Environment-dependent noncollinear magnetic orders and spin-wave spectra of Fe chains and stripes

Abstract

The ground-state magnetic properties of free-standing Fe wires having linear, zigzag, and rectangular geometries are investigated in the framework of density-functional theory. The stability of various wires geometries and types of magnetic orders is analyzed as a function of the spin-density-wave (SDW) number $q$. In particular, we consider ferromagnetic (FM) and antiferromagnetic (AF) collinear states as well as periodic and alternating noncollinear (NC) states. The relaxed interatomic bond lengths $d$, frozen-magnon dispersion relations $\ensuremath{\Delta}E(q)$, local magnetic moments ${\ensuremath{\mu}}_{i}$, spin-polarized electronic densities of states ${\ensuremath{\rho}}_{d\ensuremath{\sigma}}(\ensuremath{\varepsilon})$, and effective exchange couplings ${J}_{ij}$ are determined. Iron zigzag chains show FM order ($q=0$) at the equilibrium lattice parameter $a$ with $\ensuremath{\Delta}E(q)$ increasing monotonously with $q$. In contrast, biatomic rectangular ladders (RLs) develop spontaneously a spiral SDWs along the wire, keeping FM dimer couplings in the perpendicular direction. This NC order is further stabilized by compressing the wire. However, stretched RLs show FM order. In all cases, strong ${\ensuremath{\mu}}_{i}$ are found within the Wigner-Seitz spheres, which decrease moderately with increasing $q$. The electronic structures of collinear and NC states are analyzed by comparing the density of states ${\ensuremath{\rho}}_{d\ensuremath{\sigma}}(\ensuremath{\varepsilon})$ for different representative values of $q$. Effective exchange-interaction parameters ${J}_{ij}$ between the local moments ${\ensuremath{\mu}}_{i}$ and ${\ensuremath{\mu}}_{j}$ are derived by fitting the ab initio magnon dispersion relation $\ensuremath{\Delta}E(q)$ to a classical Heisenberg model. The interplay between the various competing ${J}_{ij}$ is shown to depend decisively on the lattice parameter and wire geometry. Comparing the ab initio results within a model phase diagram provides useful insights on the magnetic order of Fe wires from a local perspective.