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Abstract Symmetry-protected topological crystalline insulators (TCIs) have primarily been characterized by their gapless boundary states. However, in time-reversal- ($${{{{{{{\mathcal{T}}}}}}}}$$ $T$-) invariant (helical) 3D TCIs—termed higher-order TCIs (HOTIs)—the boundary signatures can manifest as a sample-dependent network of 1D hinge states. We here introduce nested spin-resolved Wilson loops and layer constructions as tools to characterize the intrinsic bulk topological properties of spinful 3D insulators. We discover that helical HOTIs realize one of three spin-resolved phases with distinct responses that are quantitatively robust to large deformations of the bulk spin-orbital texture: 3D quantum spin Hall insulators (QSHIs), “spin-Weyl” semimetals, and$${{{{{{{\mathcal{T}}}}}}}}$$ $T$-doubled axion insulator (T-DAXI) states with nontrivial partial axion angles indicative of a 3D spin-magnetoelectric bulk response and half-quantized 2D TI surface states originating from a partial parity anomaly. Using ab-initio calculations, we demonstrate thatβ-MoTe₂realizes a spin-Weyl state and thatα-BiBr hosts both 3D QSHI and T-DAXI regimes. 

The interplay of charge, spin, lattice, and orbital degrees of freedom in correlated materials often leads to rich and exotic properties. Recent studies have brought new perspectives to bosonic collective excitations in correlated materials. For example, inelastic neutron scattering experiments revealed non-trivial band topology for magnons and spin–orbit excitons (SOEs) in a quantum magnet CoTiO₃(CTO). Here, we report phonon properties resulting from a combination of strong spin–orbit coupling, large crystal field splitting, and trigonal distortion in CTO. Specifically, the interaction between SOEs and phonons endows chirality to two $E_g$phonon modes and leads to large phonon magnetic moments observed in magneto-Raman spectra. The remarkably strong magneto-phononic effect originates from the hybridization of SOEs and phonons due to their close energy proximity. While chiral phonons have been associated with electronic topology in some materials, our work suggests opportunities may arise by exploring chiral phonons coupled to topological bosons.