  At low lattice temperatures the nuclear spins in a solid form a closed
thermodynamic system that is well isolated from the lattice. Thermodynamic
properties of the nuclear spin system are characterized by the local field of
spin-spin interactions, which determines its heat capacity and the minimal
achievable nuclear spin temperature in demagnetization experiments. We report
the results of measurement of the local field for the nuclear spin system in
GaAs, which is a model material for semiconductor spintronics. The choice of
the structure, a weakly doped GaAs epitaxial layer with weak residual
deformations, and of the measurement method, the adiabatic demagnetization of
optically cooled nuclear spins, allowed us to refine the value of nuclear
spin-spin local field, which turned out to be two times less than one
previously obtained. Our experimental results are supported by calculations,
which take into account dipole-dipole and indirect (pseudodipolar and exchange)
nuclear spin interactions as well as quadrupole splitting of nuclear spins in
the vicinity of charged impurity centers.
