High-Pressure and Low-Temperature Physics pp 141-168 | Cite as

# Theoretical Approach to the Configuration Fluctuation in Sm-Chalcogenides

## Abstract

We present a theoretical approach to the problem of configuration mixing in Sm chalcogenides. Properties in the collapsed phase of SmS are discussed in terms of an essentially localized or excitonic picture of most of the Sm 5d-electrons, with a small number (≃.1 electrons per Sm) occupying the free-electron-like states at the bottom of a broad 5d-band. We review how such an essentially localized model for the 5d-electrons can lead to the observed results on volume and degree of mixing vs. pressure, low-T specific heat, dc electrical conductivity, plasma frequency, XPS intensities and magnetism. We also present new calculations of phase boundaries in the T-p plane, obtaining for SmS both a first order and a second order boundary within a simplified model. The latter boundary, which occurs e.g. at high p and low T makes contact with a recent experimental result of Guntherodt et al. The unusual shape of the observed first-order boundary is shown to be in accord with our general model, A new evaluation of the low frequency dielectric constant (ħω⋝.lev) shows behavior very similar to the unusual experimental results obtained recently by Batlogg et al. and by Allen. We compare the above picture with the more common models where all the 5d-electrons (~.7 per Sm in SmS) occupy free-electron like states, and give a critique of the latter.

## Keywords

Conduction Electron Narrow Band Hubbard Model Mixed Phase Plasma Edge## Preview

Unable to display preview. Download preview PDF.

## References

- 1.Valence Instabilities and Related Narrow-Band Phenomena, Edited by R.D. Parks, Plenum Press 1977.Google Scholar
- 2.T.A. Kaplan, S.D. Mahanti and Mustansir Barma, ref. 1, p. 153.Google Scholar
- 3.A. Jayaraman, V. Narayanamurti, E. Bucher, and R.G. Maines, Phys. Rev. B11, 2783 (1975); and ref. 1 p. 61.Google Scholar
- 4.J.M.D. Coey, S.K. Ghatak, and F. Holtzberg, AIP Conf. Proc. 24, 38 (1974); and ref. 1, p. 211.CrossRefGoogle Scholar
- 5.M.B. Maple and D. Wohlleben, Phys. Rev. Letters 27, 511 (1971).CrossRefGoogle Scholar
- 6.M. Campagna, E. Bucher, G.K. Wertheim, and L.D. Longinotti, Phys. Rev. Letters 33, 165 (1974). The X-ray photoemission studies were not made on SmS under pressure, but rather on Sm
_{1-X}R_{X}S where R = Y or Gd. The concentration x acts similarly to pressure (see e.g. ref. 3).CrossRefGoogle Scholar - 7.S.D. Bader, N.E. Phillips, and D.B. McWhan, Phys. Rev. B7, 4786 (1973).Google Scholar
- 8.E. Kaldis and P. Wachter, Sol. St. Comm. 11, 907 (1972);CrossRefGoogle Scholar
- 8a.B. Batlogg, A. Schlegel, and P. Wachter, Phys. Rev. B14, 5503 (1976).Google Scholar
- 9.B. Batlogg and P. Wachter, ref. 1, p. 537; J. W. Allen, ref. 1, p. 533 found a similar result in the mixed valence compound SmB
_{6}.Google Scholar - 10.E. Yu. Tonkov and I.L. Aptekar, Sov. Phys. Solid State 16, 972 (1974).Google Scholar
- 11.C.M. Varma, Rev. Mod. Phys. 48, 219 (1976).CrossRefGoogle Scholar
- 12.Some examples in addition to those discussed in ref. 11 are: L.L. Hirst, ref. 1, p. 3; T. Penney, ref. 1, p. 86; S.K. Ghatak and M. Avignon, ref. 1, p. 229; B. Alascio, ref. 1, p. 247; B. Coqblin, A.K. Bhattacharjee, J.R. Iglesias-Sicardi, and R. Jullien, ref. 1, p. 365; J.H. Jefferson and K.W.H. Stevens, ref. 1, p. 419. For others consult ref. 1.Google Scholar
- 13.According to the titles of the papers by S. Doniach, ref. 1, p. 169 and in Proc. of the Oxford Conference on Itinerant Electron Magnetism, Sept. 1976, to appear in Physica, his work would appear to fall under this band-model category. However, the specific model Hamiltonian studied is rigorously a localized model; whereas the connection to the band model is not rigorous.Google Scholar
- 14.T. A. Kaplan and S.D. Mahanti, Phys. Lett. 51A, 265 (1975).Google Scholar
- 15.S.D. Mahanti, T.A. Kaplan and M. Barma, Phys. Lett. 58A, 43 (1976).Google Scholar
- 15a.J. Schweitzer, Phys. Rev. B13, 3506 (1976), studied stability properties of the localized model.Google Scholar
- 16.A localized picture for most of the d-electrons in connection with SmB
_{6}, was discussed earlier by R.L. Cohen, M. Eibschütz and K.W. West, Phys. Rev. Lett. 24, 382 (1970)CrossRefGoogle Scholar - 16a.and in more detail by J.C. Nicfcerson, R.M. White, K.N. Lee, R. Bachmann, T.H. Geballe, and G.W. Hull, Jr., Phys. Rev. B3, 2030 (1971). A spatially homogeneous mixing was not considered, in contrast to ref.’s 2, 14, 15, and 15a.Google Scholar
- 17.F. Holtzberg and J. Torrance, AIP Conf. Proc. no. 5, 860 (1971).Google Scholar
- 18.The interpretation of ref. 17 followed the earlier work on the analogous situation in Eu compounds, by M.J. Freiser, S. Methfessel, and F. Holtzberg, J. Appl. Phys. 39, 900 (1968).CrossRefGoogle Scholar
- 19.J.W. McClure, J. Phys. Chem. Sd. 24, 871 (1963);CrossRefGoogle Scholar
- 19a.A. V. Golubkov, E.V. Goncharova, V.P. Zhuze and I.G. Manilova, Sov. Phys. Sol. St. 7,
*/*1963/ (1966).Google Scholar - 20.H.L. Davis, Proc. 9th Rare Earth Res. Conf., Va. Poly. Inst. and State Univ., Blacksburg, VA (1971).Google Scholar
- 21.K. Lendi, Phys. Cond. Matt. 17, 215 (1974).CrossRefGoogle Scholar
- 22.D.L. Greenaway and G. Harbeke, Optical Properties and Band Structure of Semiconductors, Pergamon Press (1968), p. 114.Google Scholar
- 23.A. Jayaraman, P.D. Dernier, and L.D. Longinotti, High Temperatures, High Pressures 7, 1 (1975).Google Scholar
- 24.The lowering of 0.6 ev. follows from T. Penney and F. Holtzberg, Phys. Rev. Lett. 33, 165 (1975), with ΔV/V — 12% across the transition.Google Scholar
- 25.Estimates were also made with a circular density of states, resulting in only minor changes.Google Scholar
- 26.C.M. Varma and V. Heine, Phys. Rev. B11, 4763 (1975).Google Scholar
- 27.One might worry about a possible discontinuous electron rearrangement as a function of V, such as that occurring in the Falicov-Kimball theory (Phys. Rev. Lett. 22, 997 (1969)), It is argued in Appendix 1 that this band theory is probably inconsistent with the stability of Sm
^{2+}at atmospheric pressure.Google Scholar - 28.L.L. Hirst, J. Phys. Chem. Solids 35, 1285 (1974).CrossRefGoogle Scholar
- 29.C.M. Varma and Y. Yafet, Phys. Rev. B13, 2950 (1976).Google Scholar
- 30.J. Hubbard, Proc. Roy. Soc. (London) A276, 238 (1963).Google Scholar
- 31.D. Penn, Physics Lett. 26A, 509 (1968).CrossRefGoogle Scholar
- 32.A marked difference between Ni and SmS is that the narrow band (3d) in Ni is much broader than that (4f) in SmS. This suggests that interactions neglected in the Varma-Yafet
^{29}Hamiltonian (e.g. interband Coulomb interactions) which, if properly treated, give a tendency for exciton formation might be crucial in understanding the difference. Haldane (ref. 1, p. 191) seems to have taken a small step in the direction of including such interactions (still within a single-impurity model).Google Scholar - 33.Like those considered by P.W. Anderson and A. Hasegawa, Phys. Rev. 100, 675 (1955).CrossRefGoogle Scholar
- 34.CM. Varma, ref. 1, p. 201.Google Scholar
- 35.J.B. Sokoloff, Phys. Rev. B2, 779 (1970);Google Scholar
- 35a.G. Beni, T. Holstein, and P. Pincus, Phys. Rev. B8, 312 (1973).Google Scholar
- 36.Lest one be misled, one should realize that the same (U → ∞) Hubbard model, for certain 3-dimensional lattices, is probably ferromagnetic (Y. Nagaoka, Phys. Rev. 147, 392 (1966)), at least for ρ ≅ 1.CrossRefGoogle Scholar
- 37.J.M. D. Coey, S.K. Ghatak, M. Avignon, and F. Holtzberg, Phys. Rev. B14, 3744 (1976); ref. 1, p. 211.Google Scholar
- 38.I. Nowik, ref. 1, p. 261.Google Scholar
- 39.I. Nowik, ref. 1, p. 167.Google Scholar
- 40.Nowik’s result is that the electron released in Sm
^{2+}→ Sm^{3+}is not felt at the Eu^{l53}probe. His conclusion^{38}that this implies that the electron is in a d-band seems strained in light of the fact that the electron released in R^{2+}→ R^{3+}where R = Y, Gd in Sm_{1-x}R_{X}S is felt at the Eu^{153}and presumably goes into the same (d) band as the electron in Sm^{2+}→ Sm^{3+}+ e. The remarkable result is the difference (observed at the Eu^{153}nucleus) between the electron in Sm^{2+}→ Sm^{3+}+ e and that in R^{2+}→ R^{3+}+e. As noted by Nowik^{38,39}, consistent with his result is localization of the extra Sm electron at that Sm site (postulated by us, and recently claimed to be found by Coey et al., ref. 37). Understanding the difference between Sm^{3+}and Gd^{3+}or Y^{3+}is a fundamental problem. A possible source is the charge asphericity of the Sm^{3+}core (4f^{5}), not present in the other ions.Google Scholar - 41.G. Güntherodt et al., ref. 1, p. 321.Google Scholar
- 42.Unfortunately, the low-p transition is found at 10 kbar in ref 41, in disagreement with the consensus of earlier results,
^{3,410}introducing some quantitative uncertainty in the experimental situation. It is important to have this resolved.Google Scholar - 43.We note here that anharmonicity, particularly in E(0,V), that might begin to become appreciable at these higher pressures goes in the direction of reducing p’
_{O}.Google Scholar - 44.S.M. Shapiro, R.J. Birgeneau and E. Bucher, Phys. Rev. Lett. 34, 470 (1976).CrossRefGoogle Scholar
- 44a.Obtaining the qualitatively correct picture (fig. 5) within the simple theoretical model we’ve presented suggests the nonexistence of a new semiconducting phase (which had been suggested, and labelled B’
^{3}). We add the comment that the calculations of this phase boundary were also carried out for rectangular and elliptical densities of states — this resulted in no important changes.Google Scholar - 45.R.L. Melcher, G. Guntherodt, T. Penney, F. Holtzberg, 1975 Ultrasonics Symposium Proc. IEEE Cat. #75 CHO 994–45A, pg. 16.Google Scholar
- 45a.P.D. Dernier, W. Weber, L.D. Longinotti, Phys. Rev. B14, 3635 (1976).Google Scholar
- 46.If one neglects the term -k(.3 1n.3-K7 In. 7) ≅.6k which arises from the different spatial configurations of 30%f
^{6}and 70%f^{5}. The latter term is appreciable in the difference AS, and increases the difficulty for the band theories.Google Scholar - 46a.D.H. Templeton and C.H. Dauben, J. Am. Chem. Soc. 76, 5237 (1954).CrossRefGoogle Scholar
- 47.N.P. Bogoroditskii, V.V. Pasynkov, Rifat Rizk Basili, and Yu. M. Volokobinskii, Sov. Phys. Doklady 10, 85 (1965).Google Scholar
- 48.J.W. Allen, private communication.Google Scholar
- 49.This was found by E. Carlson (private communication) in a Hartree-Fock Calculation for Sm
^{2+}in the excited configuration 4f^{5}d.Google Scholar - 50.The numerical value of the broad-band width used in Sections II and III is rather larger than that (~2.5 eV) used in Sec. 1. The essential reason for the difference is as follows: The smaller value is based on the picture from the band calculation (Davis, ref. 20) where the conduction-band minimum is at the X-point, with a local curvature corresponding to a nearly-free-electron mass; due to the symmetry-reiated minima, the density-of-states is 3 times that of a Γ-minimum with the same mass. The difference is completely unimportant for the thermodynamic properties considered in Sec. II. Although it wasn’t necessary to choose the (less realistic) larger value for these considerations, we did so to obtain symmetry with the simplified model used in Sec. III to crudely estimate optical properties. It will also be noted that the width of the narrow band,.047 eV, is rather larger than that quoted in ref. 2 (.033 eV); this discrepancy is due essentially to an error made in the earlier work. The value.047 eV is correct and depends only on the low-T specific heat (γT) and the value of b; for parabolic density of states it is easy to see that D
_{1}= (1-b/2)^{1/3}π^{2}k^{2}N_{a}/γ where k=Boltzmann^{f}s constant, N_{a}= Avogadro’s no. and γ is per mole. None of our qualitative conclusions are affected by these changes.Google Scholar - 50a.Comparison with experiment
^{9}of ε_{1}(ω)), as calculated above (i.e. from Eq.(6)), indeed suggests that there are large additional contributions in the range.1 to.8 eV (roughly), which might be due to these intraatomic excitations.Google Scholar - 51.D. Sherrington and S. von Molnar, Sol. St. Comm. 16, 1347 (1975).CrossRefGoogle Scholar