This is done by introducing a quntization axis for spin, SAXIS. By default it is aligned along the z-direction. In every step, the program splits the wave-functions in two up and down spinors based on this quantization axis, and then calculates the non-collinear spin-orbit coupling term H_soc=L.S with L and S being the orbital angular operator and pauli spin operators, respectively. This energy term is then added to the Hamiltonian and the whole Hamiltonian is self-consistentatly minimized until all convergence criteria are satisfied. Finally, using the converged wave function psi, the magnetization is computed as m_i= where m_i is be m_x, m_y or m_z.

Mohammad Saeed Bahramy Thanks for your reply. I agree. What I am curious is about how VASP change the spin configuration at each electronic step. At each step, from initial magnetization density to Hamitonian, wave function and generate new magnetization density. Just like at each step, the input charge density and output charge density are different. Probably, the in-out magnetizaiton density are also different at each step, where the spin direction changes. It could be just a natural result of selfconsistent calculations. I thought there has some thing like spin-dynamic in VASP. I think I am wrong about this. Thanks.

Of course, the magnetization changes at each step, but it's because the wave function varies at each step. Since this is a DFT approach, the input and output densities are mixed to create a new Kohn-Sham wave function for the next step. The magnetization at each step is computed using this wave function, as described here: https://www.vasp.at/wiki/index.php/LSORBIT