Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-27T01:49:10.107Z Has data issue: false hasContentIssue false
  • English
  • Français

The Muffin-Tin-Orbital Point of View

Published online by Cambridge University Press:  25 February 2011

O. K. Andersen ,
A. V. Postnikov  and
S. Yu. Savrasov
O. K. Andersen
Affiliation:
Max-Planck-Institut fuir Festkörperforschung, D-7000 Stuttgart 80, FRG.
A. V. Postnikov
Affiliation:
Max-Planck-Institut fuir Festkörperforschung, D-7000 Stuttgart 80, FRG.
S. Yu. Savrasov
Affiliation:
Max-Planck-Institut fuir Festkörperforschung, D-7000 Stuttgart 80, FRG.
Get access

Abstract

We review the interpretation of multiple-scattering theory in terms of muffin-tin orbitals. The use of slightly overlapping muffin-tin wells is justified rigorously. It is shown that the structure constants may be screened for a useful range of positive and negative energies, and that the screening may be chosen to yield desirable properties of the KKR matrix. Energy linearization and the linear muffin-tin-orbital method are discussed.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 253: Symposium V – Application of Multiple Scattering Theory to Materials Science , 1991 , 37
Copyright
Copyright © Materials Research Society 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. , Korringa, Physica 13, 392 (1947).Google Scholar
2. Kohn, W. and Rostoker, N., Phys. Rev. 94, 1111 (1954).Google Scholar
3. Andersen, O. K. in: Computational Methods in Band Theory, eds. Marcus, P.M., Janak, J.F., and Williams, A.R. (Plenum, 1971) p. 178.Google Scholar
4. Andersen, O.K., Europhysics News 12, 5, 1 (1981) and in, The ElecGoogle Scholar
5. Skriver, H. L., The LMTO Method (Springer, New York, 1984)Google Scholar
6. An LMTO impurity Green's-function method is described in, Gunnarsson, O., Jepsen, O., and Andersen, O. K., Phys. Rev. B 27, 7144 (1983).Google Scholar
7. For an LMTO-CPA method, see: Kudrnovsky, J., Drchal, V., and Masek, J., Phys. Rev. B 35, 2487 (1987). J. Kudrnovsky, S.K. Bose, and O.K. Andersen, Phys. Rev. B 43, 4613 (1991) is a recent application.CrossRefGoogle Scholar
8. The LMTO surface Green's-function method is described in, Skriver, H.L. and Rosengaard, N.M., Phys. Rev. B 43, 9538 (1991)Google Scholar
9. For a recent, typical LMTO application, see: Rodriguez, C.O., Liechtenstein, A.I., Mazin, I.I., Jepsen, O., Andersen, O.K., and Methfessel, M., Phys.Rev. B 42, 2692 (1990)Google Scholar
10. Andersen, O.K., Jepsen, O., and Gltzel, D., in Highlights of Condensed-Matter Theory, edited by Bassani, F., Fumi, F., and Tosi, M.P (North Holland, N.Y. 1985).Google Scholar
11. Andersen, K. and Jepsen, O., Phys. Rev. Lett. 53, 2571 (1984).Google Scholar
12. For the LMTO recursion method, see: Nowak, H.J., Andersen, O.K., Fujiwara, T., and Jepsen, O., Phys. Rev. B 44, 3577 (1991). Typical, recent applications are: S.K. Bose, J. Kudrnovsky, I.I. Mazin, and O.K. Andersen, Phys. Rev. B 41, 7988 (1990); and, P.R. Peduto, S. Frota-Pessoa, and M. Methfessel, Phys. Rev. 44, 13 2893 (1991)Google Scholar
13. Lambrecht, W.R.L. and Andersen, O.K., Phys. Rev. B 34, 2439 (1986); O.K. Andersen, T. Paxton, M. Schilfgaarde, and 0. Jepsen (unpublished).Google Scholar
14. Fernando, G.W., Cooper, B.R., Ramana, M.V., Krakauer, H., and Ma, C.Q., Phys. Rev. Lett. 56, 2299 (1986).Google Scholar
15. Weyrich, K.H., Phys. Rev. B 37, 10269 (1988)Google Scholar
16. Blöchl, P., Thesis, University of Stuttgart (1989)Google Scholar
17. Springborg, M. and Andersen, O.K., J. Chem. Phys. 87, 7125 (1987)Google Scholar
18. Methfessel, M., Phys. Rev. B 38, 1537 (1988); M. Metfessel, C.O. Rodriguez, O.K. Andersen, Phys.Rev. B 40, 2009 (1989)Google Scholar
19. Savrasov, S. and Savrasov, D., Phys. Rev. (to be published). In this full-potential LMTO method the integrals over all space are performed as sums of integrals over cells. Each cell integral is performed as a surface integral and thus avoids the slowly converging spherical-harmonics expansion of the cellular step-function ØR(r).Google Scholar
20. Andersen, O.K.: Mont Tremblant Lecture Notes 1973 (unpublished). Much of this material was published in Ref. 5.Google Scholar
21. For details, see Chapter 3 and Appendix 2 of Ref. 20.Google Scholar
22. When defining the MTO for K2>0 we could have added any constant times the Bessel function, i.e. ijim(k,r), to the partial wave. This would have made no difference for a crystal because a Bloch sum of Bessel functions Dr ΔT exp(ik.T)δ(K,r-R-T) vanishes everywhere, except when k is on the free-electron Fermi surface with energy ic 2 in which case the function diverges everywhere. In the formalism, n would then be substituted by n+ij, and cotn by cotn+i. In the addition theorem (2.7) (and (6.2)) the substitution of n by n+ij would according to what was said above, modify the structure constants to BR,m,Rim (k,k)-iσR,Rσ,π, m and the KKR equations (2.8) would thus be unchanged.0+we+could+have+added+any+constant+times+the+Bessel+function,+i.e.+ijim(k,r),+to+the+partial+wave.+This+would+have+made+no+difference+for+a+crystal+because+a+Bloch+sum+of+Bessel+functions+Dr+ΔT+exp(ik.T)δ(K,r-R-T)+vanishes+everywhere,+except+when+k+is+on+the+free-electron+Fermi+surface+with+energy+ic+2+in+which+case+the+function+diverges+everywhere.+In+the+formalism,+n+would+then+be+substituted+by+n+ij,+and+cotn+by+cotn+i.+In+the+addition+theorem+(2.7)+(and+(6.2))+the+substitution+of+n+by+n+ij+would+according+to+what+was+said+above,+modify+the+structure+constants+to+BR,m,Rim+(k,k)-iσR,Rσ,π,+m+and+the+KKR+equations+(2.8)+would+thus+be+unchanged.>Google Scholar
23. Andersen, O.K., Phys. Rev. Lett. 27, 1211 (1971).CrossRefGoogle Scholar
24. Andersen, O.K., Solid St. Commun. 13, 133 (1973).Google Scholar
25. Williams, A.R. and Morgan, J.W., J. Phys. C 7, 37 (1974).Google Scholar
28. See papers in these proceedings by Brown, R.G., Butler, W.H., Gonis, A., and Nesbet, R.K.; as well as references therein.Google Scholar
27. Appendix 13 of Ref. 20.Google Scholar
28. Andersen, O.K. and Kasowski, R.V., Phys. Rev. B 4, 1064 (1971); R.V. Kasowski and O.K. Andersen, Solid St. Commun. 11, 799 (1972)Google Scholar
29. Andersen, O.K. and Woolley, R.G., Molecular Physics 26, 905 (1973)CrossRefGoogle Scholar
30. Andersen, O.K., Phys. Rev. B 12, 3060 (1975)Google Scholar
31. Harris, J., in Electronic Structure of Complex Systems, eds. Phariseaux, P. and Temmerman, W.M (Plenum, 1984) and refs. thereinGoogle Scholar
32. Andersen, O.K., Methfessel, M., Rodriguez, C.O., Blöchl, P., Polatoglou, H.M., in Atomistic Simulation of Materials, Eds. Vitek, V. and Srolovitz, J. (Plenum, 1989), p. 1.Google Scholar
33. Andersen, O. K., Pawlowska, Z., and Jepsen, O., Phys. Rev. B34, 5253 (1986).Google Scholar
34. Andersen, O. K., Jepsen, O., and Sob, M., in Electronic Band Structure and its Applications, ed. Yussouff, M. (Springer Lecture Notes, 1987).Google Scholar
35. See, for instance, Hubbard, J., Proc. Phys. Soc. Lond. 92, 921 (1967)Google Scholar
36. Kollar, J. and Ujfalussy, B., J. Phys.: Condens. Matter (in print)Google Scholar