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Title: Ultra-deep optical cooling of nuclear spins in semiconductor structures Abstract: Nuclear spin systems in solids are known to be well isolated from the crystal lattice. As a result, they are characterized by a spin temperature that can differ from the lattice temperature by orders of magnitude. Cooling the nuclear spin down to nanokelvin temperatures can result in magnetic ordering, which indeed was realized in metals using unique purpose-build multi-stage refrigerators. Nuclear antiferromagnetism was also observed in dielectrics by NMR methods, under adiabatic demagnetization in the rotating frame. In semiconductors, nuclear spins can be cooled optically via dynamic polarization by photoexcited charge carriers. This gives one a possibility to realize ultra-deep cooling of nuclear spins in semiconductor structures, and to study thermodynamics and kinetics of the nuclear spin system by optical methods. New types of carrier-induced nuclear spin ordering are predicted.