The low-temperature structure of A1C60 (A=K, Rb) is an ordered array of polymerized C60 chains, with magnetic properties that suggest a non-metallic ground state. We study the paramagnetic state of this phase using first-principles electronic-structure methods, and examine the magnetic fluctuations around this state using a model Hamiltonian. The electronic and magnetic properties of even this polymerized phase remain strongly three dimensional, and the magnetic fluctuations favor an unusual

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... ee-dimensional antiferromagnetically ordered structure with a semi-metallic electronic spectrum.