Abstract
The effect of micromagnetic boundary conditions on the Berry curvature and topological Hall effect in granular nanostructures is investigated by model calculations. Both free surfaces and grain boundaries between interacting particles or grains affect the spin structure. The Dzyaloshinskii-Moriya interactions yield corrections to the Erdmann-Weierstrass boundary conditions, but the Berry curvature remains an exclusive functional of the local spin structure, which greatly simplifies the treatment of nanostructures. An explicit example is a model nanostructure with cylindrical symmetry whose spin structure is described by Bessel function and which yields a mean-field-type Hall-effect contribution that can be related to magnetic-force-microscopy images.
Highlights
The topological Hall effect (THE) reflects the Berry phase accumulated by conduction electrons exchange-interacting with spin structures Si = S(Ri).3,21 To yield a nonzero emergent magnetic field (Berry-phase curvature), the local spin structures must be noncoplanar, Si⋅(Sj × Sk) ≠ 0
We investigate how Berry-phase curvature and topological Hall effect depend on the physical nature and geometry of the grain boundaries
We review DM interactions in cylindrical nanoparticles of crystals belonging to the point groups Cnv and show that these nanoparticles yield a simple micromagnetic mean-field description of skyrmions in granular nanostructures
Summary
To yield a nonzero emergent magnetic field (Berry-phase curvature), the local spin structures must be noncoplanar, Si⋅(Sj × Sk) ≠ 0. Such spin structures are often associated with Dzyaloshinskii-Moriya (DM) interactions, but micromagnetic spin structures such as magnetic bubbles are noncoplanar.. The Dzyaloshinskii-Moriya interaction is linear in ∇S and yields an additional term in the EulerLagrange equations.15,23 This term needs to be specified for each point group, and there is generally no one-to-one correspondence between broken inversion symmetry and the existence of DM interactions.. We investigate how Berry-phase curvature and topological Hall effect depend on the physical nature and geometry of the grain boundaries. We review DM interactions in cylindrical nanoparticles of crystals belonging to the point groups Cnv and show that these nanoparticles yield a simple micromagnetic mean-field description of skyrmions in granular nanostructures
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