Optical phonons as a testing ground for spin group symmetries

Abstract

Lattice vibrations are highly sensitive to crystal symmetries and their changes across phase transitions. The latter can modify irreducible (co)representations and corresponding infrared and Raman selection rules of phonons. This concept is established for relativistic magnetic point groups, simultaneously transforming spatial and spin coordinates. However, in altermagnets described by non-relativistic spin groups with disjunct symmetry operations for both vector spaces, the phonon selection rules have remained unexplored. Here, we present a detailed study of the infrared- and Raman-active modes in the collinear antiferromagnet and altermagnet candidate Co${}_2$Mo${}_3$O${}_8$. Comparing to ab initio calculations accurately capturing the eigenfrequencies, we identify all expected phonon modes at room temperature and deduce their selection rules using both symmetry approaches. Importantly, we observe the change of selection rules upon antiferromagnetic ordering, agreeing with the relativistic symmetry approach, while the spin group formalism predicts no changes. Therefore, optical phonons can reveal the appropriate symmetry treatment.

References in corpus (16)

• Broken Kramers' degeneracy in altermagnetic MnTe
• Landau Theory of Altermagnetism
• Absence of altermagnetic spin splitting character in rutile oxide RuO${}_2$
• Chiral-Split Magnon in Altermagnetic MnTe
• Catalog of Unconventional Magnons in Collinear Magnets
• Diagonal magnetoelectric susceptibility and effect of Fe-doping in a polar ferrimagnet Mn2Mo3O8
• Fermi-liquid behavior of non-altermagnetic RuO${}_2$
• Structure, phonons, and orbital degrees of freedom in Fe${}_2$Mo${}_3$O${}_8$
• Electromagnon resonance in a collinear spin state of a polar antiferromagnet Fe2Mo3O8
• Spectroscopic and first principle DFT+eDMFT study of complex structural, electronic, and vibrational properties of $M_2$Mo${}_3$O${}_8$ ($M$=Fe, Mn) polar magnets
• The Crystallographic Spin Point Groups and their Representations
• Magnetization reversal through an antiferromagnetic state
• Collinear Altermagnets and their Landau Theories
• Magnetic and vibronic THz excitations in Zn doped Fe${}_2$Mo${}_3$O${}_8$
• Polar phonons and magnetic excitations in the antiferromagnet CoF${}_2$
• Optical magnetoelectric effect in the polar honeycomb antiferromagnet Fe2Mo3O8