We investigate the static and dynamic spin susceptibility of the 111 type Fe-based superconductor LiFeP with Tc ~ 5 K through the measurement of Knight shift 31K and the spin-lattice relaxation rate 1/T1 at 31P site by nuclear magnetic resonance. The constant 31K, small magnitudes of 1/T1T, along with the resistivity rho ~ T^2 all point to the weak spin correlations in LiFeP. 1/T1T display small enhancement toward Tc, indicating that the superconductivity is intimately correlated with the antiferromagnetic spin fluctuations.
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