Pseudogap phase in cuprates: Oxygen orbital moments instead of circulating currents

Circulating current loops within the cuprate unit cell are proposed to play a key role in the physics of the pseudogap phase. However, main experimental observations motivated by this sophisticated proposal and seemingly supporting the circulating current model can be explained within a simple and physically clear microscopic model. It has been argued that, instead of a well-isolated Zhang-Rice (ZR) singlet ¹ A _1g , the ground state of the hole center CuO₄]^5? (cluster analog of Cu³⁺ ion) in cuprates should be described by a complex ¹ A _1g -^1,3 B _2g -^1,3 E _u multiplet, formed by a competition of conventional hybrid Cu 3d-O 2p $b_{1g} (\sigma ) \propto d_{x^2 - y^2 }$ state and purely oxygen nonbonding O 2p?? states with a _2g (??) and e _{ux, y} (??) symmetry. In contrast to inactive ZR singlet we arrive at several novel competing orbital and spin-orbital order parameters, e.g., Ising-like net orbital magnetic moment, orbital toroidal moment, intra-plaquette??s staggered order of Ising-like oxygen orbital magnetic moments. As a most impressive validation of the non-ZR model we explain fascinating results of recent neutron scattering measurements that revealed novel type of magnetic ordering in pseudogap phase of several hole-doped cuprates.