Two theorems on electron states in helimagnets are proved. They reveal a Kramers-like degeneracy in a helical magnetic field. Since a commensurate helical magnetic system is transitionally invariant with two multiple periods (ordinary translations and generalized ones with rotations), the band structure turns out to be topologically nontrivial. Together with the degeneracy, this gives an unusual spin structure of electron bands. A two-dimensional model of nearly free electrons is proposed to describe conductive hexagonal palladium layers under an effective field of magnetically ordered ${\mathrm{CrO}}_2$ spacers in ${\mathrm{PdCrO}}_2$. The spin texture of the Fermi surface leads to abnormal conductivity.

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• Electronic structure
• Magnetic order
• Topological phases of matter
• Helimagnets
• Bloch wave theory
• Discrete symmetries in condensed matter
• Tight-binding model