We report 7Li NMR studies of single crystals of triangular-lattice Heisenberg antiferromagnet Li7RuO6. Slow critical divergence with a wide critical region of |T/TN - 1|< 7 was observed in 7Li nuclear spin-lattice relaxation rate. The slowing down of staggered spin fluctuations was analyzed in a renormalized classical region of a two-dimensional triangular-lattice non-linear sigma model. A spin stiffness constant was found to reduce to about 20 % from the value in a spin-wave approximation. The effect of spin frustration, e.g., Z2 vortex excitations on the critical phenomena is suggested.
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