  The new Kondo material YbIr$_3$Si$_7$, similar to other Kondo insulators, has
been reported to exhibit charge-neutral fermionic excitations through
measurements of specific heat and thermal conductivity at low temperatures. We
performed $^{29}$Si-NMR on YbIr$_3$Si$_7$ to investigate the magnetic response
of charge-neutral fermions from a microscopic perspective. In low magnetic
fields parallel to the $c$ axis, a single NMR peak in the paramagnetic state
splits into three peaks below $T_{\rm N}$. In contrast, only a slight shift of
the single NMR peak was observed in high magnetic fields. This spectral change
as a function of the $c$-axis magnetic field is interpreted as spin-flop
transition, at which the magnetic moments oriented along the $c$ axis (AF-I
phase) are rotated to the $ab$ plane with ferromagnetic component along the
$c$-axis (AF-II phase). In the vicinity of the spin-flop magnetic field $H_{\rm
M}$, nuclear spin-lattice relaxation rate $1/T_1$ was found to be proportional
to temperature at low temperatures, indicating the existence of charge-neutral
fermions. Furthermore, a peak of $1/T_1$ vs. the $c$-axis magnetic field
suggests that the charge-neutral fermions in YbIr$_3$Si$_7$ are closely related
to its magnetic properties. Our findings shed light on the origin of
charge-neutral fermions in insulators.
