Local magnon modes studied by dynamic magnetic pair-density function analysis

Abstract

The dynamic magnetic pair-density function (DymPDF) $D_{\mathrm{M}}(r,E)$ is obtained via the Fourier transform of the dynamic magnetic structure factor, $S_{\mathrm{M}}(Q,E)$, which is measured using nonpolarized inelastic neutron scattering. While there is a long history of magnetic excitation studies with $S_{\mathrm{M}}(Q,E)$, there are no reports on $D_{\mathrm{M}}(r,E)$. In this study, we examine simple magnet models and representative magnet examples, such as FeTiO${}_3$ and YBa${}_2$Cu${}_3$O${}_6$, to investigate the real-space dynamics of $D_{\mathrm{M}}(r,E)$. We derive the $D_{\mathrm{M}}(r,E)$ equations for simple magnet models in a low energy limit. By comparing these equations to the simulations, we demonstrate the characteristic energy dependence of real-space local magnon modes, including the transition of the magnon mode from acoustic to optical. Our novel analysis reveals the local magnon modes accompanied by a sign change in each spin-pair correlation at a given energy in nanoscale real space even under non-periodic conditions. This method is unique for studying local magnetic dynamics.

The calculated equations need to be reconsidered because the present approximation severely limits the applicable energy range