Electronic and magnetic properties of spiral spin-density-wave states in transition-metal chains

The electronic and magnetic properties of one-dimensional (1D) $3d$ transition-metal nanowires are investigated in the framework of density functional theory. The relative stability of collinear and noncollinear (NC) ground-state magnetic orders in V, Mn, and Fe monoatomic chains is quantified by computing the frozen-magnon dispersion relation $\mathrm{\ensuremath{\Delta}}E(\stackrel{P\vec}{q})$ as a function of the spin-density-wave vector $\stackrel{P\vec}{q}$. The dependence on the local environment of the atoms is analyzed by varying systematically the lattice parameter $a$ of the chains. Electron correlation effects are explored by comparing local spin-density and generalized-gradient approximations to the exchange and correlation functional. Results are given for $\mathrm{\ensuremath{\Delta}}E(\stackrel{P\vec}{q})$, the local magnetic moments ${\stackrel{P\vec}{\ensuremath{\mu}}}_i$ at atom $i$, the magnetization-vector density $\stackrel{P\vec}{m}(\stackrel{P\vec}{r})$, and the local electronic density of states ${\ensuremath{\rho}}_{i\ensuremath{\sigma}}(\ensuremath{\varepsilon})$. The frozen-magnon dispersion relations are analyzed from a local perspective. Effective exchange interactions ${J}_ij$ between the local magnetic moments ${\stackrel{P\vec}{\ensuremath{\mu}}}_i$ and ${\stackrel{P\vec}{\ensuremath{\mu}}}_j$ are derived by fitting the ab initio $\mathrm{\ensuremath{\Delta}}E(\stackrel{P\vec}{q})$ to a classical 1D Heisenberg model. The dominant competing interactions ${J}_ij$ at the origin of the NC magnetic order are identified. The interplay between the various ${J}_ij$ is revealed as a function of $a$ in the framework of the corresponding magnetic phase diagrams.