Nonrelativistic Optically-Induced Spin Torque in Noncollinear Magnets

Technical Summary: Nonrelativistic Optically-Induced Spin Torque in Noncollinear Magnets

Problem Statement
Manipulating spin direction in magnetic materials via contactless, non-invasive optical methods is a critical objective in spintronics. Existing optically-induced spin torque (OIST) mechanisms are predominantly rooted in relativistic frameworks relying on spin-orbit coupling (SOC). This reliance restricts the material platform to systems containing heavy elements, as SOC strength scales with atomic number. Furthermore, while SOC-induced spin splitting is typically small, nonrelativistic (NR) spin splitting in certain magnetic configurations can be significantly larger (0.1–1 eV). However, the theoretical framework for NR-OIST, particularly in noncollinear magnetic systems, remains underexplored. Specifically, the symmetry constraints governing second-order optical responses in these systems and the potential for strong, heavy-element-free spin control are not fully established.

Methodology
The authors employ a combination of group-theoretical analysis, perturbative quantum mechanics, and numerical simulations to investigate NR-OIST:

1. Theoretical Framework: The study utilizes a general spin group-theoretical approach within the nonrelativistic limit. The system is described by a Hamiltonian comprising a spin-independent term and an exchange field term ($H = H_0 + \sum J \hat{s}_i \cdot \sigma$).
2. Perturbative Derivation: Using a density matrix approach in the length gauge, the authors derive the second-order response expression for OIST. This response is decomposed into contributions from linearly polarized light (LPL) and circularly polarized light (CPL), governed by susceptibility functions ($\chi$ and $\xi$) derived from the quantum geometry tensor (quantum metric $g_{\alpha\beta}$ and Berry curvature $\Omega_{\alpha\beta}$).
3. Symmetry Analysis: The authors analyze the constraints imposed by spin point groups (SPGs) on the spin torque vector and quantum geometric tensors. They distinguish between collinear, coplanar, and noncoplanar magnetic configurations, determining which symmetries allow or forbid specific torque components.
4. Modeling and Calculation:
   • Tight-Binding Model: An isotropic Kagomé lattice model is used to illustrate the symmetry arguments and calculate band dispersions and quantum metrics.
   • First-Principles Calculations: Density Functional Theory (DFT) calculations are performed on realistic materials, specifically the Mn$_3$Ge and Mn$_3$Sn families, to validate the theoretical predictions and quantify the magnitude of the effect.

Key Contributions

• Extension to the Nonrelativistic Regime: The work extends the concept of optically-induced spin torque from the relativistic (SOC-dominated) limit to the nonrelativistic limit, demonstrating that strong spin torques can be generated without heavy elements.
• Symmetry Rules for Noncollinear Magnets: The paper establishes that NR-OIST is symmetry-forbidden in collinear magnets but arises in noncollinear configurations. It provides a detailed classification of site-resolved spin symmetries and their selection rules for both LPL and CPL.
• Quantum Geometry Connection: The study elucidates the relationship between OIST and the quantum geometry of Bloch wavefunctions, showing how the quantum metric (for LPL) and Berry curvature (for CPL) drive the torque in specific symmetry environments.
• Material Realization: The theory is applied to Kagomé lattice materials (Mn$_3$Ge, Mn$_3$Sn), predicting observable effects in realistic systems.

Results

• Symmetry Constraints:
  • Collinear Magnets: NR-OIST is strictly forbidden.
  • Coplanar Magnets: LPL induces an out-of-plane spin torque. However, in systems possessing inversion symmetry (such as the centrosymmetric coplanar configurations analyzed), CPL-induced torque is strictly forbidden (silent) in the NR limit.
  • Noncoplanar Magnets: All torque components are generally allowed as the spin-only group reduces to the identity.
• Kagomé Lattice Model: Simulations on a Kagomé lattice with 2/3-filling show that while the total Berry curvature vanishes due to inversion symmetry (suppressing CPL-induced torque), the quantum metric allows for LPL-induced torque. The torque is site-dependent, with specific sites being "silent" due to local mirror symmetries, while others exhibit non-zero responses.
• Mn$_3$Ge Calculations:
  • Magnitude: The calculated NR-OIST is significantly stronger than relativistic SOC-induced effects, by 1–2 orders of magnitude. For a moderate light field (0.1 V/nm), the induced torque corresponds to an effective magnetic field on the order of 30 T.
  • Mechanism: The torque drives a canting of the 120° spin configuration toward a collinear pattern, generating a small net spin moment. This effect is reversible, with the system returning to equilibrium within a few picoseconds after the light is turned off.
  • Relativistic Comparison: When SOC is included, the overall band structure remains largely unchanged, confirming that the exchange-driven NR splitting dominates the response. CPL-induced torque remains negligible in the NR limit but emerges as a weaker, relativistic effect when SOC is finite.

Significance
The paper claims to significantly broaden the realization platform for opto-spintronics by moving beyond the heavy-element constraint of relativistic SOC. By leveraging noncollinear magnetic configurations, the authors demonstrate that contactless optical control of spin order is feasible in a wide family of materials (including Mn$_3$X antiperovskites and Fe$_3$Sn$_2$) with much stronger response magnitudes than previously achievable. This work provides a theoretical foundation for detecting hidden quantum geometric properties and offers a pathway for efficient, non-invasive spin manipulation in modern spintronic devices.