Incommensuration in odd-parity magnets

Inversion-asymmetric antiferromagnets (AFMs) with odd-parity spin-polarization pattern have been proposed as a new venue for spintronics. These AFMs require commensurate ordering to ensure an effective time-reversal symmetry, which guarantees a strictly antisymmetric spin polarization of the electronic states. Recently, nonsymmorphic centrosymmetric crystals have been identified as a broad class of materials which could exhibit unit-cell doubling magnetism with odd-parity spin-polarization. Here we investigate the stability of these states against incommensuration. We first demonstrate that the symmetry conditions which permit a p-wave spin polarization pattern also permit the existence of a non-relativistic Lifshitz invariant in the phenomenological Ginzburg-Landau free energy. This implies magnetism with an incommensurate ordering vector, independent of its microscopic origin. AFMs with f- or h-wave spin-polarization are also prone to incommensurability, especially when they have an itinerant origin. Here the symmetry which ensures the odd-parity spin-polarization also guarantees the existence of van Hove saddle points off the time-reversal-invariant momenta, which promote incommensurate spin fluctuations in quasi-two-dimensional electronic systems. Finally, we study the effect of weak spin-orbit coupling in locally noncentrosymmetric materials and find that it favors antiferromagnetic phases with in-plane magnetic moments. However, the inclusion of the spin-orbit coupling also introduces a new mechanism for driving incommensuration. Our results imply that odd-parity AFMs are likely to be preceded by an incommensurate phase, or emerge directly from the normal state via a first order transition. These conclusions are consistent with the phase diagram of several candidate materials.