Is altermagnetism in vanadium oxychalcogenides a lost cause?

Vanadium-based oxychalcogenide compounds with the inverse Lieb-lattice (ILL) structural pattern have recently been proposed as candidate altermagnets (AM). However, early studies postulated ferromagnetic interlayer coupling, a critical requirement for preserving the bulk AM state. Here we present a systematic survey of the complete AV2Q2O family (A = K, Rb, Cs; Q = S, Se, Te) in terms of their magnetic ordering and interlayer coupling. While intralayer exchange interaction favors AM ordering in a single ILL layer across the entire family, the relatively weak interlayer coupling in most cases favors Kramers-degenerate antiferromagnetic order with a doubled magnetic unit cell. This means that most stoichiometric bulk materials, including the previously proposed candidate KV2Se2O, are not altermagnetic, with CsV2Te2O being the only exception. Using hole doping to simulate alkali vacancies, we show that realistic deviations from stoichiometry do not change the magnetic ground state in these compounds.