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We carried out $^{75}$As nuclear magnetic resonance (NMR) measurements on thetrigonal CaMn$_2$As$_2$ and SrMn$_2$As$_2$ insulators exhibitingantiferromagnetic (AFM) ordered states below N\'eel temperatures $T_{\rm N}$ =62 K and 120 K, respectively. In the paramagnetic state above $T_{\rm N}$,typical quadrupolar-split $^{75}$As-NMR spectra were observed for both systems.The $^{75}$As quadrupolar frequency $\nu_{\rm Q}$ for CaMn$_2$As$_2$ decreaseswith decreasing temperature, while $\nu_{\rm Q}$ for SrMn$_2$As$_2$ increases,showing an opposite temperature dependence.In the AFM state, the relativelysharp and distinct $^{75}$As NMR lines were observed in SrMn$_2$As$_2$ and theNMR spectra were shifted to lower fields for both magnetic fields $H$ $||$ $c$axis and $H$ $||$ $ab$ plane, suggesting that the internal fields $B_{\rm int}$at the As site produced by the Mn ordered moments are nearly perpendicular tothe external magnetic field direction. No obvious distribution of $B_{\rm int}$was observed in SrMn$_2$As$_2$, which clearly indicates a commensurate AFMstate. In sharp contrast to SrMn$_2$As$_2$, broad and complex NMR spectra wereobserved in CaMn$_2$As$_2$ in the AFM state, which clearly shows a distributionof $B_{\rm int}$ at the As site, indicating an incommensurate state. From theanalysis of the characteristic shape of the observed spectra, the AFM state ofCaMn$_2$As$_2$ was determined to be a two-dimensional incommensurate statewhere Mn ordered moments are aligned in the $ab$ plane. A possible origin forthe different AFM states in the systems was discussed. Both CaMn$_2$As$_2$ andSrMn$_2$As$_2$ show very large anisotropy in the nuclear spin-latticerelaxation rate 1/$T_1$ in the paramagnetic state. 1/$T_1$ for $H$ $||$ $ab$ ismuch larger than that for $H$ $|| $c$, indicating strong anisotropic AFM spinfluctuations in both compounds.

Incommensurate and commensurate antiferromagnetic states in CaMn2As2 and SrMn2As2 revealed by 75As NMR