%%% Abstract for the 225th WE-Heraeus seminar,
%%% 11-15 October 1999.
%%% Electronic Correlations in Manganites
%%% by Held and Vollhardt
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{\large\bf Electronic Correlations in Manganites} \\

\bigskip
{\underline{Karsten Held} and Dieter Vollhardt}\\

\bigskip
{\small{\em
Institut f\"ur Physik, Universit\"at Augsburg, D-86135 Ausgburg, Germany}} \\

{\tt Held@physik.uni-augsburg.de}
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The double exchange  mechanism [1] 
is generally held responsible for the ferromagnetism
of manganites with perovskite structure, 
like La$_{1-x}$Ca$_x$MnO$_3$ or La$_{1-x}$Sr$_x$MnO$_3$.
Due to the renewed interest in these compounds with respect to the
colossal magnetoresistance (CMR) [2],
the ferromagnetic Kondo lattice model (or s-d model) which is
the microscopic basis of the double exchange
was intensively investigated recently [3].
Here,
a correlated electron model taking into account local  Coulomb
repulsions  between Mn  e$_{\mbox{g}}$-electrons
is studied within the dynamical mean-field theory (DMFT). The Hamiltonian reads
  \begin{eqnarray}
   \hat{H} &=&       
   -  t \; \sum_{\nu=1}^{2} \sum_{ \langle i j \rangle \sigma} 
   \;{\hat{c}}^{\dagger}_{i \nu \sigma} 
   {\hat{c}}^{\phantom{\dagger}}_{j  \nu \sigma}  
   - 2  J \;     \sum_{\nu=1}^{2} \sum_{i} 
   \frac{\hat{n}_{i\nu\uparrow}-\hat{n}_{i\nu\downarrow}}{2} \;
   {S}^z_{i} \nonumber \\ &&
    +   \; { U}   \sum_{\nu=1}^{2} \sum_{i} 
    \hat{n}_{i\nu\uparrow}\hat{n}_{i\nu\downarrow} 
     + \; \sum_{i \;  \sigma \tilde{\sigma}}  \;
    ( V_0 -\delta_{\sigma \tilde{\sigma}}F_0)  \;
    {n}_{i  1 \sigma} {n}_{i 2  \tilde{\sigma}}, \nonumber
    \label{CMRmodel}
  \end{eqnarray} 
where ${\hat{c}}^{\dagger}_{i \nu \sigma}$ and 
${\hat{c}}^{\phantom{\dagger}}_{i \nu \sigma}$
are creation and annihilation operators for electrons
on  site $i$, with 
spin $\sigma$ and within e$_{\mbox{g}}$-orbital
 $\nu$,  $\hat{n}_{i\nu\sigma}\!=\!
c^{\dagger}_{i\nu\sigma}c^{\phantom{\dagger}}_{i
\nu\sigma}$, and ${S}^z_{i}$ is a localized t$_{\mbox{2g}}$-spin.
The first line is the two band ferromagnetic Kondo lattice model
with 
hopping $t$ between nearest neighbors $\langle i j \rangle$ 
and  a Hund's 
rule coupling to the localized spin. 
The second line adds Coulomb repulsions $U$
and $V_0$  and  Hund's rule
coupling $F_0$ between  e$_{\mbox{g}}$-electrons. 

Employing Quantum Monte-Carlo (QMC) simulations the DMFT
equations are solved numerically. 
We find [4] that electronic correlations are 
important since they change the paramagnetic spectral function
drastically. An upper Hubbard band emerges, spectral weight is
transferred from the vicinity of the Fermi energy to this Hubbard
band, and the bands are broadened. 
Furthermore, the microscopic mechanism for ferromagnetism changes from
 double exchange of the
Kondo lattice model (at Ca doping $0.6<x<1$) to super exchange 
at $x=0$.
This yields a characteristic
maximum of the Curie temperature at intermediate x as
observed in La$_{1-x}$Ca$_x$MnO$_3$.


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\noindent
[1] 
C.~Zener {\em Phys. Rev.} 82,  403 (1951);
P.~W. Anderson and H.~Hasegawa
{\em Phys. Rev.}\\
\phantom{[1]} 100, 675 (1955).

\noindent
[2] For reviews see A.~P. Ramirez {\em J. Phys. Cond. Matter} 9, 8171 (1997); E.~L. Nagaev\\
\phantom{[1]} {\em Physics--Uspekhi} 39, 781 (1996).

\noindent
[3] E.~Dagotto, S.~Yunoki, and A.~Moreo  {\em Phys. Rev. Lett.} 81,
5612 (1998);  cond--mat/\\
\phantom{[1]} 9809380;  cond-mat/9901057
(to appear in Science);
N.~Furukawa, {\em J. Phys. Soc.}\\
\phantom{[1]}{\em Jap.} 63, 3214 (1994);
cond-mat/9812066.

\noindent
[4] K. Held, Ph. D. thesis, University of Augsburg, 1999;
K. Held and D. Vollhardt, in\\
\phantom{[1]} preparation.
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