Response of the Skyrmion Lattice in MnSi to Cubic Magnetocrystalline Anisotropies.

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-(Q) over right arrow. state, where the modulus vertical bar(Q) over right arrow vertical bar is constant and the wave vectors enclose rigid angles of 120 degrees. Along a great circle across < 100 >, < 110 >, and < 111 > the normal to the Skyrmion-lattice plane varies systematically by +/- 3 degrees with respect to the field direction, while the in-plane alignment displays a reorientation by 15 degrees 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.