Order-order transitions in spin systems with double electron exchange

Spin systems in the presence of isotropic single and double electron exchange are investigated at nonzero temperature. We use a generalized mean field approximation that allows for a variable local axis of quantization. This leads to the introduction of an angular parameter Θ giving the angle between nearest neighbor quantization axes. It is shown that order-order transitions can occur between phases of partially aligned spins (general Θ) and pure ferro- (Θ = 0) or antiferromagnetic (Θ = π) spin structures for physically reasonable values of the exchange ratio J₂/J₁ of double to single exchange when J₂ > 0. The order-order critical temperature τ₀ is determined as a function of J₂/J₁ for the particular cases of atomic spin $\text{s = 1,}\text{3}\text{2}\text{, 2,}\text{5}\text{2}$, and the corresponding phase diagrams are presented. Biquadratic and three-atom double electron exchange effects are considered separately. Expressions for the paramagnetic transition temperature and for the spontaneous magnetization M_s for general atomic spin s are given, and the discontinuous change in M_s at τ₀ is also found as a function of J₂/J₁.