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

## TL;DR

This study uses first-principles calculations with the generalized Bloch theorem and LCPAO to evaluate spin-wave excitations and Curie temperatures of 3d transition metals, showing good agreement with experimental data.

## Contribution

It introduces a reliable method to compute spin stiffness and Curie temperatures of transition metals using LCPAO and the generalized Bloch theorem, with convergence analysis.

## Key findings

- Spin stiffness constants converge with specific cutoff radius and basis orbitals.
- Calculated Curie temperatures agree well with experimental data.
- The Debye approximation effectively reduces computational effort.

## Abstract

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.