Nature of a phase transition and low-temperature phase in cubic ferromagnets

A $S=2\mathrm{}$ ferromagnet with a crystalline field of the cubic symmetry is studied. It is shown that in the case of the three easy axes [100] the model which contains only the Heisenberg bilinear interaction and single-ion anisotropy terms exhibits at a finite temperature the phase transition to a nonmagnetic phase with a long-range quadrupolar order. It is also pointed out if the recent result that in three dimensions the cubic fixed point is stable for the $\mathrm{}(n=3\mathrm{})\mathrm{}$-component cubic spin model (Kleinert, Thoms, and Schulte-Frohlinde) is correct, all cubic ferromagnets with three easy axes, for example Fe, should undergo a first-order (discontinuous) phase transition.