¹³³Cs-NMR study on aligned powder of competing spin chain compound Cs₂Cu₂Mo₃O₁₂

S = 1/2 competing spin chain compound Cs₂Cu₂Mo₃O₁₂ has two dominant exchange interactions of the nearest neighbouring ferromagnetic J ₁ = 93 K and the second nearest neighbouring antiferromagnetic J ₂ = +33 K, and is expected to show the nematic Tomonaga-Luttinger liquid (TLL) state under high magnetic field region. The recent theoretical study by Sato et al. has shown that in the nematic TLL state, the spin fluctuations are expected to be highly anisotropic, that is, its transverse component is suppressed. Our previous NMR study on the present system showed that the dominant contribution to nuclear spin relaxation comes from the longitudinal component. In order to conclude that the transverse component of spin fluctuations is suppressed, the knowledge of hyperfine coupling is indispensable. This article is solely devoted to investigate the hyperfine coupling of ¹³³Cs-NMR site to prove that the anisotropic part of hyperfine coupling, which connects the nuclear spin relaxation with the transverse spin fluctuations is considerably large to be A _an = +770 Oe/μ_B. (paper)