Orbital altermagnetism on the kagome lattice and possible application to $A$V$_3$Sb$_5$

Altermagnets, which encompass a broad landscape of materials, are compensated collinear magnetic phases in which the antiparallel magnetic moments are related by a crystalline rotation. Here, we argue that collinear altermagnetic-like states can also be realized in lattices with an odd number of sublattices, provided that the electronic interactions promote non-uniform magnetic moments. We demonstrate this idea for a kagome metal whose band filling places the Fermi level close to the van Hove singularity. Combining phenomenological and microscopic modeling, we show that the intertwined charge density-wave and loop-current instabilities of this model lead to a wide parameter range in which orbital ferromagnetic, antiferromagnetic, and altermagnetic phases emerge inside the charge-ordered state. In the presence of spin-orbit coupling, their electronic structures display the usual spin-split fingerprints associated with the three types of collinear magnetic order. We discuss the possible realization of orbital altermagnetic phases in the $A$V$_3$Sb$_5$ family of kagome metals.