Quadrupole Phase Transitions in Magnetic Solids

We have studied the phase transitions of magnetic systems with large biquadratic interactions in the molecular-field approximation. Quadrupole and dipole phase transitions occur at different temperatures whenever the biquadratic interactions are greater than the bilinear terms for effective spin interactions with $\mathcal{S}>~\frac{3}{2}$. For isotropic or Ising-like interactions with $\mathcal{S}=1\mathrm{}$ there is only a quadrupole phase transition when the biquadratic interactions are larger.