We study a class of one-dimensional chains whose topology leads to flatbands in the electronic spectrum. Using the Hubbard model, we find that these materials should exhibit ferrimagnetic ordering for a half-filled band, in agreement with a theorem by Lieb. Away from half filling the system displays a very rich magnetic phase diagram. Possible experimental realizations are suggested.

• Received 11 January 1994

DOI:https://doi.org/10.1103/PhysRevLett.74.1851