  Magnetic properties of high purity stoichiometric La$_2$CuO$_4$ nanoparticles
are systematically investigated as a function of particle size. Ferromagnetic
single-domain spin clusters are shown to spontaneously form at the surface of
fine grains as well as paramagnetic defects. Hysteresis loops and
thermomagnetic irreversibility are observed in a wide temperature range $5 -
350$ K with the remnant moment and coercivity gradually decreasing with
increasing temperature. Possible origins of the spontaneous surface
ferromagnetic clusters and the relation of our data to the appearance of
unusual magnetic phenomena and phase separation of doped cuprates are
discussed.
