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Charge and Orbital Order in Transition Metal Oxides

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issue 2
212-231
EN
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.
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Spin-Orbital Physics in Transition Metal Oxides

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EN
We present the main features of the spin-orbital superexchange which describes the magnetic and optical properties of the Mott insulators with orbital degrees of freedom. In contrast to the SU(2) symmetry of spin superexchange, the orbital part of the superexchange obeys the lower cubic symmetry of the lattice and is intrinsically frustrated. This intrinsic frustration and spin-orbital entanglement induce enhanced quantum fluctuations, and we point out a few situations where this leads to disordered states. Strong coupling between the spin and orbital degrees of freedom is discussed on the example of the RVO_3 perovskites, with R standing for rare-earth ion, La,...,Lu. We explain the observed evolution of the orbital T_{OO} and Néel T_{N1} transition temperature in the RVO_3 series with decreasing ionic radius r_R. A few open problems and the current directions of research in the field of spin-orbital physics are pointed out.
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Acta Physica Polonica A
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2015
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vol. 127
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issue 2
163-169
EN
We review the consequences of intrinsic frustration of the orbital superexchange and of spin-orbital entanglement. While the Heisenberg perturbing interactions remove frustration in the compass model, the lowest columnar excitations are robust in the nanoscopic compass clusters and might be used for quantum computations. Entangled spin-orbital states determine the ground states in some cases, while in others concern excited states and lead to measurable consequences, as in the RVO₃ perovskites. On-site entanglement for strong spin-orbit coupling generates the frustrated Kitaev-Heisenberg model with a rich magnetic phase diagram on the honeycomb lattice. Frustration is here reflected in hole propagation which changes from coherent in an antiferromagnet via hidden quasiparticles in zigzag and stripe phases to entirely incoherent one in the Kitaev spin liquid.
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