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We report $^{77}$Se-nuclear magnetic resonance (NMR) results down tosufficiently low temperatures under magnetic fields parallel to both the$ab$-plane and the c-axis in a paramagnetic/superconducting (PM/SC) phase ofK$_x$Fe$_{2-y}$Se$_2$. The observation of anisotropy in the orbital part of theKnight shift results in the anisotropy of its spin part increasing onapproaching the transition temperature. The anisotropy of the Korringa relationsuggests the presence of the weak spin fluctuations with a finite wave vector$\bm{q}$, which induce the magnetic fluctuations along the ab-plane at the Sesite. Such fluctuations do not correspond to the stripe $(\pi,0)$ correlationof the Fe moment observed in many Fe-based superconductors, and are notcontradictory to weak $(\pi,\pi)$ correlations. The nuclear spin-latticerelaxation rate $1/T_1$ shows a field-independent $T_1T \sim const.$ behaviorat low temperatures for $H \parallel ab$, which is attributed to the nonzerodensity of states at the Fermi level and can be explained by the sign-changingorder parameter even for nodeless gaps. The temperature dependence of $1/T_1$is reproduced well by nodeless models with two isotropic gaps or a singleanisotropic gap. The obtained gap magnitude in the isotropic two-gap model iscomparable to those obtained in the angle-resolved photoemission spectroscopyexperiments.

Weak Spin Fluctuation with Finite Wave Vector and Superconducting Gap Symmetry in KxFe2-ySe2: 77Se Nuclear Magnetic Resonance