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The electronic and superconducting properties associated with thetopologically non-trivial bands in Weyl semimetals have recently attracted muchattention. We report the microscopic properties of the type-I Weyl semimetalTaAs measured by $^{75}$As nuclear magnetic (quadrupole) resonance under zeroand elevated magnetic fields over a wide temperature range up to 500 K. Themagnetic susceptibility measured by the Knight shift $K$ is found to benegative at low magnetic fields and have a strong field ($B$) dependence asln$B$ at $T$ = 1.56 K. Such nonlinear field-dependent magnetization can be wellaccounted for by Landau diamagnetism arising from the 3D linearly dispersedbands, and thus is a fingerprint of topological semimetals. We further studythe low-energy excitations by the spin-lattice relaxation rate 1/$T_{1}$. Atzero field and 30 K $\leq T\leq$ 250 K, 1/$T_{1}T$ shows a $T^{2}$ variationdue to Weyl nodes excitations. At $B \sim$ 13 T, $1/T_1T$ exhibits the same$T$-dependence but with a smaller value, scaling with $K^2\propto T^2$, whichindicates that the Korringa relation also holds for a Weyl semimetal. Analysisof the Korringa ratio reveals that the energy range of the linear bands isabout 250 K in TaAs.

Exotic Landau Diamagnetism and Weyl-Fermions Excitations in TaAs Revealed by $^{75}$As NMR and NQR