  We investigate magnetism and quantum phase transitions in a one-dimensional
system of integrable spin-1 bosons with strongly repulsive density-density
interaction and antiferromagnetic spin exchange interaction via the
thermodynamic Bethe ansatz method. At zero temperature, the system exhibits
three quantum phases: (i) a singlet phase of boson pairs when the external
magnetic field $H$ is less than the lower critical field $H_{c1}$; (ii) a
ferromagnetic phase of atoms in the hyperfine state $|F=1, m_{F}=1>$ when the
external magnetic field exceeds the upper critical field $H_{c2}$; and (iii) a
mixed phase of singlet pairs and unpaired atoms in the intermediate region
$H_{c1}<H<H_{c2}$. At finite temperatures, the spin fluctuations affect the
thermodynamics of the model through coupling the spin bound states to the
dressed energy for the unpaired $m_{F}=1$ bosons. However, such spin dynamics
is suppressed by a sufficiently strong external field at low temperatures. Thus
the singlet pairs and unpaired bosons may form a two-component Luttinger liquid
in the strong coupling regime.
