## Importance

For many decades, it was commonly believed that all electronic states of a collinear antiferromagnetic (FA) are spin degenerate, unless the underlying crystal structure lacks centrosymmetry and exhibits spin-orbit coupling. This has been primarily definitional for antiferromagnetism and is widely used experimentally to distinguish ferromagnets from AF. Recently, it has been demonstrated that a new class of magnets, possessing antiferromagnetic order and without sharp magnetization but exhibiting a typical ferromagnetic response in many aspects, is possible. We predict that

$FeSb2$

, which is well known but poorly understood magnetically, is a nascent unconventional magnet of this type and can be induced to become so by Co or Cr doping. In addition, the calculated magnetic anisotropy is favorable for exhibiting various anomalous properties.

## Summary

It is commonly believed that the energy bands of typical collinear antiferromagnets (AF), which have zero net magnetization, are degenerated into Kramers spin. Kramers non-degeneration is usually associated with an overall breaking of time inversion symmetry (eg, via ferromagnetism) or a combination of spin-orbit interaction and disruption of spatial inversion symmetry. Recently, it has been shown that another type of spin division emerges in some collinear magnets whose spin is fully symmetrically compensated, nonrelativistic and not even necessarily non centrosymmetric. These materials exhibit a non-zero spin density shifted in real space, as seen in traditional AFs, but also a division of spin in momentum space, typically seen only in ferromagnets. This results in a combination of material characteristics typical of ferro-magnets and AFs. Here we discuss this recently discovered class with an application to a well-known semiconductor, FeSb2, and predict that with some alloys it becomes magnetic and metallic and exhibits the aforementioned magnetic dualism. The calculated energy bands separate antisymmetrically with respect to spin-degenerate nodal surfaces rather than nodal points, as in the case of spin-orbit separation. The combination of a large spin separation (0.2 eV), a net magnetization compensated with a metallic ground state and a specific easy magnetic axis generates a large anomalous Hall conductivity (âˆ¼150 S / cm) and a strong magneto-optic Kerr effect, all considered to be characteristics of a net non-zero magnetization. We identify an important contribution to the anomalous response from the spin-orbit interaction of anti-Kramers nodal surfaces with spacing, a mechanism distinct from nodal lines and Weyl points in ferromagnets.

## Footnotes

• Accepted September 2, 2021.
• Author contributions: IIM and L.Å . designed research; IIM, KK, MDJ, RG-H. and L.Å . conducted research; IIM, MDJ and L.Å . data analyzed; and IIM, MDJ and L.Å . wrote the paper.

• The authors declare no competing interests.