Spin-wave expansion, finite temperature corrections, and order from disorder effects in the double exchange model

The magnetic excitations of a double-exchange (DE) model are usually discussed in terms of an equivalent ferromagnetic Heisenberg model. We argue that this equivalence is valid only at a quasiclassical level - both quantum and thermal corrections to the magnetic properties of a DE model differ from any effective Heisenberg model because its spin excitations interact only indirectly, through the exchange of charge fluctuations. To demonstrate this, we perform a large-S expansion for the coupled spin and charge degrees of freedom of the DE model, aimed at projecting out all electrons not locally aligned with core spins. We generalized the Holstein-Primakoff transformation to the case when the length of the spin is an operator by itself, and explicitly construct fermionic and bosonic operators to fourth order in 1/√S. This procedure removes all spin variables from the Hund coupling term, and yields an effective Hamiltonian with an overall scale of electron hopping, for which we evaluate corrections to the magnetic and electronic properties in a 1/S expansion to order O(1/S²). We also consider the effect of a direct superexchange antiferromagnetic interaction between core spins. We find that the competition between ferromagnetic double exchange and an antiferromagnetic superexchange provides on example of an "order from disorder" phenomenon-when the two interactions are of comparable strength, an intermediate spin configuration (either a canted or a spiral state) is selected by quantum and/or thermal fluctuations.