An Antisymmetric Effective Hall Matrix

A periodic composite of four isotropic phases with an almost antisymmetric effective Hall matrix is constructed. This is done through the use of a microstructure, with high contrast conductivity, which acts to twist the direction of the induced Hall field. For an applied current along the y3 axis and a magnetic field h in the y1-y2 plane the Hall field will be essentially parallel, rather than perpendicular, to h. It is also shown how to obtain composites with an effective Hall matrix matching any given symmetric positive definite matrix.