Linear spin wave theory for single-Q incommensurate magnetic structures

Linear spin wave theory provides the leading term in the calculation of the excitation spectra of long-range ordered magnetic systems as a function of $1/\sqrt{S}$. This term is acquired using the Holstein–Primakoff approximation of the spin operator and valid for small δS fluctuations of the ordered moment. We propose an algorithm that allows magnetic ground states with general moment directions and single-Q incommensurate ordering wave vector using a local coordinate transformation for every spin and a rotating coordinate transformation for the incommensurability. Finally we show, how our model can determine the spin wave spectrum of the magnetic C-site langasites with incommensurate order. (paper)