Charge and Orbital Order in Transition Metal Oxides

Abstract

A short introduction to the complex phenomena encountered in transition metal oxides with either charge or orbital or joint charge-and-orbital order, usually accompanied by magnetic order, is presented. It is argued that all the types of above ordered phases in these oxides follow from strong Coulomb interactions as a result of certain compromise between competing instabilities towards various types of magnetic order and optimize the gain of kinetic energy in doped systems. This competition provides a natural explanation of the stripe order observed in doped cuprates, nickelates and manganites. In the undoped correlated insulators with orbital degrees of freedom the orbital order stabilizes particular types of anisotropic magnetic phases, and we contrast the case of decoupled (disentangled) spin and orbital degrees of freedom in the manganites with entangled spin-orbital states which decide about certain rather exotic phenomena observed in the perovskite vanadates at finite temperature. Examples of successful concepts in the theoretical approaches to these complex systems are given and some open problems of current interest are indicated. Degrees of freedom in transition metal oxidesThe physical properties of transition metal oxides are driven by strong electron interactions [1]. It is due to strong local Coulomb interactions that these systems exhibit very interesting and quite diverse instabilities towards ordered magnetic phases when doping x or temperature T is varied -is some cases also with orbital order. These instabilities are observed, inter alia, in rapid changes of the transport properties at the metalinsulator phase transitions, or in the onset of superconductivity.One of the outstanding problems in modern condensed matter theory is the description of strongly correlated electrons in various systems. When local Coulomb interactions are strong, the usual methods used for calculating the electronic structure fail and have to be extended by the terms following from local interactions, either in the framework of the local density approximation (LDA) with Coulomb U , the so-called LDA+U method [2], or by the self-energy within the dynamical mean-field theory (DMFT) [3], in the LDA + DMFT approach [4]. This latter approach makes use of the local self-energy which becomes exact in the limit of infinite spatial dimension d = ∞ [5]. However, even these methods cannot overcome certain shortcomings of the effective one-particle theory which justifies modelling of the transition metal * Dedicated to the memory of the late Professor Jan Stankowski. * * e-mail: a.m.oles@fkf.mpg.de oxides with Hamiltonians of the Hubbard type, and looking for solutions with methods of quantum many-body theory. The advantage of recent rapid progress in the electronic structure calculations is that such models can use realistic parameters nowadays, which follow from the electronic structure calculations for a given system. Although the field of strongly correlated electronic systems is very rich, we shall concentrate here on the phe...

Direct Visualization of Spatial Inhomogeneity of Spin Stripes Order in La1.72Sr0.28NiO4

“…The detection of the complex magnetic structures in strongly correlated electron systems by X-ray diffraction [56,57] can be used to support the association of the spin signal to polaronic distortions. The new mesoscopic phase separation with scale free spatial correlation for spin stripes order found here in nickelates is in agreement with previous indications [53][54][55][56][57][58][59] and it provides the experimental smoking gun evidence that the spin ordering in spin stripes phase in nickelates is near a quantum critical point. A similar spatial fractal landscape has been found in cuprates [46][47][48][49][50][51][52] and in other oxides near a quantum phase transition as in VO 2 [60][61][62][63], in ruthenates [64,65], and in diborides [66,67].…”

“…Therefore, the phase separation reported in this work could be assigned also to the liquid-striped liquid phase separation in liquids of anisotropic polarons similar to the liquid-striped liquid phase separation in water [49,50]. The anisotropy of polaron clusters in nickelates is assigned here to misfit strain [51,52] and orbital degrees of freedom [53][54][55]. The detection of the complex magnetic structures in strongly correlated electron systems by X-ray diffraction [56,57] can be used to support the association of the spin signal to polaronic distortions.…”

Fingerprints of spin–orbital entanglement in transition metal oxides

“…It will be shown that a rather exotic behaviour of the RVO 3 perovskites cannot be understood without including the spin-orbital entangled states. This point of view is supported by several experimental observations: (i) the thermal evolution of the optical spectral weights [25], (ii) the phase diagram of the RVO 3 perovskites [21], and (iii) the observed dimerization in the magnon spectra of YVO 3 [26].An interesting situation arises also in doped Mott insulators, where doped holes introduce charge degrees of freedom which perturb the orbital order and frequently lead to phases with coexisting spin, charge and orbital order [27]. When orbital degrees of freedom are quenched, one finds that hole propagation occurs in the t-J model via a quasiparticle state that emerges due to quantum fluctuations in the spin background [28].…”

Jahn–Teller distortions and the magnetic order in the perovskite manganites

“…Investigation of doped manganites is challenging as the Jahn-Teller distortions may lead to the charge order which will also favour particular orbital order [1,27]. To make the complex situation in doped manganites tractable in the theory, several theoretical papers were focused in past on single-layer and double-layer manganites as the description of quasi two-dimensional (2D) systems was simpler than the one necessary for three-dimensional (3D) doped perovskite manganites (see for example [11] and the references therein).…”