Quantum form of the double-exchange interaction

Abstract

A quantum form of the Hamiltonian for a double-exchange ͑DE͒ system, based on the results of Anderson and Hasegawa's semiclassical treatment, is presented together with several predictions. The magnetization decreases mainly in 3/2 and 5/2 powers of temperature at low temperature but includes a T 3 term. The Curie temperature, in a rescaled DE coupling energy (ͱ2b/2S 2 )J d unit, is dependent on hole concentration x and has highest value that is about 1/3 that of ordinary Heisenberg magnet at xϭ0.5. The susceptibility at high temperatures lacks a 1/T 2 term and has a characteristic temperature in rescaled DE coupling units that is about 3/4 that of Heisenberg magnet in molecular-field theory.

Green’s function method applied to the paramagnetic properties of R1−xXxMnO3

“…Our T c s are in approximate coincidence with the experimental values [13]. Especially, for La 0.67 Ca 0.33 MnO 3 , our T c = 286 K approximately agrees with the experimental values T c = 250 K [10] and 260 K [13], but disagrees with T c = 1050 K which is calculated from the quantum DE theory [8]. If the quantum DE theory includes the lattice distortion effect [9], band-structure calculations lead to T c = 270 K [8].…”

“…lattice effect, as pointed out by Millis et al [9]. Since the lattice degree of freedom does not need to be added to explain CMR, the Curie temperature T c obtained from the semiclassical [5] and quantum [8] treatment is much higher than the experimental T c [9,10].…”

“…Recently, a quantum form of the Hamiltonian [8] for the DE system, based on the results of the Anderson and Hasegawas semiclassical treatment [5], has been presented. However, in real CMR materials there are a large number of ions and electrons.…”

Mössbauer study of the relationship between magnetic properties and Jahn–Teller distortion in La1–xBax(Mn,Fe)O3 perovskites

“…More and more evidence has indicated that the DE model alone is not sufficient to explain the CMR effect. For example, if we take only the DE interaction into account, the value of the Curie temperature (T c ) for R 1-x M x MnO 3 (R = La, Nd, Pr and M = Sr, Ca, Ba) is theoretically expected to reach a maximum at x = 0.5 [5], rather than around x = 0.33. Furthermore, the theoretical value of T c is much higher than the experimental one.…”

Green’s function treatment of the localized antiferromagnetic system

“…Previously, we developed a quantum form Hamiltonian for the double exchange (DE) interaction and showed that quantum localized spins appear in a linear form of the scalar product in the Hamiltonian that can be treated in a way similar to a pure Heisenberg magnet. 2 Second, as De Gennes 3 pointed out, in hole-doped manganites the DE interaction will compete with antiferromagnetic superexchange (SE). The latter can be written in a typical Heisenberg form.…”