Calculation of the Cross Sections for Neutron Scattering at Spin Waves in Helimagnets

Abstract

An analytical dependence of the cross section for the small-angle scattering of polarized neutrons at spin waves in helimagnets formed because of Dzyaloshinskii—Moriya interaction in cubic crystals without an inversion center (the space group is P213) is obtained. It is assumed that the dispersion of spin waves in helimagnets with the wave vector k s polarized by a magnetic field is larger than the critical field HC2 of the transition to the ferromagnetic phase and has the form E q = A(q − k s ) + gμB(H − HС2). It is shown that the cross section for neutron scattering at the two-dimensional map of angles (θ x , θ y ) is two circles of the radii θC with the centers ±θ S , corresponding to the Bragg angle of diffraction by a helix oriented along the applied magnetic field H. The radii of these two circles θC are directly related to the stiffness of spin waves A of the magnetic system and depends on the applied magnetic field: $$\theta _C^2 = \theta _0^2 - \frac{{g{\mu _B}H}}{{{E_n}}}{\theta _0}$$ , where $${\theta _0} = \frac{{{h^2}}}{{2A{m_n}}}$$ and E n and m n are the neutron energy and mass. It is shown that the scattering cross section depends on the neutron polarization, which is evidence of the chiral character of spin waves in the Dzyaloshinskii—Moriya helimagnets even in the completely polarized phase. The cases of neutron scattering at magnons where θ0 ≤ θ S and θ S ≥ θ0 are considered. The case of neutron scattering at spin waves in helimagnets is compared with analogous scattering at ferromagnets where θ S → 0.