Nematic Spin Liquid State in the $S=frac{5}{2}$ Heisenberg Kagome Antiferromagnet Li$_9$Fe$_3$(P$_2$O$_7$)$_3$(PO$_4$)$_2$

We investigate the low temperature magnetic properties of a $S=frac{5}{2}$ Heisenberg kagome antiferromagnet, the layered monodiphosphate Li$_9$Fe$_3$(P$_2$O$_7$)$_3$(PO$_4$)$_2$, using magnetization measurements and $^{31}$P nuclear magnetic resonance. An antiferromagnetic-type order sets in at $T_{rm N}=1.3$ K and a characteristic magnetization plateau is observed at 1/3 of the saturation magnetization below $T^* sim 5$ K. A moderate $^{31}$P NMR line broadening reveals the development of anisotropic short-range correlations within the plateau phase concomitantly with a gapless spin-lattice relaxation time $T_1 sim k_B T / hbar S$, which both point to the presence of a semiclassical nematic spin liquid state predicted for the Heisenberg kagome antiferromagnetic model.