Spin-One Heisenberg Ferromagnet in the Presence of Biquadratic Exchange

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Abstract
The statistical-mechanical properties of a spin-one Heisenberg ferromagnet with isotropic nearest-neighbor biquadratic interactions are discussed. First, conditions for having an exact ferromagnetic ground state are found and the dispersion relation for magnons is derived. Then the relevant thermodynamical properties are obtained in a generalized molecular-field approximation (MFA). It is shown that if three stable phases, paramagnetic, "quadrupolar," and ferromagnetic, come into play in the discussion, ferromagnetic ordering is always preferred to "quadrupolar" ordering, preventing the latter from appearing as a separate phase transition. The critical ratio of bilinear to biquadratic exchange for the onset of a first-order ferromagnetic transition is obtained.