Spin current generation via magnetic skyrmion, bimeron, and meron crystals

Problem Statement
The central challenge in spintronics is the efficient generation and control of spin currents to enable energy-efficient, high-speed information processing. While various mechanisms exist for nonmagnetic systems (e.g., spin Hall effects in heavy metals) and ferromagnetic systems (e.g., spin pumping, spin Seebeck effect), the potential of topological spin textures as efficient spin current sources remains not fully understood. Previous theoretical studies on topological textures, such as magnetic skyrmions, have largely focused on systems with net magnetization and often neglected the effects of spin-orbit coupling (SOC). Furthermore, most prior work has concentrated on spin currents with out-of-plane polarization, leaving the generation of in-plane polarized spin currents and the behavior of textures with zero net magnetization (such as meron crystals) largely unexplored.

Methodology
The authors theoretically investigate spin current generation in a two-dimensional model where itinerant electrons are coupled to localized moments forming topological spin textures on a square lattice. The study employs the following approach:

• Model Hamiltonian: The system is described by a Kondo lattice (s–d) model coupled with Rashba-type spin-orbit coupling. The localized spins are treated as classical vectors with unit length.
• Spin Textures: Three distinct two-dimensional topological textures are analyzed:
  1. Skyrmion Crystal (SkX): Features out-of-plane magnetization.
  2. Bimeron Crystal (BmX): Features in-plane magnetization.
  3. Meron Crystal (MX): Features zero net magnetization.
     All three share a common out-of-plane emergent magnetic field but differ in their magnetization directions and symmetries.
• Calculation Techniques: The electronic structure is obtained via exact diagonalization of the Bloch Hamiltonian in the magnetic Brillouin zone. Transport properties are evaluated using linear response theory, calculating both intrinsic contributions (via the Kubo formula and Berry curvature) and dissipative contributions (via Boltzmann transport theory).
• Symmetry Analysis: The results are cross-verified using group theoretical analysis based on the spin space group (for systems without SOC) and the magnetic space group (for systems with SOC).

Key Contributions and Results
The study systematically evaluates spin conductivities for all spin-polarization components (x, y, z) in both longitudinal and transverse channels, comparing scenarios with and without SOC.

1. Behavior Without SOC:

   • SkX and BmX: Both generate spin currents polarized along their respective magnetization directions (out-of-plane for SkX, in-plane for BmX). The transport properties of the BmX are identical to those of the SkX under a 90° spin rotation.
   • MX: Despite having a nontrivial topological number and an emergent magnetic field, the MX generates no spin current in the absence of SOC due to the lack of spin splitting in the band structure.

2. Behavior With Rashba SOC:

   • SkX: The behavior remains qualitatively unchanged; spin currents are generated only along the out-of-plane magnetization direction.
   • BmX: The introduction of SOC breaks the fourfold rotational symmetry of the electronic structure. Consequently, the BmX generates nonzero spin currents in multiple polarization directions (both along and perpendicular to the magnetization), distinguishing it from the SkX.
   • MX: This is the most significant finding. Despite having zero net magnetization, the MX exhibits a pronounced spin current with out-of-plane spin polarization at specific electron fillings (e.g., $n_e = 1$). This arises from an enhanced spin Berry curvature driven by specific band degeneracies protected by nonsymmorphic symmetries at the Brillouin zone boundary (XM and YM lines). The calculated spin Hall angle for the MX is estimated to be significantly larger than that of typical heavy metals, reaching over 110% at zero temperature in the ideal model.

3. Symmetry Analysis:
   The authors demonstrate that the observed transport properties are strictly governed by magnetic symmetries. The spin space group dictates the allowed components in the absence of SOC, while the magnetic space group determines the allowed components when SOC is present. The analysis confirms that the unique spin current generation in the MX is a direct consequence of its specific symmetry-protected band degeneracy.

Significance and Claims
The paper claims that topological spin textures serve as efficient sources of spin currents even in the absence of net magnetization. Specifically:

• The study expands the design space for spintronic devices based on topological magnetic metals by highlighting textures like the Meron Crystal (MX) and Bimeron Crystal (BmX).
• It establishes that SOC is a critical factor that can qualitatively alter spin transport, enabling spin current generation in zero-net-magnetization systems (MX) and diversifying polarization directions in in-plane magnetized systems (BmX).
• The findings suggest that the MX, which produces sizable spin-polarized currents without generating stray magnetic fields, is a promising candidate for integration into densely packed spintronic architectures, potentially offering advantages over traditional ferromagnetic sources.
• The work underscores the importance of considering both intrinsic and dissipative contributions, as well as the full symmetry of the system, when evaluating spin current generation in topological magnets.