Continua with spin structure

A continuum Lagrangian-Hamiltonian description of alloys with spin glass structure in magnetic saturation conditions is presented here, paying attention to the interaction between gross deformation and spin substructures. A version of Noether theorem accounting for gyroscopic inertia of spins is proven so that the covariance of the balance of spin interactions and, as a special case, the one of Landau-Lifshitz-Gilbert equation follow. The formalism is also applied to the description of topological transitions in spin fluids. Finally, evolution equations of point defects and disclination lines are derived in covariant way.