Magnetic Flux Density Superposition in Nonlinear Anisotropic Ferromagnetic Material and Resulting Magnetic Barkhausen Noise

Tetrapole probes, also known as double-core probes, which consist of two pairs of orthogonal electromagnets, apply orthogonal magnetic fields to the surface of a ferrous sample and rotate the field by superposition of these fields. Tetrapole probes have the potential to perform rapid characterization of the magnetic anisotropy of ferromagnetic materials. Conventional understanding dictates that magnetic field superposition is linear. However, superposition in ferromagnetic materials is inherently nonlinear. In this work, an equation for the magnetic flux density generated by superposition of orthogonal fields from a tetrapole probe in a ferromagnetic, anisotropic, single net easy-axis material, is derived, along with an equation for magnetic Barkhausen noise root mean square (rms) and energy, for application to materials with flat surfaces. The model approximates the nonlinear superposition as cubic, inline with analogous optics results, and is accurate for low applied fields. Data, which are accurately fit with the model, are shown. The model facilitates useful analyses of measurements made by tetrapole probes and addresses the inherent nonlinearity of magnetic fields applied to ferromagnetic materials.