2026/07/21 by Yichen Liu, Junxi Yu, Pu Zhang +1
#cond-mat.mtrl-sci #cond-mat.mes-hall
Momentum-dependent nonrelativistic spin splitting provides a symmetry fingerprint of collinear magnets and can govern unconventional electronic, magnonic, and transport phenomena. Whereas even-parity s-, d-, g-, and i-wave splittings in collinear magnets have been extensively studied, odd-parity counterparts remain unexplored beyond the p-wave and f-wave classes. Here, using group theory, we establish the complete classification of odd-parity spin splitting in collinear magnets. We show that, in addition to the p-wave and f-wave forms, h- and k-wave splittings with ℓ=5 and 7 are allowed, while m-wave splitting with ℓ=9 constitutes the upper bound. We derive a complete mapping from crystallographic point-group irreducible representations to the lowest-order odd-parity basis functions and formulate the coupling rule between a symmetry-breaking axial field and the parent Néel order that selects the induced odd-parity class. We further construct minimal lattice models that realize h-, k-, and m-wave splitting. Guided by this classification, we screen the MAGNDATA database and show that circularly polarized light can drive the PT-symmetric antiferromagnets Fe2TeO6 and MgFe6Ge6 into h-wave and k-wave phases, respectively, exhibiting the hallmark spin splittings in both electronic bands and magnon spectra. Symmetry analysis and Berry-curvature calculations show that collinear odd-parity magnets of both h- and k-wave allow an anomalous Hall response, whereas the m-wave class forbids it. Together, these results complete the partial-wave hierarchy of odd-parity spin splitting in collinear magnets and establish symmetry criteria for anomalous transport in the high-partial-wave classes.