  In Mott insulators, the strong electron-electron Coulomb repulsion prevents
metallicity and charge excitations are gapped. In dimensions greater than one,
their spins are usually ordered antiferromagnetically at low temperatures.
Geometrical frustrations can destroy this long-range order, leading to exotic
quantum spin liquid (QSL) states. However, their magnetic ground states have
been a long-standing mystery. Here we show that a QSL state in the organic Mott
insulator EtMe$_3$Sb[Pd(dmit)$_2$]$_2$ with two-dimensional triangular lattice
has Pauli-paramagnetic-like low-energy excitations, which are a hallmark of
itinerant fermions. Our torque magnetometry down to low temperatures (30 mK) up
to high fields (32 T) reveal distinct residual paramagnetic susceptibility
comparable to that in a half-filled two-dimensional metal. This demonstrates
that the system is in a magnetically gapless ground state, a critical state
with infinite magnetic correlation length. Moreover, our results are robust
against deuteration, pointing toward the emergence of an extended `quantum
critical phase', in which low-energy spin excitations behave as in paramagnetic
metals with Fermi surface, despite the frozen charge degree of freedom.
