We present a study of the magnetic susceptibility in carefully detwinned La_{2-x}Sr_{x}CuO_4 single crystals in the lightly-doped region (x=0-0.03), which demonstrates a remarkable in-plane anisotropy of the spin system. This anisotropy is found to persist after the long-range antiferromagnetic (AF) order is destroyed by hole doping, suggesting that doped holes break the AF order into domains in which the spin alignment is kept essentially intact. It turns out that the freezing of the spins taking place at low temperatures is also notably anisotropic, implying that the spin-glass feature is governed by the domain structure as well.
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