  The ground-state phases of mixed diamond chains with ($S, \tau^{(1)},
\tau^{(2)})=(1/2,1/2,1)$, where $S$ is the magnitude of vertex spins, and
$\tau^{(1)}$ and $\tau^{(2)}$ are those of apical spins, are investigated. The
apical spins $\tau^{(1)}$ and $\tau^{(2)}$ are connected with each other by an
exchange coupling $\lambda$. Other exchange couplings are set equal to unity.
This model has an infinite number of local conservation laws. For large
$\lambda$, the ground state is equivalent to that of the uniform spin $1/2$
chain. Hence, the ground state is a gapless spin liquid. For $\lambda \leq 0$,
the ground state is a Lieb-Mattis ferrimagnetic phase with spontaneous
magnetization $m_{\rm sp}=1$ per unit cell. For intermediate $\lambda$, we find
a series of ferrimagnetic phases with $m_{\rm sp}=1/p$ where $p$ takes positive
integer values. The phases with $p \geq 2$ are accompanied by the spontaneous
breakdown of the $p$-fold translational symmetry. It is suggested that the
phase with arbitrarily large $p$, namely infinitesimal spontaneous
magnetization, is allowed as $\lambda$ approaches the transition point to the
gapless spin liquid phase.
