We report high-precision small-angle neutron scattering of the orientation of the Skyrmion lattice in a spherical sample of MnSi under systematic changes of the magnetic field direction. For all field directions the Skyrmion lattice may be accurately described as a triple-$\overrightarrow{Q}$ state, where the modulus $|\overrightarrow{Q}|$ is constant and the wave vectors enclose rigid angles of 120°. Along a great circle across $⟨100⟩$, $⟨110⟩$, and $⟨111⟩$ the normal to the Skyrmion-lattice plane varies systematically by $\pm 3°$ with respect to the field direction, while the in-plane alignment displays a reorientation by 15° for magnetic field along $⟨100⟩$. Our observations are qualitatively and quantitatively in excellent agreement with an effective potential, which is determined by the symmetries of the tetrahedral point group $T$ and includes contributions up to sixth order in spin-orbit coupling, providing a full account of the effect of cubic magnetocrystalline anisotropies on the Skyrmion lattice in MnSi.

• Received 16 February 2018
• Revised 5 October 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.187205