGa/[Cu $_{0.5}$ Fe $_{0.5}$ ][Cu $_{0.5}$ Fe $_{0.5}$ ], obtained from the ordered inverted configuration by mixing Fe and Cu randomly in plane. The dashed red and blue lines correspond to the distributions derived from the previous two configurations via additional in-plane random spread of Ga and Fe: [Fe $_{0.5}$ Ga $_{0.5}$ ][Fe $_{0.5}$ Ga $_{0.5}$ ]/CuFe (red dashed line) and [Fe $_{0.5}$ Ga $_{0.5}$ ][Fe $_{0.5}$ Ga $_{0.5}$ ]/[Cu $_{0.5}$ Fe $_{0.5}$ ][Cu $_{0.5}$ Fe $_{0.5}$ ] (blue dashed line). The absolute energy minimum of the inverted (FeGa/CuFe) phase is taken as a reference.Reuse & Permissions
Figure 3
Comparison of the magnetic exchange coupling (a) in the inverted FeGa/FeCu and (b) in the most stable FeGa/[Fe $_{0.5}$ Cu $_{0.5}$ ][Fe $_{0.5}$ Cu $_{0.5}$ ] configurations. The atoms are arranged within Fe-Ga and Fe-Cu layers marked by light and dark blue horizontal planes, respectively. Fe, Cu, and Ga atoms are shown as green, yellow, and white spheres, respectively. Magnetic moments are shown by arrows. The bond thickness reflects the strength of the exchange interaction. The interlayer Fe-Fe interactions dominate: $J_{inter l ayer} \approx 25$ meV (thick green bonds). The in-plane interactions are negligibly small, except those in Fe-Cu planes. (b) illustrates the typical distinction from the ordered inverted structure: the random in-plane swap of one Fe and one Cu atom brings two Fe atoms closer to one another within the Cu-Fe plane. This alters the nearest in-plane Fe-Fe exchange from antiferromagnetic ( $J_{in - plane} = - 1.4$ meV, thin red bond) in (a) to ferromagnetic ( $J_{in - plane} = 5.2$ meV, thin green bond) in (b).Reuse & Permissions
Figure 4
Comparison of the spin-resolved electronic band structures and related densities of states for the (a) regular cubic CuGa/FeFe, (b) inverse cubic FeGa/CuFe, and (c) FeGa/[Fe $_{0.5}$ Cu $_{0.5}$ ][Fe $_{0.5}$ Cu $_{0.5}$ ] configurations. The majority- and minority-spin states are distinguished by red and blue, respectively.Reuse & Permissions

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