Incommensurate magnetic structures in rhombohedral Heisenberg antiferromagnet

The phase diagram of the ground state has been calculated for a rhombohedral antiferromagnet of the R3m symmetry with frustrated exchange in the base plane and competition of exchanges between the nearest and next-nearest planes. The diagram contains phases of collinear antiferromagnetic ordering of various types separated by five incommensurate magnetic states of the helicoidal type, differing in the ordering type and in the direction of the modulation vector. The commensurate and incommensurate phases converge at multi-critical points lying on a line corresponding to an antiferromagnet with an undistorted simple cubic lattice.