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 $\mathcal{S}=1$ there is only a quadrupole phase transition when the biquadratic interactions are larger.

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