Magneto-resistance in three-dimensional composites.

Marc Briane (1) , Laurent Pater (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

In this paper we study the magneto-resistance, i.e. the second-order term of the resistivity perturbed by a low magnetic field, of a three-dimensional composite material. Extending the two-dimensional periodic framework of [M. Briane, Homogenization of the magneto-resistance in dimension two, M3AS, 20 (7) (2010), 1161-1177], it is proved through a H-convergence approach that the dissipation energy induced by the effective magneto-resistance is greater or equal to the average of the dissipation energy induced by the magneto-resistance in each phase of the composite. This inequality validates for a composite material the Kohler law which is known for a homogeneous conductor. The case of equality is shown to be very sensitive to the magnetic field orientation. We illustrate the result with layered and columnar periodic structures.

Mots clés: magneto-transport; Hall effect; homogenization; magneto-resistance; magneto-transport.

Domaines: Equations aux dérivées partielles [math.AP]

Marc Briane, Laurent Pater. Magneto-resistance in three-dimensional composites.. Asymptotic Analysis, 2014, 86 (3-4), pp.165-197. ⟨10.3233/ASY-131192⟩. ⟨hal-00713779⟩