Field and temperature dependence of the NMR relaxation rate in the magnetic quadrupolar liquid phase of spin-1/2 frustrated ferromagnetic chains

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.