Filled skutterudite compound EuFe$_4$As$_{12}$ shows the highest magnetic ordering temperature of $T_{rm C}$ = 154 K among Eu-based skutterudite compounds, but its magnetic ground state has not been determined yet. Here, we performed $^{153}$Eu nuclear magnetic resonance (NMR) and $^{75}$As nuclear quadrupole resonance (NQR) measurements on EuFe$_4$As$_{12}$ to reveal its magnetic ground state as well as the physical properties from a microscopic point of view. From the temperature and magnetic field dependence of $^{153}$Eu NMR spectrum in the magnetically ordered state, we found that the Eu ions are in Eu$^{2+}$ state with a nearly 7 $mu_{rm B}$ corresponding to $S$ = 7/2 spins. Combined with the magnetization measurements which show the reduced saturation moments of 4.5 $mu_{rm B}$/f.u., we determined the ground magnetic structure in EuFe$_4$As$_{12}$ to be ferrimagnetic where the Eu$^{2+}$ 4$f$ and the Fe 3$d$ ordered moments are ferromagnetically aligned in each sublattice but the moments between the sublattices are antiferromagnetically aligned. We also found the local distortion at the Eu site from the cubic symmetry in the magnetically ordered state. The relationship between the rattling motion of Eu atoms and the local symmetry of the Eu ions is discussed. From the $^{75}$As NQR nuclear spin-lattice relaxation time measurements as well as $^{153}$Eu NMR measurements, we found that the 4$f$ electrons of the Eu ions are well described by the local moment picture in both the magnetic and paramagnetic metallic states.
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