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

## TL;DR

This study investigates MoOPO$_4$, a $4d^1$ insulator, revealing a $J_1$-$J_2$ Heisenberg model on a square lattice with a magnetic transition at 16 K, negligible spin-orbit effects, and collinear antiferromagnetic order.

## Contribution

It provides detailed experimental and theoretical evidence that MoOPO$_4$ hosts a pure spin-$1/2$ magnetic moment with a $J_1$-$J_2$ model, highlighting $4d$ molybdates as quantum magnet candidates.

## Key findings

- Magnetic transition at 16 K confirmed by multiple techniques.
- Mo$^{5+}$ ions have a spin-$1/2$ moment with negligible spin-orbit coupling.
- Neutron diffraction shows collinear Néel order and a spin-flop transition.

## Abstract

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 N\'eel-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.