We have performed electron spin resonance (ESR) and de magnetization measur
ements on single crystals of La2(1-x)Sr1+2xMn2O7 up to 800 K with special e
mphasis on the x=0.4 composition. The ESR linewidth shows behavior similar
to that observed in the three-dimensional perovskites and above similar to
500 K can be described by a universal expression DeltaH(pp)(T)=[C/T chi (T)
]DeltaH(pp)(infinity). The linewidth and the resonance field become anisotr
opic below similar to 500 K. The anisotropy in the resonance field is propo
rtional to the magnetization M, and we concluded that it is intrinsic to th
e system. We show that demagnetization effects can explain only part of the
anisotropy. The remainder arises from short-range uniaxial terms in the Ha
miltonian that are associated with the crystal field and Dzialozhinsky-Mori
ya interactions. The anisotropy in the linewidth is attributed to the easy-
plane ferromagnetic ordering, which also arises from the short-range anisot
ropy.