On the calculation of the response of (planar) hall-effect devices to inhomogeneous magnetic fields

The calculation of Hall potentials in a rectangular Hall plate is treated for the case in which the device is subject to a magnetic field B that is inhomogeneous in the y-direction perpendicular to the direction of initial current flow. The potentials are presented in the form φH(→r′) = const. ∫widthB(y)G(y,→r′)dy for the normal Hall effect (→r′ is the position vector). Analytical expressions are given for the weight function G (which depends on the form of the device), together with graphs for a number of typical examples. An analogous expression is derived for the planar Hall effect in ferromagnetic thin films.