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The ground state properties of the high spin Heisenberg chains withalternating single site anisotropy are investigated by means of the numericalexact daigonaization and DMRG method. It is found that the ferrimagnetic stateappears between the Haldane phase and period doubled N\'eel phase for theinteger spin chains. On the other hand, the transition from theTomonaga-Luttinger liquid state into the ferrimagnetic state takes place forthe half-odd-integer spin chains. In the ferrimagnetic phase, the spontaneousmagnetization varies continuously with the modulation amplitude of the singlesite anisotropy. Eventually, the magnetization is locked to fractional valuesof the saturated magnetization. These fractional values satisfy theOshikawa-Yamanaka-Affleck condition. The local spin profile is calculated toreveal the physical nature of each state. In contrast to the case offrustration induced ferrimagnetism, no incommensurate magnetic superstructureis found.Comment: 5 pages, 7 figure

Ferrimagnetic and Long Period Antiferromagnetic Phases in High Spin Heisenberg Chains with D-Modulation