Proton-spin—lattice relaxation in the antiferromagnetic state of CsMn<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Cl</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>·2<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">H</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>O

The spin-lattice relaxation times of protons in the nearly one-dimensional Heisenberg system CsMn${\mathrm{Cl}}_{3}$\ifmmode\cdot\else\textperiodcentered\fi{}2${\mathrm{H}}_{2}$O were measured between 1.1 and 3.9 K in the antiferromagnetic state. From the comparison of the ratio of the relaxation rates of two nonequivalent protons with the calculated ratio, it was concluded that the two-magnon process dominates at low temperatures and the exchange-enhanced three-magnon process at high temperatures. A quantitative calculation of these contributions, without the restriction of a small-$k$ approximation, based on the values for the exchange constants available in the literature, gives a fair agreement with the experimental results. The relaxation time is very sensitive to the interchain coupling and a fitting procedure to our experimental data yields an interchain coupling of (5\ifmmode\pm\else\textpm\fi{}1)% of the intrachain coupling.

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