I went to the Wikipedia entry for altermagnetism and read the first paragraph. I didn't make it very far before I was reading it in Hubert Farnsworth's voice.

In condensed matter physics, altermagnetism is a type of persistent magnetic state in ideal crystals.[1][2][3][4][5] Altermagnetic structures are collinear and crystal-symmetry compensated, resulting in zero net magnetisation.[1][5][6][7] Unlike in an PT-symmetric collinear antiferromagnet, the electronic bands in PT-non-symmetric antiferromagnets (altermagnets) are not Kramers degenerate, but instead depend on the wavevector in a spin-dependent way due to the intrinsic crystal symmetry connecting different magnetic sublattices.[8][9][1][10] Related to this feature, key experimental observations were published in 2024.[11] It has been speculated that altermagnetism may have applications in the field of spintronics

Until now, there were two known magnetic phases: ferromagnetic and antiferromagnetic.
The best analogy I've seen, though significantly over-simplified, is a great way to visualize the basics magnetic phases. Think of any given material as being a highway, and the electromagnetic energy within that material as two types of cars: blue cars and orange cars. It may be useful to think of the highway as a "North/South" highway, as in magnetic poles, but again, that is a significant oversimplification, and only meant as an illustration, not an explanation of what is actually happening within the material at a quantum level.

A ferromagnetic "highway" is basically a one-way road; the conditions of the road only allow blue cars to move in a single direction, no other color or direction of travel is allowed. This phase attracts only blue cars moving in one direction, and repels orange cars, as well as blue cars moving in the opposing direction. This type of "highway" is what creates what we commonly know as magnetism.

An antiferromagnetic "highway" allows both colors to travel equally in both directions; this phase of motion has an equal amount of force in both directions regardless of a car's direction or color, and so this type of "highway" is what we would find in non-magnetic materials.

The new phase of magnetism is called altermagnetism. In a conventional antiferromagnet, both kinds of cars generally experience the same road conditions. In an altermagnet, the roads effectively favor different kinds of cars depending on which direction they travel. Travel along one direction, and the blue cars might be favored. Travel along another, and the orange cars might be favored. Importantly, neither kind of car dominates the entire road.

That's the unusual feature of altermagnetism: the car's behavior depends on direction, even though the material has no net magnetization.