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Magnetic flux densities ( B-fields) and field intensities ( H-fields) in thin films are investigated from the viewpoints of Berry phase and topological Hall effect. The well-known origin of the topological Hall effect is an emergent B-field originating from the Berry phase of conduction electrons, but Maxwell’s equations predict the relevant perpendicular component B z to be zero. This paradox is solved by treating the electrons as point-like objects in Lorentz cavities. These cavities can also be used to interpret magnetization measurements in the present and other contexts, but structural and magnetic inhomogeneities lead to major modifications of the Lorentz-hole picture.

A Verilog-A based model for the magneto-electric field effect transistor (MEFET) device is implemented and a variety of logic functions based on this device are proposed. These models are used to capture energy consumption and delay per switching event and to benchmark the MEFET with respect to CMOS. Single-source MEFET devices can be used for conventional logic gates like NAND, NOR, inverter and buffer and more complex circuits like the full adder. The dual source MEFET is an enhanced version of the MEFET device which functions like a spin multiplexer (spin-MUXer). Circuits using MEFETs require fewer components than CMOS to generate the same logic operation. These devices display a high on-off ratio., unlike many magneto-electric devices., and they operate at very low voltages., resulting in lower switching energy. Benchmarking results show that these devices perform better in terms of energy and delay., for implementing more complex functions., than the basic logic gates.