Neutron-scattering signature of the Dzyaloshinskii-Moriya interaction in nanoparticles

Abstract

The antisymmetric Dzyaloshinkii-Moriya interaction (DMI) arises in systems with broken inversion symmetry and strong spin-orbit coupling. In conjunction with the isotropic and symmetric exchange interaction, magnetic anisotropy, the dipolar interaction, and an externally applied magnetic field, the DMI supports and stabilizes the formation of various kinds of complex mesoscale magnetization configurations, such as helices, spin spirals, skyrmions, or hopfions. A question of importance in this context addresses the neutron-scattering signature of the DMI, in particular in nanoparticle assemblies, where the related magnetic scattering signal is diffuse in character and not of the single-crystal diffraction-peak-type, as it is e.g.\ seen in the B20 compounds. Using micromagnetic simulations we study the effect of the DMI in spherical FeGe nanoparticles on the randomly-averaged magnetic neutron scattering observables, more specifically on the spin-flip small-angle neutron scattering cross section, the related chiral function, and the pair-distance distribution function. Within the studied parameter space for the particle size ($60 \, \mathrm{nm} \leq L \leq 200 \, \mathrm{nm}$) and the applied magnetic field ($-1 \, \mathrm{T} \leq μ_0 H_0 \leq 1 \, \mathrm{T}$), we find that the chiral function is only nonzero when the DMI is taken into account in the simulations. This result is discussed within the context of the symmetry properties of the magnetization Fourier components and of the involved energies under space inversion. Finally, for small applied magnetic fields, we provide an easy-to-implement analytical correlation function for the DMI-induced spin modulations (with wave vector $k_{\mathrm{d}}$). The corresponding randomly-averaged spin-flip SANS cross section reproduces the main features found in the numerical simulations.