Peculiarities in the electron structure of weakly doped fullerites AxC60 (x ≪ 1)

Elastic interactions and superstructures in manganites and other Jahn-Teller systems

“…One can see that indeed the signs of the QQ interactions in (17) coincide with those of elastic interactions (see Table 1); this gives an extra support to these values used in the main part of our paper. Moreover, even the ratios of the interaction constants are rather close, at least for cases 1) -4).…”

“…For anisotropic impurities, like JT centers considered in this paper, this interaction depends not only on the relative direction between sites in a crystal, but also on the relative local distortions on each site. As a result, this interaction becomes very complicated [16,17]. In addition to long-range interactions mediated by the strain field in a crystal, there exists also the interaction mediated by the short-range, or optical, vibrations.…”

“…Often, for analysis of elastic interactions of impurities, further simplifications are introduced, namely the longitudinal and transverse sound velocities are taken to be equal. This leads to a rather simple explicit expression for the interaction between Jahn-Teller ions with different occupied orbitals, situated at arbitrary positions with respect to crystal axes [17]. For some problems (e.g.…”

Why stripes? Spontaneous formation of inhomogeneous structures due to elastic interactions

“…The interaction between such impurities also decays as 1/R 3 and has different signs depending on both the relative position of such centres in a crystal and on the orientation of the corresponding orbitals (i.e. local distortions) [20,21]. Thus, for example, for two quadrupolar ions along the z-axis with the electron density elongated parallel to x, y, or z axes, as is the case of e g -ions like Mn 3+ , one obtains from the general expressions [20] the interaction in the form V = (c 11 + c 44 ) 8π(c 11 + 2c 44 )R 3 5σ (1) zz σ (2) zz + 2 σ (1) xx σ (2) xx + σ (1) yy σ (2) yy + + 1 4πR 3 2σ (1) zz σ (2) zz − σ (1) xx σ (2) xx − σ (1) yy σ (2) yy , (5) where c 11 and c 44 are elastic moduli, and σ αα is a stress tensor such that, e.g.…”