  We have employed the generalized Bloch theorem to evaluate the spin stiffness
constants of 3$d$ transition metals (bcc-Fe, fcc-Co, and fcc-Ni) within the
linear combination of pseudo-atomic orbitals (LCPAO). The spin stiffness
constants were obtained by fitting the spin-wave energy curve, which relates to
the total energy difference and the spiral vectors. In order to convince the
reliable spin stiffness constants, we also provided the convergences of spin
stiffness constants in terms of the cutoff radius and the number of orbitals.
After observing the specific cutoff radius and the basis orbital, at which the
spin stiffness constant converges, we used those two parameters to compute the
Curie temperature by using the mean field approximation and the random phase
approximation. For the latter approximation, we applied the so-called Debye
approximation, which is intended to reduce very significantly many required
wavevectors to evaluate the Curie temperature. We claimed that our results are
in good agreement with both other calculations and experiments.
