  A mixed Heisenberg spin chain with frustrated side chains is investigated by
numerical and perturbational calculations. A frustration-induced quantum
partially polarized ferrimagnetic phase and a nonmagnetic spin quadrupolar
phase are found adjacent to the conventional Lieb-Mattis type ferrimagnetic
phase or the nonmagnetic singlet cluster solid phases. The partially polarized
ferrimagnetic phase has an incommensurate spin structure. Similar structures
are commonly found in other frustration-induced partially polarized
ferrimagnetic phases. Numerical results also suggest a series of almost
critical nonmagnetic ground states in a highly frustrated regime if the side
chain spins weakly couple to the main chain.
