This article is a mess and badly written.
Basicly magnetism comes from electron spin orientation. There are two well known spin configurations.
Ferromagnetism: there is at least one electron with a spin that isn't paired with an opposite spin electron. That atom then has a north and south magnetic pole. Like iron. Arrange all the atoms pointing the same way and you have a refrigerator magnet.
antiferromagnetism: all the electrons in the atom are paired with an opposite spin election. It's complicated but basically they couple together and there isn't a magnetic pole outside the atom. Like in copper.
Altermagnetism: what this article is about. You have a crystal of atoms with an unpaired electrons. The crystal would normally be ferromanetic. However they are arranged in a regular set of pairs that cause the electron spin to cancle out. Think of a checkerboard pattern where each white square cancels a black square next to it.
The antiferromagnetism and altermagnetism both have the spins cancelled out but the mechanism is different so there are different properties. Kramers degenerate vs wavevector.
In theory this gives you an extra state spin. So a magnetic drive uses a pattern of north and south to encode information. Ie NNSN becomes 0010.
With this you have north, south but also spin left, right. So you can encode more information.
