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We report magnetic and thermodynamic properties of a $4d^1$ (Mo$^{5+}$)magnetic insulator MoOPO$_4$ single crystal, which realizes a $J_1$-$J_2$Heisenberg spin-$1/2$ model on a stacked square lattice. The specific-heatmeasurements show a magnetic transition at 16 K which is also confirmed bymagnetic susceptibility, ESR, and neutron diffraction measurements. Magneticentropy deduced from the specific heat corresponds to a two-level degree offreedom per Mo$^{5+}$ ion, and the effective moment from the susceptibilitycorresponds to the spin-only value. Using {\it ab initio} quantum chemistrycalculations we demonstrate that the Mo$^{5+}$ ion hosts a purely spin-$1/2$magnetic moment, indicating negligible effects of spin-orbit interaction. Thequenched orbital moments originate from the large displacement of Mo ionsinside the MoO$_6$ octahedra along the apical direction. The ground state isshown by neutron diffraction to support a collinear N\'eel-type magnetic order,and a spin-flop transition is observed around an applied magnetic field of 3.5T. The magnetic phase diagram is reproduced by a mean-field calculationassuming a small easy-axis anisotropy in the exchange interactions. Our resultssuggest $4d$ molybdates as an alternative playground to search for modelquantum magnets.

$J_1$-$J_2$ square lattice antiferromagnetism in the orbitally quenched insulator MoOPO$_4$