The major argument to promote the development of spin electronics and topological materials is the low power dissipation when using spin degrees of freedom and transverse configurations such as Hall configurations. Indeed, in the case of a topological phase, the generated effective magnetic field is expected not to dissipate. However, such an assertion must be the subject of a theoretical description in the context of a realistic electronic device in steady state. The aim of the thesis is to determine the useful power of these devices, in a study that is both experimental and theoretical.

In this context, the definition of the useful power is an open problem. Indeed, the thermodynamics of this type of non-equilibrium system involves cross effects between the degrees of freedom of the electric charge carriers, those of the spin of these carriers, as well as those of the magnetization. The non-equilibrium cross effects are described in a very general way by the famous Onsager reciprocity relations. We have developed a variational method to establish the steady state of a Hall bar and the power dissipated in a load circuit, as a function of the load resistance and the Hall angle. An unexpected result predicts the existence of a maximum ('maximum power transfer theorem'). Preliminary measurements based on the anomalous Hall effect have recently validated the prediction. This experimental confirmation allows us to establish a thesis project that aims to reproduce the measurements on a large set of materials (metals, semiconductors, oxides) and in particular magnetic topological materials, called altermagnetic.

In addition, a ferromagnetic resonance study (called spin pumping) will involve thermoelectric effects, whose dissipative properties, measured on an adjacent load circuit, remain to be determined.