  To gain insights into the fundamental and characteristic features of the
surface of doped manganites, we constructed a general magnetic phase diagram of
La$_{1-x}$Sr$_{x}$MnO$_3$ (001) surfaces in the plane spanned by $x$ and the
bulk tetragonal distortion $c/a$, from the first-principles calculations. We
found that the surfaces are quite different from the bulk in the sense that
both the (La, Sr)O and MnO$_2$ terminated surfaces show strong tendency toward
antiferromagnetism (A-type and C-type respectively). The basic physics
governing the phase diagram can be understood in terms of the surface orbital
polarizations. It is also found that the strong surface segregation of Sr atoms
is mostly caused by the electrostatic interaction and will further enhance the
tendency to surface antiferromagnetism.
