Relation between double exchange and Heisenberg model spectra: Application to the half-doped manganites

Abstract

The Zener polarons recently found in half-doped manganites are usually seen as mixed valence entities ruled by a double exchange Hamiltonian involving only correlated electrons of the metals. They can however be considered as ferrimagnetic local units if the holes are localized on the bridging oxygen atoms as implicitely suggested by recent mean-field ab initio calculations. In the latter case, the physics is ruled by a Heisenberg Hamiltonian involving magnetic oxygen bridges. This paper shows that the spectra resulting from the resolution of both models are analytically identical. This single resulting model spectrum accurately reproduces the spectrum of Zener polarons in Pr0.6Ca0.4MnO3 manganite studied by means of explicitely correlated ab initio calculations. Since the physics supported by each model are different, the analysis of the exact Hamiltonian ground state wave function should a priori enables one to determine the most appropriate model. It will be shown that neither the spectrum nor the wavefunction analysis bring any decisive arguments to settle the question. Such undecidability would probably be encountered in experimental information. [6,7] show an important O to Mn charge transfer, resulting in a localization of the holes on the bridging oxygens. This charge distribution suggests a dominant purely magnetic local order (Mn 3+ O − Mn 3+ ) in which the Zener polarons would be ferrimagnetic entities involving an antiferromagnetic coupling between the magnetic oxygen and the high spin manganese centers. In the latter case the model Hamiltonian which provides a relevant description of the local electronic order is a Heisenberg Hamiltonian. The holes localization has been a matter of debate in the literature and concerns a large number of materials like doped cuprates [8](where there is at most one unpaired electron per metal resulting in a t-J model), nickelates or manganites (in which there are several open-shells per center leading to a double exchange interaction). Besides, as far as the correlated electrons are only localized on the metallic centers, the comparison of the models has been the subject of intense discussion and controversy which ended up with the demonstration that the two models were strictly different and lead to different spectra [9]. The aim of this paper is to show that when considering a magnetic oxygen in the Heisenberg model the analytical resolution of the two Hamiltonians leads to identical spectra. For this purpose we have derived an analytical solution of the Heisenberg Hamiltonian energies for three magnetic centers.Since the discrimination between the two models is impossible from the spectrum determination, we will then adress this question from wavefunction analysis. Indeed, the projection of the ab initio ground state wavefunction onto both model spaces should a priori determine the choice. However, it will be shown that when the charge of the oxygen is around -1.5, the wavefunction analysis does not infer any decidable argument. In order to illustrate this asserti...

First-principles study of magnetic interactions in cupric oxide

“…Many articles have been published in which the magnetic coupling in ionic insulators has been successfully calculated (see for example Refs. [24][25][26][27]. Furthermore, access to the wave functions enables one to extract parameters using effective-Hamiltonian theory.…”

Study of the Electronic Structure of NiGa2S4 and Extraction of the Spin Hamiltonian Parameters from Ab Initio Calculations

“…From this identification, both the relevant operators and the values of their corresponding interactions can be determined rigorously and univocally. Such a procedure has been used successfully to extract subtle interactions such as electron transfer, [29][30][31][32] Coulomb repulsion, [33] isotropic magnetic coupling, [34][35][36][37][38][39][40] zero-field splitting (ZFS) parameters, [41][42][43][44][45][46][47][48][49][50][51] double exchange interactions, [52][53][54] exchange transfer terms, [30,33,[55][56][57] and three-and four-body terms. [58,59] The NiGa 2 S 4 material is a triangular quasi-two-dimensional lattice constituted of S = 1 (Ni 2+ ) interacting centers.…”

“…From this identification, both the relevant operators and the values of their corresponding interactions can be determined rigorously and univocally. Such a procedure has been used successfully to extract subtle interactions such as electron transfer, Coulomb repulsion, isotropic magnetic coupling, zero‐field splitting (ZFS) parameters, double exchange interactions, exchange transfer terms,, , and three‐ and four‐body terms , …”

Ab initiostudy of the CE magnetic phase in half-doped manganites: Purely magnetic versus double exchange description

“…The latter electronic structure is referred as a Zener polaron order in reference to Zener who first proposed the DE mechanism. 6 Ab initio calculations confirm the existence 7 of a charge-ordered phase (partial localization of the holes on one type of Mn ions) in the crystallographic structure of Radaelli et al 4 while a polaronic order 7,8,9,10 (delocalized holes between pairs of Mn ions) is obtained for the crystallographic structure of Daoud Aladine et al 5 It is worth to note that in both cases correlated ab initio calculations point out that there is a rather strong O to Mn charge transfer, resulting in a partial localization of the holes on the bridging oxygens. UHF and DFT periodic calculations 11,12,13 on La 0.5 Ca 0.5 MnO 3 even lead to a dominantly Mn 3+ O − Mn 3+ ground state charge distribution.…”

“…9 ii) the energies of the eight lowest states of the Heisenberg and the usual DE models are analytically identical and in qualitative agreement with those of the ab initio spectrum. 9,10 iii) a significant improvement is observed when the non-Hund excited atomic states are explicitely introduced in the modelization. 8 The remarkable accuracy of the resulting model spectrum finally shows that the Zener polaron physics is actually ruled by a refined DE mechanism where non-Hund atomic states play a non negligible role.…”