  It is generally difficult to experimentally distinguish magnetic multipolar
orders in spin systems. Recently, it was proposed that the temperature
dependence of the nuclear magnetic resonance relaxation rate 1/T_1 can involve
an indirect, but clear signature of the field-induced spin nematic or
multipolar Tomonaga-Luttinger (TL) liquid phase [Phys. Rev. B79, 060406(R)
(2009)]. In this paper, we evaluate accurately the field and temperature
dependence of 1/T_1 in spin-1/2 frustrated J1-J2 chains combining
field-theoretical techniques with numerical data. Our results demonstrate that
isotherms of 1/T_1 as a function of magnetic field also exhibit distinctive
non-monotonic behavior in spin nematic TL liquid, in contrast with the standard
TL liquid in the spin-1/2 Heisenberg chain. The relevance of our results to
quasi one-dimensional edge-sharing cuprate magnets, such as LiCuVO4, is
discussed.
