Electron spin resonance data of Cu2+ ions in La14-xCaxCu24O41 single crysta
ls (x = 9, 11, 12) reveal a very large width of the resonance line in the p
aramagnetic state. This signals an unusually strong anisotropy of similar t
o 10% of the isotropic Heisenberg superexchange in the Cu-O chains of this
compound. The strong anisotropy can be explained by the specific geometry o
f two symmetrical 90 degrees Cu-O-Cu bonds, which boosts the importance of
orbital degrees of freedom. Our data show the apparent limitations of the a
pplicability of an isotropic Heisenberg model to the low-dimensional cuprat
es.