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Volumn 79, Issue 22, 2009, Pages

Orbitally induced string formation in the spin-orbital polarons

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EID: 68949108616     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.79.224433     Document Type: Article
Times cited : (45)

References (50)
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    • Apart from considered here processes connected with the hopping t (string formation) other coupling mechanisms, e.g., due to the electron-phonon interaction, may contribute to orbital polaron formation; see, e.g., 10.1103/PhysRevB.60.13458
    • Apart from considered here processes connected with the hopping t (string formation) other coupling mechanisms, e.g., due to the electron-phonon interaction, may contribute to orbital polaron formation; see, e.g., R. Kilian and G. Khaliullin, Phys. Rev. B 60, 13458 (1999). 10.1103/PhysRevB.60.13458
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    • Note that although the string picture alone cannot explain the previously mentioned hole motion in the AF ordered state, it may serve as a perfect starting point for the investigation of the behavior of holes doped into the AF phases; see 10.1103/PhysRevB.78.064501
    • Note that although the string picture alone cannot explain the previously mentioned hole motion in the AF ordered state, it may serve as a perfect starting point for the investigation of the behavior of holes doped into the AF phases; see P. Wróbel, W. Suleja, and R. Eder, Phys. Rev. B 78, 064501 (2008). 10.1103/PhysRevB.78.064501
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    • A simpler case of a hole doped into the generic spin-orbital t-J model was studied in Ref., where the hole could move only by its coupling either to orbitons or to magnons, but not to both of them simultaneously. Besides, the formation of the spin-orbital polarons was discussed in the lightly doped cobaltates but the orbital degrees of freedom there were integrated out; see 10.1103/PhysRevLett.96.216404
    • A simpler case of a hole doped into the generic spin-orbital t-J model was studied in Ref., where the hole could move only by its coupling either to orbitons or to magnons, but not to both of them simultaneously. Besides, the formation of the spin-orbital polarons was discussed in the lightly doped cobaltates but the orbital degrees of freedom there were integrated out; see M. Daghofer, P. Horsch, and G. Khaliullin, Phys. Rev. Lett. 96, 216404 (2006). 10.1103/PhysRevLett.96.216404
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    • It is only the unusual coexistence of the C-AF phase and the metallic phase that was to some extent explained using the classical double exchange model adopted to the t2g orbital symmetries; see: K. Wohlfeld and A. M. Oleś, Phys. Status Solidi B 243, 142 (2006). 10.1002/pssb.200562500
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    • We have verified analytically that these terms would not lead to any k dependence in the spectra as in the self-energies describing such processes one can shift the summation over the momenta in such a way that the self-energies are momentum independent (See also Sec. 3 for a similar calculation concerning the self-energies for two boson lines). Thus, these terms would not change the qualitative feature of the calculated spectra, i.e., that the k dependence of the quasiparticle states originates entirely from the three-site terms. Besides, we note that inclusion of such terms would require going beyond the LSW and LOW approximation, i.e., we would have to include the interactions between magnons and/or orbitons.
    • We have verified analytically that these terms would not lead to any k dependence in the spectra as in the self-energies describing such processes one can shift the summation over the momenta in such a way that the self-energies are momentum independent (See also Sec. 3 for a similar calculation concerning the self-energies for two boson lines). Thus, these terms would not change the qualitative feature of the calculated spectra, i.e., that the k dependence of the quasiparticle states originates entirely from the three-site terms. Besides, we note that inclusion of such terms would require going beyond the LSW and LOW approximation, i.e., we would have to include the interactions between magnons and/or orbitons.
  • 45
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    • Note, that only for didactic purpose in Secs. 5 5 we calculate the spectral functions for η=0. However, one should bear in mind that such a value is unphysical and inconsistent with the assumed infinite value of the Hund's coupling in Eq. 2.2.
    • Note, that only for didactic purpose in Secs. 5 5 we calculate the spectral functions for η=0. However, one should bear in mind that such a value is unphysical and inconsistent with the assumed infinite value of the Hund's coupling in Eq. 2.2.
  • 47
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    • The obtained value of the incoherent bandwidth W=4t in the classical limit well agrees with the retraceable path approximation (RPA) formula W=4 teff l, where the effective hopping teff =t/2 due to the double exchange and l=2 is the number of possible forward going steps in the classical spin-orbital model, cf. discussion in the end of Sec. VC in Ref.. Note also that the narrowing of the bandwidth in the quantum case is due to the fact that the effective number of forward going steps, which the hole can make so that the spins become misaligned (which is the essence of RPA), is slightly reduced. This is because some of the spins are already overturned due to the quantum spin fluctuations in the full quantum model.
    • The obtained value of the incoherent bandwidth W=4t in the classical limit well agrees with the retraceable path approximation (RPA) formula W=4 teff l, where the effective hopping teff =t/2 due to the double exchange and l=2 is the number of possible forward going steps in the classical spin-orbital model, cf. discussion in the end of Sec. VC in Ref.. Note also that the narrowing of the bandwidth in the quantum case is due to the fact that the effective number of forward going steps, which the hole can make so that the spins become misaligned (which is the essence of RPA), is slightly reduced. This is because some of the spins are already overturned due to the quantum spin fluctuations in the full quantum model.
  • 49


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