Effect of interchain coupling on ultrasonic attenuation in nearly one-dimensional antiferromagnets

A quantitative theory is presented for the frequency dependence of the ultrasonic attenuation in the nearly one-dimensional antiferromagnet which has small, but not negligible, interchain couplings. At temperatures well above the Neel temperature T_N, the ultrasonic attenuation alpha is described by a scaling function, alpha = omega ³G( omega t₀), where t₀ indicates the characteristic time after which the three-dimensional diffusion takes over. The theory is compared with the frequency dependence of the ultrasonic attenuation in CsNiCl₃ (a one-dimensional Heisenberg antiferromagnet) and the effect of the interchain coupling on the one-dimensional spin dynamics is discussed.