  We extend the Mermin-Wagner theorem to a system of lattice spins which are
spin-coupled to itinerant and interacting charge carriers. We use the
Bogoliubov inequality to rigorously prove that neither (anti-) ferromagnetic
nor helical long-range order is possible in one and two dimensions at any
finite temperature. Our proof applies to a wide class of models including any
form of electron-electron and single-electron interactions that are independent
of spin. In the presence of Rashba or Dresselhaus spin-orbit interactions (SOI)
magnetic order is allowed and intimately connected to equilibrium spin
currents. However, in the special case when Rashba and Dresselhaus SOIs are
tuned to be equal, magnetic order is excluded again. This opens up a new
possibility to control magnetism in magnetic semiconductors electrically.
