In the framework of the three-band model for CuO 2 plane in hightemperature superconductors the spectrum of the spin-polaron hole exitation is investigated. The problem is treated taking into account the coupling of a local polaron with the antiferromagnetic spin wave with Q = (π, π).This leads to the essential changes of the lowest polaron band ǫ 1 (k) and the strong redistribution of the bare electron filling. PACS number(s): 74.72.-h. 75.10-b In order to understand the nature of high-temperature superconductors it is important to describe properly the motion of a hole in the CuO 2 plane [1,2]. This motion takes place on the antiferromagnetic (AFM) spin background of copper spins and it must be treated as a correlated motion of a hole coupled to spin excitations (a spin polaron). Usually the spin polaron is studied within the frameworks of the t-J model [1] and the three-band Hubbard model [3,4,5]. In the previous works the spin polaron problem was studied mainly in the approximation of a small radius polaron ( an analogous of a Zang -Rise polaron). In the present work, for the first time, the long range order of the AFM background is taken into account by introducing an additional new spin polaron of an infinite radius -a bound state of a charge exitation and a spin wave with Q = (π, π).We shall show that the introduction of such a 1
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