The origin of noise and magnetic hysteresis in crystalline permalloy ring-core fluxgate sensors
Authors: Narod B. B. 
Published: September 2014

Abstract. Developed in the 1960s for use in high-performance ring-core fluxgate sensors, 6–81.3 Mo permalloy remains the state of the art for permalloy-cored fluxgate magnetometers. The magnetic properties of 6–81.3, namely magnetocrystalline and magnetoelastic anisotropies and saturation induction, are all optimum in the Fe–Ni–Mo system. In such polycrystalline permalloy fluxgate sensors, a single phenomenon may cause both fluxgate noise and magnetic hysteresis; explain Barkhausen jumps, remanence and coercivity; and avoid domain denucleation. This phenomenon, domain wall reconnection, is presented as part of a theoretical model. In the unmagnetized state a coarse-grain high-quality permalloy foil ideally forms stripe domains, which present at the free surface as parallel, uniformly spaced domain walls that cross the entire thickness of the foil. Leakage flux "in" and "out" of alternating domains is a requirement of the random orientation, grain by grain, of magnetic easy axes' angles with respect to the foil free surface. Its magnetostatic energy together with domain wall energy determines an energy budget to be minimized. Throughout the magnetization cycle the free-surface domain pattern remains essentially unchanged, due to the magnetostatic energy cost such a change would elicit. Thus domain walls are "pinned" to free surfaces. Driven to saturation, domain walls first bulge then reconnect via Barkhausen jumps to form a new domain configuration that I have called "channel domains", which are attached to free surfaces. The approach to saturation now continues as reversible channel domain compression. Driving the permalloy deeper into saturation compresses the channel domains to arbitrarily small thickness, but will not cause them to denucleate. Returning from saturation the channel domain structure will survive through zero H, thus explaining remanence. The Barkhausen jumps, being irreversible exothermic events, are sources of fluxgate noise powered by the energy available from domain wall reconnection. A simplified domain energy model can then provide a predictive relation between ring-core magnetic properties and fluxgate sensor noise power. Four properties are predicted to affect noise power, two of which are well known: saturation total magnetic flux density and magnetic anisotropy. The two additional properties are easy axes alignment and foil thickness. Flux density and magnetic anisotropy are primary magnetic properties determined by an alloy's chemistry and crystalline lattice properties. Easy axes alignment and foil thickness are secondary, geometrical properties related to an alloy's polycrystalline fabric and manufacture. Improvements to fluxgate noise performance can in principle be achieved by optimizing any of these four properties in such a way as to minimize magnetostatic energy. Fluxgate signal power is proportional to B − H loop curvature [d2B/dH2]. The degree to which Barkhausen jumps coincide with loop curvature is a measure of noise that accompanies the fluxgate signal. B − H loops with significant curvature beyond the open hysteresis loop may be used to advantage to acquire the fluxgate signal with reduced noise.