Non-collinear ground state from a four-spin chiral exchange in a tetrahedral magnet

We propose a quartic chiral term $m_x{m}_y{m}_z\mathrm{\nabla }\cdot \mathbf{m}$ for the energy density of a cubic ferromagnet with broken parity symmetry (point group $T_d$). We demonstrate that this interaction causes a phase transition from a collinear ferromagnetic state to a non-collinear magnetic cone ground state provided its strength exceeds the geometric mean of magnetic exchange and cubic anisotropy. The corresponding non-collinear ground state may also be additionally stabilized by an external magnetic field pointing along certain crystallographic directions. The four-spin chiral exchange does also manifest itself in peculiar magnon spectra and favors spin waves with the wave vector that is perpendicular to the average magnetization direction.