Phenomena concerning altermagnets have opened up a window for unconventional analysis of the momentum space spin polarization (MSSP) of antiferromagnetic materials. Taking the example of one of the widely investigated altermagnets, CrSb, we explore the underlying mechanisms leading to the formation or breaking of altermagnetism. With the aid of density function theory calculation and symmetry analysis, we study the behavior of MSSP in the altermagnetic bands of pristine CrSb, along with a few model structures designed from the pristine one by hypothetical vacancy engineering and interstitial doping. We show that the sixfold rotational symmetry of the pristine CrSb can be reduced to a twofold rotational symmetry via vacancy and doping engineering. We discover the formation of fragmented nodal curves (FNCs) across the Brillouin zone in an altermagnetic material when the symmetry is restricted to twofold rotation. Unlike the typical nodal planes and axes, the location of the FNCs in the momentum space is found to be band specific. The formation of FNCs is further validated by introducing uniaxial strain to CrSb and by examining the band structure of ${\mathrm{RbMnPO}}_4$, as they both exhibit a twofold rotational symmetry responsible for altermagnetism. We observe that, unlike the pristine case, these FNCs have the potential to manifest anomalous Hall conductivities (AHC), while the Néel vector orients along both in-plane and out-of-plane directions. This flexibility of the AHC will pave the way for the application of altermagnets in the futuristic quantum devices.

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• Altermagnetism
• Anomalous Hall effect
• Electronic structure
• Density functional theory
• First-principles calculations