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The retarded Green's function G(k, ω) of a single small spin polaron in the three-band model for the CuO 2 plane is calculated in the self-consistent Born approximation. It is shown that such a spin polaron is a good quasiparticle excitation for realistic values of spin exchange J and effective hopping τ . The polaron spectral density A p (k, ω) demonstrates small damping in contrast to the results of calculations starting from the bare hole, i.e. the pole strength of the energetically low-lying quasiparticle peak Z p (k) varies from 50% to 82%

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We study the phase diagram of the spin-orbital model in both the weak and strong limits of the quartic spin-orbital exchange interaction. This allows us to study quantum phase transitions in the model and to approach from both sides the most interesting intermediate-coupling regime and in particular the SU (4)-symmetric point of the Hamiltonian. It was suggested earlier by Li et al [Phys. Rev. Lett. 81, 3527 (1999)] that at this point the ground state of the system is a plaquette spin-orbital liquid. We argue that the state is more complex. There is plaquette order, but it is anisotropic: bonds in one direction are stronger than those in the perpendicular direction. This order is somewhat similar to that found recently in the frustrated J1 − J2 Heisenberg spin model. 75.10.Jm, 75.40.Gb