Noncollinear Ground State from a Four-Spin Chiral Exchange in a Tetrahedral Magnet

We propose a quartic chiral term m_{x}m_{y}m_{z}∇·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 noncollinear magnetic cone ground state provided its strength exceeds the geometric mean of magnetic exchange and cubic anisotropy. The corresponding noncollinear 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.