Temperature dependence of exchange narrowing in the one-dimensional antiferromagnet ${\mathrm{N}\left(\mathrm{C}{\mathrm{H}}_3\right)}_4$Mn${\mathrm{Cl}}_3$ (TMMC)

A quantitative analysis of the temperature and angular dependence of the exchange-narrowed EPR linewidth $\Delta H(\theta ,T)$ at $K$ band is presented between $40<T<\mathrm{}300\mathrm{}$ °K for the one-dimensional antiferromagnet ${\mathrm{N}\left(\mathrm{C}{\mathrm{H}}_3\right)}_4$Mn${\mathrm{Cl}}_3$ (TMMC). The $s=\left(\frac{5}{2}\right)$ Mn(II) moments are treated as classical spins in order to avoid decoupling four-spin correlation functions arising from the antiferromagnetic coupling at either short or long time. The proper treatment of spin correlations accounts for the $T$ dependence of $\Delta H$ and provides a 20% correction to the high-$T$ limit even at 300°K. No adjustable parameters are needed for a quantitative fit at $\theta =54\mathrm{}°$ (between the applied field and the chain axis), where the absorption is Lorentzian. The dominant broadening arising from intrachain dipolar interactions ${\mathcal{H}}^{\prime }$ limits diffusive behavior and leads to an adjustable parameter which controls the magnitude of $\Delta H(0,T)\mathrm{}$ and the non-Lorentzian profile at $\theta =0\mathrm{}$. The increasing importance of short-time effects and the decreasing importance of diffusive contributions to $\Delta H$ are quantitatively illustrated at $T=77\mathrm{}$ °K. This trend continues to lower $T$, although the $T=20\mathrm{}$ °K and $T=4.2\mathrm{}$ °K data cannot be treated by the present model of only including spin correlations due to isotropic exchange. The angular anisotropy of $\Delta H(\theta ,300)$ and $K$ and $X$ bands shows the expected ${\omega }_0$ dependence on the Larmor frequency at $\theta =54\mathrm{}°$.