A compact expression has been obtained for the superexchange coupling of magnetic ions via intermediate anions with regard to polaron effects at both magnetic ions and intermediate anions. This expression is used to analyze the main features of the behavior of isotope shifts for temperatures of three types in layered cuprates: the Neel temperatures (TN ), critical temperatures of transitions to a superconducting state (TC), and characteristic temperatures of the pseudogap in the normal state (T * ).
In a frame of the $t-J-G$ model we derive the microscopical expression for
the circulating orbital currents in layered cuprates using the anomalous
correlation functions. In agreement with $\mu$-on spin relaxation ($\mu$SR),
nuclear quadrupolar resonance (NQR) and inelastic neutron scattering(INS)
experiments in YBa$_2$Cu$_3$O$_{6+x}$ we successfully explain the order of
magnitude and the monotonous increase of the {\it internal} magnetic fields
resulting from these currents upon cooling. However, the jump in the intensity
of the magnetic fields at T$_c$ reported recently seems to indicate a
non-mean-field feature in the coexistence of current and superconducting states
and the deviation of the extended charge density wave vector instability from
its commensurate value {\bf Q}$\approx(\pi,\pi$) in accordance with the
reported topology of the Fermi surface
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