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The ground-state phase diagram of $S=2$ antiferromagnetic Heisenberg chainswith coexisting uniform and alternating single-site anisotropies isinvestigated by the numerical exact diagonalization and density matrixrenormalization group methods. We find the Haldane, large-$D$, N\'eel,period-doubled N\'eel, gapless spin fluid, quantized and partial ferrimagneticphases. The Haldane phase is limited to the close neighborhood of the isotropicpoint. Within numerical accuracy, the transition from the gapless spin-fluidphase to the period-doubled N\'eel phase is a direct transition. Nevertheless,the presence of a narrow spin-gap phase between these two phases is suggestedon the basis of the low-energy effective theory. The ferrimagnetic ground stateis present in a wide parameter range. This suggests the realization ofmagnetized single-chain magnets with a uniform spin magnitude by controllingthe environment of each magnetic ion without introducing ferromagneticinteractions.

Ground-State Phase Diagram of S=2 Heisenberg Chains with Alternating Single-Site Anisotropy