(J_1\)-\(J_2\) square lattice antiferromagnetism in the orbitally quenched insulator MoOPO\(_4\)

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-heat measurements show a magnetic transition at 16 K which is also confirmed by magnetic susceptibility, ESR, and neutron diffraction measurements. Magnetic entropy deduced from the specific heat corresponds to a two-level degree of freedom per Mo\(^{5+}\) ion, and the effective moment from the susceptibility corresponds to the spin-only value. Using {\it ab initio} quantum chemistry calculations we demonstrate that the Mo\(^{5+}\) ion hosts a purely spin-\(1/2\) magnetic moment, indicating negligible effects of spin-orbit interaction. The quenched orbital moments originate from the large displacement of Mo ions inside the MoO\(_6\) octahedra along the apical direction. The ground state is shown by neutron diffraction to support a collinear Néel-type magnetic order, and a spin-flop transition is observed around an applied magnetic field of 3.5 T. The magnetic phase diagram is reproduced by a mean-field calculation assuming a small easy-axis anisotropy in the exchange interactions. Our results suggest \(4d\) molybdates as an alternative playground to search for model quantum magnets.