  Using x-ray and neutron scattering, we have studied the structural and
magnetic properties of the single-layer manganite La{1-x}Sr{1+x}MnO4 (0 < x <
0.7). Single crystals were grown by the traveling-solvent floating-zone method
at 18 La/Sr concentrations. The low-temperature phase diagram can be understood
by considering the strong coupling of the magnetic and orbital degrees of
freedom, and it can be divided into three distinct regions: low (x < 0.12),
intermediate (0.12< x < 0.45), and high (x > 0.45) doping. LaSrMnO_4 (x=0) is
an antiferromagnetic Mott insulator,and its spin-wave spectrum is
well-described by linear spin-wave theory for the spin-2 square-lattice
Heisenberg Hamiltonian with Ising anisotropy. Upon doping, as the e_g electron
concentration (1-x) decreases, both the two-dimensional antiferromagnetic spin
correlations in the paramagnetic phase and the low-temperature ordered moment
decrease due to an increase of frustrating interactions, and Neel order
disappears above xc = 0.115(10). In the intermediate region, there exists
neither long-range magnetic nor superstructural order. Short-range-correlated
structural "nanopatches" begin to form above x ~ 0.25. At high doping (x >
0.45), the ground state of La{1-x}Sr{1+x}MnO4 exhibits long-range
superstructural order and a complex (CE-type) antiferromagnetic order which
differs from that at low doping. The superstructural order is thought to arise
from charge and orbital ordering on the Mn sites. For x > 0.50, the
superstructural order becomes incommensurate with the lattice, with a
modulation wavevector that depends linearly on the e_g electron concentration.
On the other hand, the magnetic order remains commensurate, but loses its
long-range coherence upon doping beyond x = 0.50.
