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Note that in this paper phase separation in the (Formula presented) model between hole-rich ferromagnetic and hole-poor antiferromagnetic regions was also proposed. However, in the (Formula presented) model the ferromagnetic region occurs for unphysically small values of (Formula presented) while in the model for manganites studied in the present paper it occurs in a realistic region of parameter space. We thank S. Kivelson for this comment
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V. J. Emery, S. A. Kivelson, and H. Q. Lin, Phys. Rev. Lett. 64, 475 (1990). Note that in this paper phase separation in the (Formula presented) model between hole-rich ferromagnetic and hole-poor antiferromagnetic regions was also proposed. However, in the (Formula presented) model the ferromagnetic region occurs for unphysically small values of (Formula presented) while in the model for manganites studied in the present paper it occurs in a realistic region of parameter space. We thank S. Kivelson for this comment.
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this paper it was proposed that stripes and related structures are a generic feature of doped correlated insulators, in agreement with the results for manganites discussed here. We thank S. Kivelson for this comment
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V. J. Emery and S. A. Kivelson, Physica C 209, 597 (1993). In this paper it was proposed that stripes and related structures are a generic feature of doped correlated insulators, in agreement with the results for manganites discussed here. We thank S. Kivelson for this comment.
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particular, ferromagnetism appears as the density changes away from half-filling. At (Formula presented) an insulator was found. One may wonder if phase separation could not exist also in the AF Kondo model with localized spin 1/2, since at least for classical localized spins the FM and AF Kondo models are related by symmetry. With this motivation, and using the DMRG technique, results were collected on lattices with up to 40 sites, using an electronic (Formula presented) density (Formula presented) and with Hund couplings in the range from 0.0 to 4.0 in absolute value. However, and contrary to the naive expectation expressed above, the compressibility remained positive in the entire region explored and no indications of phase separation were found
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For completeness, the case of a Hund coupling of antiferromagnetic sign was also studied here. The motivation is the work in the context of the Kondo model for heavy fermions where similarities with the phase diagrams discussed in the present paper are observed [H. Tsunetsugu, M. Sigrist, and K. Ueda, Rev. Mod. Phys. 69, 809 (1997)].In particular, ferromagnetism appears as the density changes away from half-filling. At (Formula presented) an insulator was found. One may wonder if phase separation could not exist also in the AF Kondo model with localized spin 1/2, since at least for classical localized spins the FM and AF Kondo models are related by symmetry. With this motivation, and using the DMRG technique, results were collected on lattices with up to 40 sites, using an electronic (Formula presented) density (Formula presented) and with Hund couplings in the range from 0.0 to 4.0 in absolute value. However, and contrary to the naive expectation expressed above, the compressibility remained positive in the entire region explored and no indications of phase separation were found.
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See also J. Q. Li et. al Phys. Rev. Lett. 79, 297 (1997) for phase segregation in (Formula presented)
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