The formalism of canonical balance laws (energy and pseudomomentum) and material forces, and their associated jump relations is used to establish the thermodynamical constraint of evolution on coherent phase-transition fronts in thermoelastic ferromagnetic, electric insulators. The expression of the driving (Hugoniot-Gibbs) force acting on the front is found in the quasi-magnetostatic framework but accounting for both magnetic ordering and magnetic-spin inertia of gyroscopic nature. Simple criteria of progress of the front are proposed on this basis. The case of ferromagnetic domain walls is viewed as a special one. This in turn allows one to establish a relationship with the theory of irreversible macroscopic magnetization by wall movement. Furthermore, a comparison with the dynamics of magneto-acoustic domain walls considered as solitonic structures (quasi-particles) is given. Here also, the driving forces acting on the walls in the dissipative case are material forces in their own right.
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