Mean-field study of the disordered ground state in theβ−Mnlattice

The type-II atoms in the $\beta$ phase of manganese form a three-dimensional network of corner-sharing triangles in a cubic symmetry. This peculiar geometry induces a very strong topological frustration that can explain the absence of magnetic ordering in the $\beta$ phase of manganese. Within a mean-field theory, we show that the classical antiferromagnetic Heisenberg model with nearest-neighbor interactions exhibits a line of zero energy modes. Thus this model does not order at any temperature on this lattice in the mean-field approximation. Longer-range interactions or slight deformations do not always remove the ground-state degeneracy, and the model will order only for peculiar sets of exchange parameters.