Electron-spin resonance in the impurity-doped Heisenberg linear chain (CH3)N4MnCl3:Cu

The room-temperature 23.4-GHz electron-spin-resonance linewidth and line shape are reported in a linear-chain crystal of (C${\mathrm{H}}_3$)${}_4{}^{}{}_{}{}^{}\mathrm{N}$Mn${\mathrm{Cl}}_3$ (TMMC) containing 4-at.% ${\mathrm{Cu}}^{++}$ substituted for ${\mathrm{Mn}}^{++}$. The width at $\theta =0\mathrm{}$ is 50% greater than for pure TMMC but is the same as in pure TMMC at $\theta =55\mathrm{}°$, where $\theta$ is the angle of applied field with respect to the chain axis. The line shapes are the same in pure and impure TMMC at both angles. These results are explained in terms of a model in which the only effect of impurities is to alter the rate of diffusion along the chain. The slower diffusion produces a marked increase in width at $\theta =0\mathrm{}°$, where long-time effects dominate the one-dimensional ($1d$) spin dynamics, but has no effect at the "magic angle" ($\theta =55\mathrm{}°,3\mathrm{}{cos}^2\theta -1=0\mathrm{}$), where there is no secular contribution to the broadening and thus the $1d$ character is unimportant. A continuum calculation is presented in which an impurity is replaced by a region in which the diffusion coefficient is $D^{\prime }$, compared with the host value $D$. The line shape is not altered in this model, in agreement with experiment, and the width, compared with pure TMMC, is related to $\frac{D^{\prime }}{D}$. A relation is then assumed between $\frac{D^{\prime }}{D}$ and $\frac{J^{\prime }}{J}$ from which we estimate $\left|\frac{J^{\prime }}{J}\right|=0.06\mathrm{}$, where $J^{\prime }$ and $J$ are impurity-host and host-host intrachain interactions, respectively.