Theoretical study of the temperature dependence of the magnon dispersion relation in transition-metal wires and monolayers

Abstract

The effects of temperature-induced electronic Stoner excitations on the spin-wave spectrum of one- and two-dimensional 3$d$ transition metals are investigated in the framework of ab initio density-functional theory by using a generalized-gradient approximation to the exchange and correlation energy. The dispersion relation of frozen-magnon spiral states is calculated as a function of spin-wave vector $\stackrel{P\vec}{q}$ and electronic temperature ${T}_{\mathrm{e}}$ for Fe, V, Co, and Ni monoatomic chains and for periodic Ni square lattices. The resulting temperature dependence of the magnetic order and its stability are analyzed in some detail. A variety of element-specific behaviors are identified including ferromagnetic, antiferromagnetic, and spiral orders. In all considered cases, the local magnetic moments are found to be remarkably stable both as a function of $\stackrel{P\vec}{q}$ and ${T}_{\mathrm{e}}$. Effective exchange interactions ${J}_{ij}$ between these moments are derived in the framework of a classical Heisenberg model by fitting the ab initio electronic free energy $\ensuremath{\Omega}$ as a function of $\stackrel{P\vec}{q}$. The changes in the magnetic order as a function of ${T}_{\mathrm{e}}$ are interpreted as the result of the interplay between competing ${J}_{ij}$ among different nearest neighbors. Finally, the electronic internal-energy and entropy contributions to the magnon dispersion relation $\ensuremath{\Omega}(\stackrel{P\vec}{q})$ are discussed.