Alloying route to tailor giant magnetic anisotropy in transition-metal nanowires

First-principles theoretical investigations of one-dimensional ordered $3d$-$5d$ alloys reveal magnetic anisotropy energies $\Delta E$, which are extraordinary high for transition-metal nanostructures. The results show that $\Delta E$ of Pt-$X$ and Ir-$X$ wires with $X\equiv \text{Ti}$–Ni strongly oscillates as a function $3d$-band filling showing both giant values (e.g., $\Delta E=25$, 58, and 57 meV/atom for Pt-Ni, Ir-Cr, and Ir-Ni) as well as modest enhancements (e.g., $\Delta E=2.3$ and $6.5$ meV/atom for Pt-Cr and Pt-Fe). The robustness of the results with respect to strain and relaxation is demonstrated. The microscopic mechanisms behind the trends in $\Delta E$ are analyzed from a local perspective.

Figure 1

(a) Ab initio MAE per atom $\Delta E=E_x-E_z$ of linear Pt-$3d$ wires having FM (circles, full lines) or AF (triangles, broken lines) orders at their equilibrium NN distances $r_0$. The solid symbols indicate the ground-state magnetic order. Positive (negative) values of $\Delta E$ correspond to an in-line (perpendicular) easy axis as illustrated in the inset. (b) Comparison between the ground-state ab initio $\Delta E$, the model spin-orbit anisotropy energy $\Delta E_{\mathrm{SO}}$, and the element-specific local MAEs $\Delta E_{3d}$ and $\Delta E_{\mathrm{Pt}}$.

Figure 2

Local density of states (LDOS) of FM Pt-Ti, Pt-Cr, and Pt-Ni wires at their equilibrium NN distances. Results are given for the projections on the $d$-electron irreducible subspaces ${\Delta }_0$, ${\Delta }_1$, and ${\Delta }_2$ of the Pt (left) and $3d$ (right) atoms.

Figure 3

(a) Ab initio MAE per atom $\Delta E=E_x-E_z$ of linear Ir-$3d$ wires having FM (circles, full lines) or AF (triangles, broken lines) orders at their equilibrium NN distances $r_0$. The solid symbols indicate the ground-state magnetic order (see the inset). Positive (negative) values of $\Delta E$ correspond to an in-line (perpendicular) easy axis.

Figure 4

MAE per atom $\Delta E=E_x-E_z$ of (a) Pt-Ni and (b) Ir-Cr wires as a function of the NN distance $r$. Results are given for linear (dots) and zigzag (crosses) alloy wires, as well as for pure linear $5d$ wires (open circles). The magnetization directions $x$ and $z$ are illustrated in the inset. The dotted (dashed) vertical lines indicate the equilibrium NN distance $r_0$ in pure $5d$ (alloy $3d$-$5d$) linear wires.