We present a series of electron spin resonance (ESR) and infrared
transmission experiments in antiferromagnetic (AF), lightly hole-doped
YBa2Cu3O6 in search for the effect of a spatially inhomogeneous ground
state on the magnetic and electric properties. Crystal compositions
were CaxGdyY1-x-yBa2Cu3O6 with x=0, 0.008, 0.02, and 0.03 and y
approximate to 0.01. Gd3+ ESR satellites from sites with first-neighbor
Ca atoms show that holes are not preferentially localized at low
temperatures in the vicinity of Ca dopants. We mapped by multifrequency
Gd3+ ESR the AF domain structure as a function of hole concentration,
temperature, and magnetic fields up to 8 T. We attribute the
hole-doping-induced rotation of the magnetic easy axis from collateral
to diagonal (with respect to the tetragonal CuO2 lattice) to the
pinning of the AF magnetization to a static modulation or a
phase-separated network of the hole density. The dominantly fourfold
symmetry of pinning suggests that the hole density network has this
symmetry also and is not an array of stripes. At higher temperatures
the pinning to the diagonal direction becomes weak and the possibility
of domain wall fluctuations is discussed. There is no magnetic field
dependence and no in-plane anisotropy of the infrared transmission
polarized in the CuO2 planes in an x=0.02 crystal placed in magnetic
fields up to 12 T. Thus, the network of holes is rigid and is not
affected by magnetic fields that are, however, strong enough to rotate
the AF magnetization into a single domain.