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

First-principles Study of Spin-wave Excitations of 3$d$ Transition Metals with Linear Combination of Pseudo-atomic Orbitals