Edge non-collinear magnetism in nanoribbons of Fe3GeTe2 and Fe3GaTe2

Technical Summary: Edge Non-Collinear Magnetism in Nanoribbons of Fe3GeTe2 and Fe3GaTe2

Problem Statement
The manipulation of magnetic ordering in nanoscale systems is critical for advancing spintronic, orbitronic, and magnonic devices. While two-dimensional (2D) van der Waals (vdW) ferromagnets like Fe3GeTe2 (FGeT) and Fe3GaTe2 (FGaT) offer promising properties such as high Curie temperatures and perpendicular magnetic anisotropy, their behavior in reduced dimensions (e.g., nanoribbons) remains to be fully characterized. Specifically, there is a need to understand how edge effects alter magnetic interactions and whether these modifications can enhance the efficiency of magnetization manipulation via angular momentum torques (Spin-Transfer Torque, STT, and Spin-Orbit Torque, SOT). A key challenge in current torque-based manipulation is that effectiveness often depends on the alignment between the spin polarization and the local magnetic moment; if they are parallel, the torque vanishes.

Methodology
The authors employed a multi-stage computational approach to investigate single-layer nanoribbons of FGeT and FGaT with armchair edges:

1. Electronic Structure Calculations: Density Functional Theory (DFT) calculations were performed using the Quantum ESPRESSO code (plane-wave basis) and PAOFLOW (pseudo-atomic orbitals) to determine band structures, magnetic moments, and anisotropy energies. These calculations also yielded the anomalous, spin, and orbital Hall conductivities.
2. Effective Spin Hamiltonian: Based on the electronic structure, the authors derived an effective spin Hamiltonian ($H = -\sum J_{ij} \hat{m}_i \hat{m}_j - \sum \vec{D}_{ij} \cdot (\hat{m}_i \times \hat{m}_j) - K \sum (\hat{m}_i \cdot \hat{k}_i)^2$). The exchange interactions ($J_{ij}$) and Dzyaloshinskii-Moriya (DM) vectors ($\vec{D}_{ij}$) were computed using the Liechtenstein, Katsnelson, Antropov, and Gubanov (LKAG) formalism combined with Green's function methods expanded via Chebyshev polynomials.
3. Magnetic Ground State Determination: The magnetic configurations of the nanoribbons were determined by minimizing the energy of the effective Hamiltonian using the UppASD code.
4. Spin Dynamics Simulations: To evaluate magnetization switching, the authors simulated the time evolution of the magnetic moments under the influence of SOT. They modeled the nanoribbons deposited on a Mn3Sn substrate, assuming the dominant torque contribution arises from the magnetic spin Hall effect (mSHE) of the substrate, with a spin-Hall angle ($\theta_{SH}$) of 0.3.

Key Results

• Edge-Induced Non-Collinearity: While the bulk monolayers exhibit collinear ferromagnetic (FM) ordering with perpendicular anisotropy, the nanoribbons display a non-collinear magnetic ground state specifically at the edges. This arises from a competition between bilinear exchange and DM interactions, which are significantly altered by the breaking of translational symmetry at the boundaries.
• Modified Exchange Interactions: The effective exchange couplings ($J_{ij}$) and DM vectors ($\vec{D}_{ij}$) near the edges differ markedly from the bulk. The highest coupling remains the interplane FM interaction between nearest-neighbor FeI atoms, but in-plane and interplane couplings between FeI and FeII sites show complex FM and antiferromagnetic (AFM) contributions that vary with atomic relaxation and symmetry breaking.
• Orbital Torque Potential: The calculations indicate that the orbital Hall conductivity ($\sigma_{xy}^{(O)}$) around the Fermi energy is approximately 7 to 8.5 times larger than the spin Hall conductivity ($\sigma_{xy}^{(S)}$) for FGaT and FGeT, respectively. This suggests that orbital torques could be a highly effective mechanism for magnetization manipulation in these systems.
• Efficient Magnetization Switching: Simulations of SOT-driven switching at low temperatures (1.0 K) and current densities of $10^{12}$ A/m² demonstrated that the magnetization of both nanoribbons can be reversed in less than 100 ps.
  • FGaT: Exhibits a switching process dominated by magnetic domain formation, characterized by less pronounced oscillations and the presence of plateaus.
  • FGeT: Shows a precession-dominated switching mechanism with more pronounced oscillations in the transverse magnetization components.
• Robustness: Once the current is switched off, the magnetization remains stable in the switched state, with transverse components relaxing to zero, indicating the feasibility of non-volatile memory applications.

Significance and Claims
The paper claims that the emergence of non-collinear magnetic ordering at the edges of FGeT and FGaT nanoribbons fundamentally enhances their utility for spintronic applications. Specifically:

• Universal Torque Efficiency: The non-collinear edge states allow angular momentum currents to generate magnetic torques regardless of the polarization direction of the current. This overcomes the limitation where torque vanishes if the spin polarization is parallel to the magnetic moment.
• Low-Power Operation: The ability to achieve rapid magnetization reversal (sub-100 ps) with relatively low current densities makes these nanostructures highly suitable for non-volatile magnetic memory units and high-speed data processing.
• Theoretical Support for Experiments: The findings provide a theoretical basis for previous experimental observations, such as the survival of long-range Josephson supercurrents in FGeT flakes, by suggesting that edge non-collinearity may facilitate transitions to spin-triplet states, thereby reducing supercurrent damping.
• Experimental Validation: The authors propose that their predictions can be verified using high-resolution magnetic imaging techniques, such as spin-polarized scanning tunneling microscopy (SP-STM), to directly visualize the predicted edge configurations.

In conclusion, the study establishes Fe3GeTe2 and Fe3GaTe2 nanoribbons as versatile platforms for advancing low-dimensional magnetism, offering a pathway toward miniaturized, efficient, and non-volatile magnetic devices.