  S = 1/2 competing spin chain compound Cs2Cu2Mo3O12 has two dominant exchange
interactions of the nearest neighbouring ferromagnetic J1= 93 K and the second
nearest neighbouring antiferromagnetic J2= +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/mu_B.
