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S = 1/2 competing spin chain compound Cs2Cu2Mo3O12 has two dominant exchangeinteractions of the nearest neighbouring ferromagnetic J1= 93 K and the secondnearest neighbouring antiferromagnetic J2= +33 K, and is expected to show thenematic Tomonaga-Luttinger liquid (TLL) state under high magnetic field region.The recent theoretical study by Sato et al. has shown that in the nematic TLLstate, the spin fluctuations are expected to be highly anisotropic, that is,its transverse component is suppressed. Our previous NMR study on the presentsystem showed that the dominant contribution to nuclear spin relaxation comesfrom the longitudinal component. In order to conclude that the transversecomponent of spin fluctuations is suppressed, the knowledge of hyperfinecoupling is indispensable. This article is solely devoted to investigate thehyperfine coupling of 133Cs-NMR site to prove that the anisotropic part ofhyperfine coupling, which connects the nuclear spin relaxation with thetransverse spin fluctuations is considerably large to be A_an=+770 Oe/mu_B.

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