Dynamic response of local magnons: Single-impurity limit in one-dimensional magnets

The dynamic response of local magnon modes associated with a single-impurity spin in one-dimensional ferro- and antiferromagnetic insulators is studied theoretically with the use of a Green's-function formulation solved exactly, by transfer-matrix techniques, for zero temperature. The calculations are applied to the typical one-dimensional (1D) ferromagnet CsNi${\mathrm{F}}_3$ and the antiferromagnet ${\left(\mathrm{C}{\mathrm{H}}_3\right)}_4$NMn${\mathrm{Cl}}_3$ (TMMC) as functions of the impurity parameters in a way to allow the interpretation of possible future measurements of defect modes in these materials. The theory also explains qualitatively recent measurements in the three-dimensional defect anti-ferromagnets Fe${\mathrm{F}}_2$: ${\mathrm{Mn}}^{2+}$, Co${\mathrm{F}}_2$: ${\mathrm{Mn}}^{2+}$, and Fe${\mathrm{F}}_2$: ${\mathrm{Co}}^{2+}$.