Using the exact diagonalization technique, we study the properties of the ground state of a
spin- antiferromagnetic Heisenberg model for a zigzag polymer chain with side
radicals connected to the even sites. We consider the nearest-neighbour exchange
J
and the next-nearest-neighbour exchange
αJ along the main
chain, and J1
between the even site on the main chain and the radical site. For small
α the ground state is
ferrimagnetic. For α>αc 1, the ground state is a spiral phase, which is characterized by a peak of the static structure factor
S(q) locating at an
incommensurate value qmax. For α>αc 2, the ground state is antiferromagnetic. With increasing
J1,
αc 1 decreases while
αc 2 has a maximum
at about J1 = 0.5. For
very small J1
and α = 0.5, the
spin configuration on the main chain is a product of nearest-neighbour singlets. In the antiferromagnetic
phase, if J1
is large enough the even site and the radical site form a singlet with exchange-decoupling
from the odd site while the odd sites approximately form an antiferromagnetic chain.