Three-body correlation effects on the spin dynamics of double-exchange ferromagnets

Abstract

We present a variational calculation of the spin wave excitation spectrum of double-exchange ferromagnets in different dimensions. Our theory recovers the Random Phase approximation and 1/S expansion results as limiting cases and can be used to study the intermediate exchange coupling and electron concentration regime relevant to the manganites. In particular, we treat exactly the long range three-body correlations between a Fermi sea electron-hole pair and a magnon excitation and show that they strongly affect the spin dynamics in the parameter range relevant to experiments in the manganites. The manifestations of these correlations are many-fold. We demonstrate that they significantly change the ferromagnetic phase boundary. In addition to a decrease in the magnon stiffness, we obtain an instability of the ferromagnetic state against spin wave excitations close to the Brillouin zone boundary. Within a range of intermediate concentrations, we find a strong softening of the spin wave dispersion as compared to the Heisenberg ferromagnet with the same stiffness, which changes into hardening for other concentrations. We discuss the relevance of these results to experiments in colossal magnetoresistance ferromagnets.

Magnetization relaxation and collective spin excitations in correlated double-exchange ferromagnets

“…Using this method, we derived a closed system of equations that treat the magnetic exchange and Coulomb interactions non-perturbatively and solved it to obtain the Green's function that determines the transverse spin susceptibility. Our results for the spin-wave dispersion reproduce previous variational 30, 41 and exact diagonalization 46,47 results (in the limit Γ,γ →0) and therefore allow us to draw definite conclusions regarding the magnitude of the spin-wave softening. Using the properties of the fully polarized Hartree-Fock ground state with maximum spin, we showed that our method gives the exact spin Green's function within a subspace of states that include up to one Fermi sea pair excitation.…”

“…(7), in the limit γ,Γ→0 the exact calculation of the Green's function within a given subspace it equivalent to the variational calculation of the spinwave energy using a variational wavefunction that is a linear combination of the states that span the subspace (obtained in Refs. [30,41] for the problem at hand). One could include multipair correlations, e.g., by extending the approach of Refs.…”

“…Similar to Refs. [30,41], our method becomes exact in the limits of one electron (N e =1, n=1/N ), half filling (N e =N , n=1), and in the atomic limit (t=0 for any n). It interpolates between the weak and strong coupling limits and agrees with exact diagonalization results for the spin-wave dispersion.…”

Magnons in ferromagnetic metallic manganites

“…Although the DE interaction is still the basic ingredient for the understanding of spin dynamics in the FM metallic manganites, at least three major classes of theoretical approaches beyond the canonical DE interaction haven been proposed. The first class is based on the DE interaction and under the ferromagnetic Kondo lattice model, considering the effects of finite Hund's coupling [60], quantum and thermal corrections [12], on-site Coulomb repulsion [11], three-body correlation [61], conducting electron band (e g ) filling dependence of the DE and superexchange interactions [42,62], and the non-Stoner continuum in the DE model [63]. The second class emphasizes the effect due to the quantum fluctuations of different e g -orbitals [64,65,28].…”

Spin Dynamics in (III,Mn)V Ferromagnetic Semiconductors: The Role of Correlations

“…In the simpler RPA case, which neglects inelastic effects, a sixband effective mass approximation [16] revealed an order of magnitude enhancement of D. The single-band RPA model [15] also predicts maximum D at very small hole concentrations, while in the six-band model D increases and then saturates with hole doping. Here we illustrate the main qualitative features due to ubiquitous correlations important in different ferromagnets [19,24] by adopting the single-band Hamiltonian [15]. We then discuss the role of the multi-band structure of (III,Mn)V semiconductors by using a heavy and light hole band model.…”