Field and temperature dependence of NMR relaxation rate in the magnetic quadrupolar liquid phase of spin-12frustrated ferromagnetic chains

Abstract

It is generally difficult experimentally to 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 [M. Sato, T. Momoi, and A. Furusaki, Phys. Rev. B 79, 060406(R) (2009)]. In this paper, we evaluate accurately the field and temperature dependence of $1/{T}_{1}$ in spin-$\frac{1}{2}$ frustrated ${J}_{1}$-${J}_{2}$ 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 nonmonotonic behavior in spin nematic TL liquid, in contrast with the standard TL liquid in the spin-$\frac{1}{2}$ Heisenberg chain. The relevance of our results to quasi-one-dimensional edge-sharing cuprate magnets, such as ${\mathrm{LiCuVO}}_{4}$, is discussed.