Commensurability and Defect-Induced Phason Gaps in Incommensurate Systems

The phason energy gap has been observed to increase on going from the incommensurate to higher-order commensurate phases in the "devil's staircase" compound ${\left[\mathrm{N}{\left(\mathrm{C}{\mathrm{H}}_3\right)}_4\right]}_2$Zn${\mathrm{Cl}}_4$. The gap was determined via the phason-induced ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ spin-lattice relaxation contribution, which was obtained from the variation of the effective spin-lattice relaxation rate over the inhomogeneous incommensurate frequency distribution. Here, as well as in ${\mathrm{Rb}}_2$Zn${\mathrm{Cl}}_4$ and ${\mathrm{Rb}}_2$Zn${\mathrm{Br}}_4$, the phason gap in the incommensurate phase is defect induced.