Detecting weak magnetic fields is paramount in areas such as scanning magnetometers and manipulation of magnetic nanoparticles, thus rendering it crucial to increase the weak-field sensitivity for developing next-generation magnetic sensors. The current approaches for high-sensitivity sensors, such as superconducting quantum interference devices, are complex and expensive. By contrast, magnetoresistive sensors and particularly extraordinary magnetoresistive sensors offer a simple operation at room temperature but, to date, at inferior sensitivity. To overcome these challenges, we induce device symmetry breaking to enhance the weak magnetic field sensitivity in semiconductor-metal hybrid structures exhibiting extraordinary magnetoresistance. Retaining the device mirror symmetry yields symmetric magnetoresistance curves with $R\left(B\right)=R(-B)$, which results in inferior detection of weak magnetic fields as ${[dR/dB]}_{B\to 0}=0$. Using finite element modeling, we study the change in device behavior as the symmetry is broken by varying the device geometry by spatially varying the constituent material properties or both. We show that symmetry breaking has three important implications: First, breaking the mirror symmetry causes an asymmetric sensor response with $R\left(B\right)\ne R(-B)$, benefiting from a largely enhanced sensitivity to weak magnetic fields and detection of the magnetic field direction. Second, an interplay with the Hall effect causes a large negative magnetoresistance exceeding 79% at $B=1$ T and room temperature without magnetic constituents or explicit optimization of this property. Third, the asymmetric geometries can be used as a key ingredient toward designing on-demand magnetoresistive characteristics such as linearity at low magnetic fields, step functions, and magnetic switchlike behavior. These implications pave the way for asymmetric topology optimization of magnetoresistive devices with unparalleled performance.

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• Electrical conductivity
• Magnetometry
• Magnetoresistance
• Magnetotransport
• Finite-element method