Ab initio calculations of spin waves: A review of theoretical approaches and applications

Spin waves represent an important class of low-energy excitations in magnetic solids, which influence the thermodynamic properties and play a major role in technical applications, such as spintronics or magnetic data storage. Despite the enormous advances of ab initio simulations in materials science, quantitative calculations of spin-wave spectra still pose a significant challenge, because the collective nature of the spin dynamics requires an accurate treatment of the Coulomb interaction between the electrons. As a consequence, simple lattice models like the Heisenberg Hamiltonian are still widespread in practical investigations, but modern techniques like time-dependent density-functional theory or many-body perturbation theory also open a route to material-specific spin-wave calculations from first principles. Although both are in principle exact, actual implementations necessarily employ approximations for electronic exchange and correlation as well as additional numerical simplifications. In this review, we recapitulate the theoretical foundations of ab initio spin-wave calculations and analyze the common approximations that underlie present implementations. In addition, we survey the available results for spin-wave dispersions of various magnetic materials and compare the performance of different computational approaches. In this way, we provide an overview of the present state of the art and identify directions for further developments.