New type of antiferromagnetic polaron and bipolaron in HTc - superconductors

The possibility of formation of a new type of polaron based on the quantum aniferromagnet (AF) model is reported. We take into account exchange interactions between localized d-d spins of the AF, as well as the p-d interaction of the AF with p-carriers. The energy minimum is found when maximum charge density occurs on every second spin. The formation of such “comb”-like polarons results from the damping of quantum fluctuations and the appearance of Van Vleck-like staggered magnetization. Such polarons tend to form pairs coupled by an AF “glue”. There are some convincing arguments that occurrence of small polarons and bipolarons is responsible for the formation of a Bose liquid in HTc-superconductors [1, 2]. The mechanism of polaron and bipolaron formation, however, still remains an open question. Theoretical models of this effect invoke the phonons, excitons, plasmons as well as a magnetic “glue” [3, 4]. In this paper we show that the spin exchange interactions alone can lead to the formation of magnetic polarons. Moreover, a specific type of magnetic polarons, called by us the “comb-like” polarons, is characterized by a strong tendency for pair formation. For CuO2-based superconductors their binding energy is comparable to d-d coupling, Jd−d, i.e., of the order of 7.5 meV. We solve numerically the spin Hamiltonian which contains the term of d-d coupling between neighboring d-spins within the antiferromagnetic (AF) cluster, 2Jd−d Si · Sj , and the term of p-d exchange between the p-carrier and the dspins, Jp−d(i)Si · σ. The p-d exchange constants Jp−d(i) are assumed to be proportional to the carrier density at the i-th spin. The normalization condition of the carrier wave function guarantees that the sum of Jp−d(i) does not depend on the distribution, but is equal to a parameter Noα which describes the strength of the p-d coupling. We examine various polaron shapes. We found “comb-like” polarons, where the electron density is distributed on spins from only one of Neel sublattices, as the most energetically favorable (see