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We report high-precision small angle neutron scattering of the orientation ofthe skyrmion lattice in a spherical sample of MnSi under systematic changes ofthe magnetic field direction. For all field directions the skyrmion lattice maybe accurately described as a triple-$\vec{Q}$ state, where the modulus $\vert\vec{Q} \vert$ is constant and the wave vectors enclose rigid angles of$120^{\circ}$. Along a great circle across $\langle 100\rangle$, $\langle110\rangle$, and $\langle 111\rangle$ the normal to the skyrmion-lattice planevaries systematically by $\pm3^{\circ}$ with respect to the field direction,while the in-plane alignment displays a reorientation by $15^{\circ}$ formagnetic field along $\langle 100\rangle$. Our observations are qualitativelyand quantitatively in excellent agreement with an effective potential, that isdetermined by the symmetries of the tetrahedral point group $T$ and includescontributions up to sixth-order in spin-orbit coupling, providing a fullaccount of the effect of cubic magnetocrystalline anisotropies on the skyrmionlattice in MnSi.

Response of the skyrmion lattice in MnSi to cubic magnetocrystalline anisotropies