  The chemical separation of Li+ ions induced by a magnetic field during the
hierarchical structure formation can reduce initial Li abundances in cosmic
structures. It is shown that cosmological reionization of neutral Li atoms
quickly completes as soon as the first star is formed. Since almost all Li is
singly ionized during the main course of structure formation, it can
efficiently separate from gravitationally collapsing neutral gas. The
separation is more efficient in smaller structures which formed earlier. In the
framework of the hierarchical structure formation, extremely metal-poor stars
can have smaller Li abundances because of their earlier formations. It is found
that the chemical separation by a magnetic field thus provides a reason that Li
abundances in extremely metal-poor stars are lower than the Spite plateau and
have a large dispersion as well as an explanation of the Spite plateau itself.
In addition, the chemical separation scenario can explain Li abundances in NGC
6397 which are higher than the Spite plateau. Thus, Li abundances in metal-poor
stars possibly keep information on the primordial magnetic field and the
structure formation history.
