I'm going to tell you about part of my work on manganites. Ken Ahn told you about charge-ordering and orbital-ordering phases a couple of weeks ago but I'll focus on other doping regimes where double-exchange can overwhelm the strength of the lattice distortions.
So I'll introduce you the manganites and the double-exchange model which was introduced back in the fifties. I will show you why, within this model, the low energy spin waves have to be a combination of ion and electron density spin waves. My main interest is to understand the behaviour of the resistivity with temperature at low temperatures so I will go through the scattering processes which are likely to be dominant within this regime.
By the end of this forum you will know the meaning of:
If you are very interested in this subject, my thesis is available in PDF format upon request (e-mail: calderon@icmm.csic.es). The specific work I told you about is still not published but it is included in the thesis.
Double exchange model:
The origin of the model, by C. Zener:
``Interaction between d shells in the transition metals'',
Physical Review 81, 440 (1951)
and ``Interaction between d shells in the transition metals. II.
Ferromagnetic compounds of manganese with perovskite structure'',
Physical Review 82, 403 (1951)
The Hamiltonian, by Anderson and Hasewaga:
``Considerations on Double Exchange'', Physical Review 100, 675 (1955)
And by Mueller-Hartmann and Dagotto:
``Electronic Hamiltonian for transition-metal oxide compound'',
Physical Review B, 54, R6819 (1996).
Other classics that you should know:
``Effects of double exchange in magnetic crystals'', P.-G. de Gennes,
Physical Review 118, 141 (1960).
``A quantum theory of double exchange'', K. Kubo and N. Ohata,
J. Phys. Soc. Jpn. 33, 21 (1972). In this paper, the resistivity at
low temperatures due to two spin-wave scattering is calculated.
Limitations of double exchange model to explain the transport properties of
manganites:
``Double exchange alone does not explain the resistivity of
La_{1-x} Sr_x Mn O_3'', A.J. Millis, P.B. Littlewood and B.I. Shraiman,
Physical Review Letters 74, 5144 (1995).
The literature about manganites is colossal, as their magnetoresistance, so
you should better go to a review where you can get an idea of what is going on:
``Mixed valence manganites'', J.M.D. Coey, M. Viret and S. von Molnar.
Adv. Phys. 48, 167 (1999).
The state-of-the-art of manganites can be found in
``Colossal Magnetoresistant Materials: The Key Role of Phase
Separation'' Elbio Dagotto, Takashi Hotta and Adriana Moreo,
cond-mat/0012117. To appear in Physics Reports.
Some especulation and review can be found in
``The self-organised phases of manganites'', N.D. Mathur and P.B. Littlewood,
cond-mat/0104238. To appear in a special issue of Solid State Communications
on MESOSPIN.