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

The dynamic magnetic pair-density function (DymPDF) $D_{\rm M}(r, E)$ is obtained via the Fourier transform of the dynamic magnetic structure factor, $S_{\rm M}(Q, E)$, which is measured using nonpolarized inelastic neutron scattering. While there is a long history of magnetic excitation studies with $S_{\rm M}(Q, E)$, there are no reports on $D_{\rm M}(r, E)$. 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 $D_{\rm M}(r, E)$. We derive the $D_{\rm M}(r, E)$ 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.