  Two well-known Hall-like effects are occurring in ferromagnets: the Anomalous
Hall effect and the Planar Hall effect. The former is analogous to the
classical Hall effect and is defined by the Onsager reciprocity relation of the
second kind (antisymmetric conductivity matrix), while the latter is defined by
the Onsager reciprocity relation of the first kind (symmetric conductivity
matrix). The difference is fundamental, as it is based on time-invariance
symmetry breaking at the microscopic scale. We study the Hall current generated
in both cases, together with the power that can be extracted from the edges of
Hall device. The expressions of the distribution of the electric currents, the
distribution of electric carriers, and the power efficiencies (i.e. the power
that can be injected into a load circuit) are derived at stationary regime from
a variational method based on the second law of thermodynamics. It is shown
that the distribution of the transverse Hall-current is identical in both cases
but the longitudinal current and the power dissipated differ at the second
order in the Hall angle.
