  We study $k$-radially symmetric solutions corresponding to topological
defects of charge $\frac{k}{2}$ for integer $k \neq 0$ in the Landau-de Gennes
model describing liquid crystals in two-dimensional domains. We show that the
solutions whose radial profiles satisfy a natural sign invariance are stable
when $|k| = 1$ (unlike the case $|k|>1$ which we treated before). The proof
crucially uses the monotonicity of the suitable components, obtained by making
use of the cooperative character of the system. A uniqueness result for the
radial profiles is also established.
