Study of nuclear spin-lattice relaxation in the one-dimensional easy-plane ferromagnet CsNiF3

The nuclear spin-lattice relaxation time $T_1$ of ${}_{}{}^{133}{}_{}{}^{}\mathrm{Cs}$ in one-dimensional easy-plane ferromagnet CsNi${\mathrm{F}}_3$ has been measured with external fields between 1.5 and 12 kOe applied in the easy-magnetization plane at temperatures between 1.5 and 20 K. The primary purpose of this work is to find experimental evidence for solitons in this compound. First the experimental data are compared with the numerical calculations for the two-magnon and the three-magnon relaxation processes based on linear spin-wave theory. The data for relatively low temperatures and relatively high fields are found to be interpreted by the sum of the relaxation rates of both processes quantitatively as well as qualitatively. A significant contribution of the second-order exchange-scattered three-magnon process is revealed. For other field and temperature regions, however, there appear discrepancies between the experiment and the calculation, thus suggesting the appearance of the effect of solitons. Next we consider the relaxation mechanism due to collision between the nuclear spin and one-dimensional dilute soliton gases. This approach leads to a qualitative equation such that $T_1^{-1\mathrm{}}\sim T^{-1\mathrm{}}\exp (-\frac{{\epsilon }_s}{k_{B}T})$, where ${\epsilon }_s$ is soliton activation energy given by $8S{\left(2\mathrm{JSg}{\mu }_{B}H\right)}^{\frac{1}{2}}$. When $\frac{{\epsilon }_s}{k_B}$ is chosen as $10.3\sqrt{H}$ K ($H$ in kOe), this equation explained well the relevant experimental data qualitatively. Quantitative calculation carried out by taking account of the contributions of the solitons passing on the nearest three linear chains resulted in the relaxation rate which is larger, by a factor of 5, compared with the data. The soliton energy obtained from the above best-fit relation is smaller by about 30% than the classical theoretical value estimated using the exchange parameters. In view of the validity of the soliton feature, the characteristics of soliton in CsNi${\mathrm{F}}_3$ were discussed.