Matter with apparent and hidden spin physics

Technical Summary: Matter with Apparent and Hidden Spin Physics

Problem Statement
The identification of physical effects in condensed matter physics is traditionally guided by "enabling conditions"—specific symmetry breakings and physical interactions required for an effect to exist globally. For instance, the Rashba effect (spin splitting) is classically understood to require broken inversion symmetry ($I$) and spin-orbit coupling (SOC) in nonmagnetic systems. When a material's global symmetry appears to forbid such an effect (e.g., a centrosymmetric crystal), the effect is often dismissed as an artifact of sample imperfections or extrinsic factors. However, recent discoveries suggest that "hidden" effects can exist intrinsically within perfect crystals. These effects arise when local sectors of a unit cell possess broken symmetries that are mutually compensating on a global scale, or when simplified theoretical models (using small basis sets or average symmetries) fail to resolve lower, local symmetries. The paper addresses the need to systematically classify, rationalize, and distinguish between "apparent" effects (globally allowed) and "hidden" effects (globally forbidden but locally allowed) within the realm of spin physics, specifically focusing on spin splitting and spin polarization.

Methodology
The authors employ a unified framework based on the condensed matter theory of real materials, moving beyond schematic model Hamiltonians. The methodology involves:

1. Symmetry Analysis: Utilizing magnetic space groups and spin space groups to classify spin-splitting types (SST) based on the presence or absence of specific symmetries: time-reversal ($\Theta$), inversion ($I$), spin-rotation ($U$), and fractional translation ($T$).
2. Categorization: Grouping spin effects into four primary categories based on two binary switches:
   • Whether the enabling symmetry is broken globally (Apparent) or only locally (Hidden).
   • Whether the physical interaction is SOC-induced or SOC-independent (non-relativistic).
3. Material Case Studies: Analyzing specific compounds (both nonmagnetic and magnetic) to exemplify each category, using first-principles calculations and existing experimental data to validate the theoretical classifications.
4. Extension to "Farsightedness": Investigating cases where "hidden" effects arise not from local sector compensation, but from the failure of low-resolution theories (e.g., truncated $k \cdot p$ methods) to capture the correct atomistic or reciprocal space symmetries.

Key Contributions and Classification
The paper establishes a comprehensive classification of spin-related phenomena into four categories, each with subtypes depending on magnetic configurations (nonmagnetic, antiferromagnetic, ferromagnetic):

• Category (A): Apparent SOC-induced Spin Splitting.

  • Mechanism: Global breaking of inversion symmetry combined with SOC.
  • Subtypes: (A,1) Nonmagnetic (NM) materials (e.g., BiTeI, GeTe) exhibiting Rashba or Dresselhaus textures; (A,2) Antiferromagnetic (AFM) materials where AFM order is a passive background (e.g., BiCoO3).
  • Features: Spin textures (helical, radial) are shaped by auxiliary symmetries (polarity, chirality).

• Category (B): Hidden SOC-induced Spin Polarization.

  • Mechanism: Global inversion symmetry is preserved, but local sectors are non-centrosymmetric. Local spin polarizations exist but cancel out globally.
  • Subtypes: (B,1) NM centrosymmetric materials (e.g., BaNiS2, LaOBiS2) where local Rashba/Dresselhaus polarization is hidden; (B,2) AFM materials with passive AFM backgrounds.
  • Detection: Requires resolving local sectors (e.g., via spin-ARPES with specific beam penetration) or measuring indirect properties like circular photocurrents.

• Category (C): Apparent SOC-independent Spin Splitting.

  • Mechanism: Spin splitting driven by magnetic exchange interactions (Zeeman-type) without requiring SOC. Enabled by breaking both $\Theta I$ and $UT$ symmetries globally.
  • Subtypes: (C,1) AFM materials (e.g., MnF2, MnTe, RuO2) exhibiting "non-relativistic spin splitting" (NRSS); (C,2) Ferromagnetic (FM) materials (e.g., Fe, Ni, Fe3O4) with Zeeman splitting.
  • Significance: Includes "altermagnets" (a subgroup of C,1) where spin-splitting occurs despite zero net magnetization, with splitting magnitudes reaching hundreds of meV.

• Category (D): Hidden SOC-independent Spin Polarization.

  • Mechanism: Global symmetry preserves $\Theta I$ or $UT$ (preventing global NRSS), but local sectors (AFM or FM) break these symmetries, allowing local SOC-independent polarization that cancels globally.
  • Subtypes: (D,1) AFM materials with AFM local sectors (e.g., Ca2MnO4, "hidden altermagnetism"); (D,2) AFM materials with FM local sectors (e.g., CuMnAs, Mn2Au).
  • Features: These materials can exhibit hidden Zeeman-type splitting or hidden altermagnetism, coexisting with global spin degeneracy.

Results

• Unified Framework: The paper successfully maps diverse phenomena (Rashba, Dresselhaus, Zeeman, Altermagnetism) onto a single 4-category matrix defined by global vs. local symmetry and SOC dependence.
• Material Discovery: It identifies and validates numerous real materials for each category, including centrosymmetric NM crystals with hidden Rashba polarization and AFM crystals with hidden non-relativistic splitting.
• Electric Tunability: The authors demonstrate that in AFM compounds, electric fields can switch between apparent and hidden spin states. For instance, ferroelectric phases can couple to NRSS, and antiferroelectric phases can host hidden NRSP, allowing for electric control of spin textures.
• "Farsightedness" Effects: The paper highlights that some "hidden" effects are actually artifacts of theoretical approximations. For example, heavy-hole/light-hole mixing and linear Rashba splitting in quantum wells are enabled by reduced local interfacial symmetries ($C_{2v}$) that are masked by the higher global symmetry ($D_{2d}$) in simplified models.

Significance
The paper claims that this framework provides a "farsighted" view that resolves the paradox of effects existing in materials where global symmetry seemingly forbids them. By distinguishing between apparent and hidden effects, the authors argue that:

1. Material Pools are Expanded: Researchers can now target materials with global centrosymmetry or specific magnetic orders for spintronic applications, knowing that local symmetries may still enable the desired physics.
2. Theoretical Clarity: The classification clarifies the relationship between "altermagnets," hidden spin polarization, and traditional spin-splitting mechanisms, rationalizing seemingly contradictory phenomena.
3. Design Principles: It offers a systematic guide for discovering materials with targeted properties (e.g., switchable spin polarization) by focusing on the interplay of local symmetry breaking and specific physical interactions (SOC or magnetism), rather than relying solely on global symmetry constraints.

The work does not propose new experimental setups but rather provides the theoretical taxonomy necessary to interpret existing data and guide the search for materials with specific spin functionalities, emphasizing that "hidden" effects are intrinsic properties of perfect crystals, not experimental errors.