Concentration-tuned tetragonal strain in alloys: Application to magnetic anisotropy of ${\mathrm{FeNi}}_{1\text{−}x}{\mathrm{Co}}_x$

We explore an opportunity to induce and control tetragonal distortion in materials. The idea involves formation of a binary alloy from parent compounds having body-centered and face-centered symmetries. The concept is illustrated in the case of ${\mathrm{FeNi}}_{1\text{−}x}{\mathrm{Co}}_x$ magnetic alloy formed by substitutional doping of the ${L1}_0$ FeNi magnet with Co. Using electronic structure calculations we demonstrate that the tetragonal strain in this system can be controlled by concentration and it reaches maximum for $x=0.5$. This finding is then applied to create a large magnetocrystalline anisotropy (MAE) in ${\mathrm{FeNi}}_{1\text{−}x}{\mathrm{Co}}_x$ system by considering an interplay of the tetragonal distortion with electronic concentration and chemical anisotropy. In particular, we identify an ordered ${\mathrm{FeNi}}_{0.5}{\mathrm{Co}}_{0.5}$ system with MAE larger by a factor 4.5 from the ${L1}_0$ FeNi magnet.

Figure 1

Relation between fcc and bcc lattices. (Top) fcc is equivalent to the bct lattice with $c/a=\sqrt{2}$. Compression of the lattice until $c/a=1$ (Bain transformation) results in cubic bcc lattice (bottom). For intermediate values of $c/a$ (middle) the lattice has tetragonal symmetry.

Figure 2

Schematic illustration of supercell models for disordered (right) and ordered (left) ${\mathrm{Ni}}_{1\text{−}x}{\mathrm{Co}}_x$ alloy in the case of $x=0.5$. The red, green, and blue spheres denote Fe, Ni, and Co atoms, respectively.

Figure 3

Calculated $c/a$ ratio, tetragonal distortion parameter (top), MA energy (middle), and spontaneous magnetization (bottom) of ${\mathrm{FeNi}}_{1\text{−}x}{\mathrm{Co}}_x$ as a function of the Co content. Open (filled) circles correspond to the random (ordered) alloy case. The dotted horizontal line denotes $c/a=\sqrt{2}$ that corresponds to the face-centered cubic symmetry.

Figure 4

Concentration dependence of the site-resolved MAE for disordered (top) and ordered (bottom) ${\mathrm{FeNi}}_{1\text{−}x}{\mathrm{Co}}_x$ alloy. The shown values are averaged over different nonequivalent atoms of the same specie in the considered supercells. The error bars denote the corresponding standard deviation when the latter is significant.

Figure 5

MAE of the ordered ${\mathrm{FeNi}}_{0.5}{\mathrm{Co}}_{0.5}$ alloy as a function of the $c/a$ ratio. The green circle denotes MAE for equilibrium $c/a$.