  Previous heat-capacity measurements of our group had shown the possible
existence of an anomalous quantum phase containing the zero-point vacancies
(ZPVs) in 2D $^{3}$He. The system is monolayer $^{3}$He adsorbed on graphite
preplated with monolayer $^{4}$He at densities ($\rho$) just below the 4/7
commensurate phase ($0.8\leq \rho /\rho_{4/7}\leq 1$). We carried out
pulsed-NMR measurements in order to examine the microscopic and dynamical
nature of this phase. The measured decay of spin echo signals shows the
non-exponential behaviour. The decay curve can be fitted with the double
exponential function, but the relative intensity of the component with a longer
time constant is small (5%) and does not depend on density and temperature,
which contradicts the macroscopic fluid and 4/7 phase coexistence model. This
slowdown is likely due to the mosaic angle spread of Grafoil substrate and the
anisotropic spin-spin relaxation time $T_{2}$ in 2D systems with respect to the
magnetic field direction. The inverse $T_2$ value deduced from the major echo
signal with a shorter time constant, which obeys the single exponential
function, decreases linearly with decreasing density from $n=1$, supporting the
ZPV model.
