In DFT calculations using vasp, symmetry analysis are performed to determine space group symmetries at first, if symmetrization is turned on, such as ISYM = 2. When magmoms are set in INCAR, symmetries broken by local magnetic moments are removed and magnetic symmetries are obtained. To test whether a symmetry $g$ is compatible with local magnetic moments, given a site $r_i$, an equivalent site, $r_j = gr_i+R$, related by the symmetry is found at first. $R$ is a Bravais lattice. After applying the symmetry to the magnetic moment on the site $m_i$, if resulting magnetic moments is equal to the magnetic moment on the equivalent site,$m_j=gm_i$, the symmetry is preserved. The equality must be hold within some tolerance, that is $$ |m_j-gm_i|<\delta. $$ My question is what is value of the tolerance give a value of SYMPREC?
Without any testing, I think the value of
SYMPREC is also used for the tolerance $\delta$ in your expression.
The subroutine related to the magnetic sites is called
MAGSYM that can be found in
symlib.F. In the subroutine, the magnetic moment of sites are compared with that of their corresponding sites after symmetry operation and the tolerance is set to a variable called
TINY with a default value of 1E-5. The default value of
TINY can be found in module
sim_prec at the beginning of
TINY variable is also read in by
READER subroutine inside
SYMPREC tag in your
So, I would suppose that changing the value of
SYMPREC also changes the magnetic tolerance.