A novel spin wave expansion, finite temperature corrections and order from disorder effects in the double exchange model

TL;DR

This paper develops a novel large S expansion for the double exchange model, revealing that quantum and thermal corrections lead to complex magnetic behaviors beyond the simple Heisenberg model, including order from disorder phenomena.

Contribution

It introduces a new spin wave expansion and effective Hamiltonian for the double exchange model, explicitly incorporating charge fluctuations and quantum corrections.

Findings

Quantum and thermal corrections differ from effective Heisenberg models.

Competition between double exchange and superexchange leads to order from disorder.

Intermediate magnetic states are stabilized by fluctuations when interactions are comparable.

Abstract

The magnetic excitations of the 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 quasi--classical level -- both quantum and thermal corrections to the magnetic properties of 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 novel 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 by itself an operator, and explicitly constructed new fermionic and bosonic operators to fourth order in 1/\sqrt{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 1/S expansion to order O(1/S^2). 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 a new 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.