Inelastic neutron scattering (INS) from polycrystalline antiferromagnetic LaMnAsO, LaMnSbO, and BaMnAsF are analyzed using a $J_1\text{−}{J}_2\text{−}{J}_c$ Heisenberg model in the framework of the linear spin-wave theory. All three systems show clear evidence that the nearest- and next-nearest-neighbor interactions within the Mn square lattice layer ($J_1$ and $J_2$) are both antiferromagnetic (AFM). However, for all compounds studied the competing interactions have a ratio of $2J_2/J_1<1$, which favors the square lattice checkerboard AFM structure over the stripe AFM structure. The interplane coupling $J_c$ in all three systems is on the order of $\sim 3\times {10}^{-4}{J}_1$, rendering the magnetic properties of these systems with quasi-two-dimensional character. The substitution of Sb for As significantly lowers the in-plane exchange coupling, which is also reflected in the decrease of the Néel temperature, $T_{\mathrm{N}}$. Although BaMnAsF shares the same MnAs sheets as LaMnAsO, their $J_1$ and $J_2$ values are substantially different. Using density functional theory, we calculate exchange parameters $J_{ij}$ to rationalize the differences among these systems.

• Received 7 January 2020
• Revised 5 March 2020
• Accepted 6 March 2020

DOI:https://doi.org/10.1103/PhysRevB.101.155119