$J_1-J_2$ Square-Lattice Heisenberg Antiferromagnets with 4$d^1$ spins: AMoOPO$_4$Cl (A = K, Rb)
Hajime Ishikawa, Nanako Nakamura, Makoto Yoshida, Masashi Takigawa,, Peter Babkevich, Navid Qureshi, Henrik M. R{\o}nnow, Takeshi Yajima, Zenji, Hiroi

TL;DR
This study investigates the magnetic properties of AMoOPO$_4$Cl (A = K, Rb), revealing their behavior as model $J_1-J_2$ square-lattice antiferromagnets with unique interpenetrating lattice structures and columnar order.
Contribution
It provides the first detailed experimental characterization of 4$d^1$ square-lattice antiferromagnets with interpenetrating $J_2$ lattices and identifies their unconventional magnetic order.
Findings
Both compounds exhibit magnetic transitions around 6-8 K.
They display columnar antiferromagnetic order stabilized by dominant $J_2$ interactions.
The compounds realize two interpenetrating $J_2$ square lattices weakly coupled by $J_1$.
Abstract
Magnetic properties of AMoOPOCl (A = K, Rb) with Mo ions in the 4 electronic configuration are investigated by magnetization, heat capacity and NMR measurements on single crystals, combined with powder neutron diffraction experiments. The magnetization measurements reveal that they are good model compounds for the spin-1/2 square lattice magnet with the first and second nearest-neighbor interactions. Magnetic transitions are observed at around 6 and 8 K in the K and Rb compounds, respectively. In contrast to the normal N\'eel-type antiferromagnetic order, the NMR and neutron diffraction experiments find a columnar antiferromagnetic order for each compound, which is stabilized by a dominant antiferromagnetic . Both compounds realize the unusual case of two interpenetrating square lattices weakly coupled to each other by .
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