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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 confluence between high-energy physics and condensed matter has produced groundbreaking results via unexpected connections between the two traditionally disparate areas. In this work, we elucidate additional connectivity between high-energy and condensed matter physics by examining the interplay between spin-orbit interactions and local symmetry-breaking magnetic order in the magnetotransport of thin-film magnetic semimetal FeRh. We show that the change in sign of the normalized longitudinal magnetoresistance observed as a function of increasing in-plane magnetic field results from changes in the Fermi surface morphology. We demonstrate that the geometric distortions in the Fermi surface morphology are more clearly understood via the presence of pseudogravitational fields in the low-energy theory. The pseudogravitational connection provides additional insights into the origins of a ubiquitous phenomenon observed in many common magnetic materials and points to an alternative methodology for understanding phenomena in locally-ordered materials with strong spin-orbit interactions.