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The magnetocrystalline anisotropy of 5f transition-metal atoms (actinides) is investigated. A simple model Hamiltonian reproduces the observed huge low-temperature anisotropy of cubic actinide compounds such as US and predicts the temperature dependence of the anisotropy. The dominance of the spin–orbit and crystal–field interactions means that the magnitude of the anisotropy is limited only by interatomic exchange. One consequence is that cubic and uniaxial 4f magnets have similar magnitudes of the anisotropy and similar temperatures dependencies.