Chemical separation of primordial Li$^+$ during structure formation
  caused by nanogauss magnetic field
  During the structure formation, charged and neutral chemical species may have
separated from each other at the gravitational contraction in primordial
magnetic field (PMF). A gradient in the PMF in a direction perpendicular to the
field direction leads to the Lorentz force on the charged species. Resultantly,
an ambipolar diffusion occurs, and charged species can move differently from
neutral species, which collapses gravitationally during the structure
formation. We assume a gravitational contraction of neutral matter in a
spherically symmetric structure, and calculate fluid motions of charged and
neutral species. It is shown that the charged fluid, i.e., proton, electron and
$^7$Li$^+$, can significantly decouple from the neutral fluid depending on the
field amplitude. The charged species can, therefore, escape from the
gravitational collapse. We take the structure mass, the epoch of the
gravitational collapse, and the comoving Lorenz force as parameters. We then
identify a parameter region for an effective chemical separation. This type of
chemical separation can reduce the abundance ratio of Li/H in early structures
because of inefficient contraction of $^7$Li$^+$ ion. Therefore, it may explain
Li abundances of Galactic metal-poor stars which are smaller than the
prediction in standard big bang nucleosynthesis model. Amplitudes of the PMFs
are controlled by a magneto-hydrodynamic turbulence. The upper limit on the
field amplitude derived from the turbulence effect is close to the value
required for the chemical separation.
