Matter with apparent and hidden spin physics

Materials with interesting physical properties are often designed based on our understanding of the target physical effects. The physical properties can be either explicitly observed (“apparent”) or concealed by the perceived symmetry (“hidden”) but still exist. Both are enabled by specific symmetries and induced by certain physical interactions. Using the underlying approach of condensed matter theory of real materials (rather than schematic model Hamiltonians), we discuss apparent and hidden physics in real materials focusing on the properties of spin splitting and spin polarization. Depending on the enabling symmetries and underlying physical interactions, we classify spin effects into four categories with each having two subtypes; representative materials are pointed out. We then discuss the electric tunability and switch of apparent and hidden spin splitting and polarization in antiferromagnets. Finally, we extend “hidden effects” to views that are farsighted in the sense of resolving the correct atomistic and reciprocal symmetry and replaced by the incorrect higher symmetry. This framework could guide and enable systematic discovery of such intriguing effects.

💡 Research Summary

The manuscript “Matter with apparent and hidden spin physics” presents a comprehensive symmetry‑based classification of spin‑related phenomena in real crystalline materials, focusing on spin‑band splitting and spin polarization. The authors distinguish between “apparent” effects, which are observable under the global symmetry of the crystal, and “hidden” effects, which are forbidden by the global symmetry but become allowed locally because sub‑units (layers, sublattices, or atomic clusters) break inversion or other symmetries. By systematically analyzing the enabling symmetries (global inversion, time‑reversal, spin‑rotation, fractional translation) and the required physical interactions (spin‑orbit coupling (SOC) or its absence, magnetic ordering), they construct a taxonomy consisting of four main categories (A–D) and two sub‑types within each, yielding seven distinct Spin‑Splitting Types (SST‑0 to SST‑6).

Category A covers systems where global inversion symmetry is broken. When SOC is present, Rashba/Dresselhaus spin splitting appears (SST‑0). If inversion is globally preserved but broken locally, a hidden Rashba‑type spin polarization emerges (SST‑6). Category B includes SOC‑independent cases: hidden spin polarization can arise in non‑magnetic crystals with locally broken inversion (SST‑1) or in antiferromagnets (AFM) where local magnetic sub‑lattices lack inversion (SST‑2). Category C deals with SOC‑required but globally inversion‑symmetric materials; here conventional spin splitting vanishes, yet hidden spin polarization can survive in AFM (SST‑4) or ferromagnets (FM) (SST‑5). Category D comprises SOC‑required, globally inversion‑broken magnetic systems, leading to Zeeman‑type spin splitting (SST‑5). The sub‑type distinction (1 vs. 2) reflects whether the relevant symmetry breaking is global versus local and whether auxiliary symmetries (polar vs. non‑polar sectors, fractional translations) shape the spin texture without changing its existence.

The authors illustrate each SST with concrete material examples drawn from experiment and first‑principles calculations. BaNiS₂ (non‑magnetic, globally centrosymmetric) exhibits hidden Rashba polarization due to locally non‑centrosymmetric Ni–S layers (SST‑6). Ca₂MnO₄ (AFM) shows electric‑field‑controlled Zeeman‑type spin splitting, demonstrating tunability of hidden spin polarization (Category D). LaOBiS₂ and NaCaBi illustrate how polar and non‑polar sub‑domains generate local helicity (Category B, subtype 1). MnF₂, MnTe, Mn₄Nb₂O₉, and BiCrO₃ are cited as non‑relativistic spin‑splitting‑free AFM compounds where hidden spin polarization arises from spin‑interconversion rotation symmetry (SST‑4). Ni₂FeGa (FM) provides a Zeeman‑type example where global inversion is preserved yet spin splitting appears due to magnetic order (SST‑5).

A significant portion of the paper is devoted to the electric tunability of these effects, especially in antiferromagnets. By applying an external electric field or current, one can switch local inversion breaking on or off, thereby converting an apparent effect into a hidden one or vice versa. This controllability opens pathways for spin‑tronic devices such as non‑volatile memory, spin‑orbit torque switches, and electrically reconfigurable spin filters.

Beyond the explicit classification, the authors introduce the concept of “far‑sighted hidden effects.” They argue that low‑resolution theoretical models (e.g., minimal basis sets) or experimental setups that assume a higher, erroneous symmetry can miss hidden phenomena that only become visible when the correct lower symmetry is recognized. Re‑examining such cases can reveal hidden valley, orbital, or spin polarizations in materials previously thought to be symmetry‑forbidden, exemplified by hidden spin polarization in certain Bi‑based cuprate superconductors.

In the discussion, the paper emphasizes that the two axes—symmetry (global vs. local) and interaction (SOC vs. magnetic exchange)—provide a universal framework for predicting and engineering spin phenomena. The taxonomy not only clarifies existing observations but also serves as a design guide: by selecting target SSTs, researchers can engineer the necessary symmetry breaking (through strain, layering, chemical substitution, or external fields) and choose appropriate SOC strength or magnetic order to realize desired spin textures.

Overall, the work delivers a unified, materials‑focused perspective on apparent and hidden spin physics, bridges the gap between abstract symmetry arguments and concrete material realizations, and proposes practical routes for discovery and manipulation of exotic spin effects in both non‑magnetic and magnetic crystals. This framework is poised to accelerate the systematic search for new spin‑functional materials and to inspire novel device concepts that exploit hidden symmetries.