Phase diagram of a generalized Hubbard model applied to orbital order in manganites

Abstract

The magnetic phase diagram of a two-dimensional generalized Hubbard model proposed for manganites is studied within Hartree-Fock approximation. In this model the hopping matrix includes anisotropic diagonal hopping matrix elements as well as off-diagonal elements. The antiferromagnetic ͑AF͒, ferromagnetic ͑F͒, canted ͑C͒, and paramagnetic ͑P͒ states are included in the analysis as possible phases. It is found that away from half-filling only the canted and F states may exist and AF and P states which are possible for the usual Hubbard model do not appear. This is because the F order has already developed for on-site repulsion Uϭ0 due to the hopping matrix of the generalized model. When applied for manganites the orbital degree is described by a pseudospin. Thus our ''magnetic'' phase diagram obtained physically describes how orbital order changes with U and with doping for manganites. Part of our results are consistent with other numerical calculations and some experiments.

Orbital liquid in ferromagnetic manganites: The orbital Hubbard model foregelectrons

“…28 The AO order is then followed by the FOx phase above a critical doping, which decreases with increasing U/t. We note that the region of the FOx phase is enlarged by the offdiagonal hopping terms ∝ γt, 38 in agreement with the above observation that these terms stabilize the FO phases at finite U due to the respective SE energy contributions.…”

“…56 The situation could be somewhat different in the 2D case, however, where a tendency towards particular orbital orderings with larger amplitude of x 2 −y 2 orbitals is favored by geometry. 28,38 We considered specifically the U = ∞ limit, where the OL competes with fully polarized ordered phases and we have shown that it is more stable than any of either uniform FO (4.21) or staggered AO (4.22) states. However, at finite U and for sufficiently low doping x, real-orbital C-AO order is stabilized by a superposition of the SE and the JT effect.…”

Colossal magnetoresistant materials: the key role of phase separation

“…The unstable character of the low hole-density region of the phase diagram corresponding to the one-orbital model for manganites has also been analyzed by other authors using mostly analytic approximate techniques. In fact, Arovas and Guinea (1998) found an energy convex at small hole concentration, indicative of phase separation, within a mean-field treatment of the one-orbital model using the Schwinger formalism (see also Mishra et al (1997), Arovas, Gomez-Santos, and Guinea (1999); Guinea, Gomez-Santos, and Arovas (1999); ; Chattopadhyay, Millis and Das Sarma (2000); and Yuan, Yamamoto, and Thalmeier, 2000). Nagaev (1998) using the one-orbital model also arrived at the conclusion that the canted AF state of the small hole density region is unstable.…”

Magnetic, orbital, and charge ordering in the electron-doped manganites

“…11a -above this value A-phase shifts below x = 0.5 at J H S 0 = 5. In the large U ′ limit and in the absence of J AF and V , the Hamiltonian can be mapped onto a pseudospin Hubbard model [24,90] with off-diagonal hopping (that breaks the SU(2), while still retaining the global U(1) symmetry). Such a model overestimates the orbital order [90] and the orbital-paramagnetic state is almost never obtained.…”